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The Five Stages of Small-Business Growth

• Neil C. Churchill
• Virginia L. Lewis

No researcher has explored the earliest period of a business’s development in detail—until now.

Categorizing the problems and growth patterns of small businesses in a systematic way that is useful to entrepreneurs seems at first glance a hopeless task. Small businesses vary widely in size and capacity for growth. They are characterized by independence of action, differing organizational structures, and varied management styles.

• NC Neil C. Churchill was a professor and leader in the field of innovation and entrepreneurship, holding positions at Carnegie-Mellon, Harvard Business School, Babson, INSEAD, and the Anderson School at UCLA.
• VL Virginia L. Lewis is a senior research associate of the Caruth Institute at SMU.

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What Is A Growth Model and How To Create One For Your Business

Apr 28, 2022

Your startup offers an innovative product or service that is meant to make lives easier, help people achieve more and/ or provide solutions to complex problems. However, you will never get there if you don’t do your best to reach out to potential customers and convince them of your value proposition.

Realizing that growth isn’t just about hacking your way to the top of Google to drive all the traffic to your website, or reaching out to thousands of accounts a day on LinkedIn. 

You need a solid, reliable model that will help you get there in a strategic way and realize growth by leveraging the ‘right’ marketing channels at the ‘right moment’.

In this article, we are going to talk about what a growth model is, why you need one and how you can create one for your business. 

What is a growth model?

Simply put, a growth model is a strategy to maximize revenue and profit by focusing on acquiring new customers while retaining existing ones. You may even call it the North star of your growth efforts. 

It can also be explained as the process of building a sustainable customer base that generates repeat revenue over time. 

You can implement this by looking at what others have done before you who had similar goals and values or you can create one from scratch but adapt it along the way as needed for your specific business needs. 

But in essence, the growth model consists of two elements – the marketing channel you choose will determine how you get your product/ service in front of potential customers, while the elements of your product/ service are what will convince them to buy from you. These two components work together to drive growth for your company.

But more importantly, a growth model is a process that makes your efforts towards growth measurable at each step of the marketing funnel. It involves the viewing of a dashboard that includes the most relevant metrics and how to connect each step in the customer’s buying journey, to lead them across the sales funnel until you secure a sale that gets added to the business revenue. 

Why do you need a growth model?

A business lives and dies by its ability to grow, so having an effective growth strategy should be at the center of your business plan. 

A growth model helps you understand how your customers will use your product or service, and what marketing channels you should focus on in order to drive adoption and sales.

Growth models lay down the framework of your strategy to ensure your startup’s growth. If a business model is the reason why customers buy your product or service, then a growth model explains how your company will attain new customers and scale. 

This is because it loops in your stakeholders, marketing team, sales department, customer success managers, and even those looking into finances. It also helps you establish your ability to leverage your team’s strengths to create a concrete bottom line.

The purpose of a growth model is to enable you to understand where you are heading and what it takes to get there. A strong growth model consists of a few parts:

• The overall strategy for your business wherein you can create a workflow and a series of events that your marketing, sales, support and finance team can follow as you take your value proposition to the market.
• The channels that you need to focus on to reach your goals.
• The product and service elements that will help you acquire more customers.

How do you create a growth model? 

To define your growth model, it’s critical that you have a complete understanding of your ideal customer profile and user journey map. If you haven’t done that yet, go back to the drawing board and create them first.

Or you could visit this guide from HubSpot on creating detailed customer personas to access their templates. They make for a good starting point that can be built on as you start to learn more about your audience! 

Once you have those the foundational elements ready, you can start building out the rest of your growth model: 

1. Define the individual steps of your funnel (i.e., Pirate Funnel)

The Pirate Funnel is a framework that helps growth hackers segment a company into 6 metrics of where they should focus their attention. Developed by Dave McClure, the Pirate Funnel is called so because of the first letters of the metrics to be observed. They are: 

• Acquisition
• Retention 

Finding the weaknesses in your business and more importantly, the reasons behind them can be extremely helpful in finding ways to improve your strengths. Pirate Funnels are a great way of evaluating what’s working and where the issues lie – almost like a SWOT analysis. 

For example, a lot of visitors on your website did not take the action you wanted them to like signing up for your product. What would your next step be? Determining retention tactics like a signup discount.

2. Describe your metrics per funnel stage

The sales funnel is a concept that refers to the route that customers go through in order to become conversions. According to sales professionals, any given customer will enter your marketing funnel and as it progresses, they will move along and convert until they reach the gate at the end– becoming customers. 

However, not all visitors will actually reach this point; many will drop off for any number of reasons before reaching their destination, which means that sales teams have to do something about it if they want the business to be successful. 

Smart teams clearly define and then monitor their sales funnel metrics at each stage to help determine why visitors are dropping out. They aim to find out what causes this behavior leading them to start making adjustments until they produce better results.

3. Decide on the key metric(s)

To measure the success of your campaigns, you need to decide on key metrics. For example, is your campaign focused on converting leads? You may want to track the conversion rate. Are you looking to acquire new customers? Track your customer acquisition rate. 

Having a data-driven approach will not only help your team remain on the same page and work towards the same goals but it will also make your success quantifiable and capable of future replication.

Also read: How to define your OKRs and success metrics .

4. Make forecasts based on assumptions and research

Creating an outstanding sales forecast can be a great way to help you to keep an eye on the future. It helps avoid unanticipated cash flow problems, with production, staff and financing needs. 

A well-crafted system for sales forecasting based on research and even a few assumptions can minimize waste and provide several enormous long term benefits: resource allocation, cost control, risk management, and competitive analysis.

Forecasting your success teaches you to adapt quickly and stay ahead of things.

5. Learn and optimize on a weekly basis

While developing strategies and monitoring necessary metrics are an important part of growth, it is equally important to stay on top of your plan by regularly optimizing it. 

Using the data at your disposal, you have the opportunity to evaluate exactly what’s being done in terms of your growth strategy and tailor it to fit future goals by tweaking it based on the analytics. Essentially, you’re implementing a continuous growth strategy that will only get better as tactics shift and goals change, becoming more efficient with each new learning experience.

How do you use a growth model? 

A detailed growth model can be the ultimate hack to product improvement and business growth. But how do you use it? Let’s look at it here-

By tracking metrics

Each week, or even every day, you and your growth team look at important progress metrics to see if they match up with the goals you have set related specifically to your business growth. You can also compare them to see how far along in the right direction you are as a result of your previous predictions and the proactive strategies you worked on to get to your goal.

Comparing results with predictions 

It is extremely important to continually check your results in comparison to the predictions you have made earlier. You can even keep updating your predictions three months in advance so that you can plan in advance and decide where to put your money or even to help you predict market movements.

Knowing if the results you are getting are in line with your predictions is a way to gauge the validity of your product. If you are shrewdly able to predict the graph of your success, you may be able to keep replicating your results to achieve exponential growth.

Focusing on certain sections of the funnel

If you receive results in sync with your predictions, great! It means you are on the right track. However, this may not always be the case. When you notice inconsistencies in your predictive analysis, the growth model will guide you on what part of the funnel you’ll need to focus more on.

Since predictive analysis essentially impacts your business’ bottom line by showing you the real picture of the demand for your product, market awareness, etc., an inconsistency should be tackled head-on. 

When you break down your growth funnel and observe the metrics at each stage, you will be able to gauge where the leaks and your team can proactively start tweaking existing plans and devising new strategies to find solutions. 

The secret here is adapting and being resilient at all stages of the marketing funnel.

Determining future steps

Once you know the results of your ongoing efforts, you can’t just stop there! Your team needs to focus on determining future steps regardless of the outcome. In case you are on the right track, this will help you sustain your growth and eventually help better the results. However, if you are not yet achieving the results you initially desired and forecasted, planning ahead will help you become more efficient and make better decisions.

Here’s how you can implement this- 

• Understand your current market position
• Identify opportunities for the future
• Prepare for future expansion
• Keep reviewing your strategy 
• Tweak it as required

Executing and looping back

Growth loops are a part of growth hacking, which is a system of rapid iteration driven towards identifying the quick wins that drive growth for startups. Growth hacking techniques can help startup ideas to identify these growth loops and take advantage of them before their competitors and stay ahead of the curve! 

For example, if the way to increase growth in your business is by acquiring more customers through signups, then steps relevant to that particular goal should be taken within each growth cycle to attract new clients without fail. 

The end of each growth cycle will be determined by reaching a milestone that serves as direction for the next growth loop– like getting 100 new customers. The next step then would be to get 100 more clients at no added cost and so the cycle continues reaching higher heights with each new trajectory.

This will eventually create a self-sustaining cycle that compounds exponentially with each step and can help lead your startup from seed to maturity if executed well.

Conclusion – You do need a growth model.

Finally, a good growth model is one that aims for real results, not just theoretical results that have no potential of being realized. Implementing the above shared information is a great starting point to incrementally improve your customer base and grow your business.

Reach out to us to get your growth model framework.

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Course 5 • Lesson 4

What is a Growth Model? + How to Identify Your Company’s

This lesson walks through what a growth model is, some great examples, and most importantly how to identify and build your own growth model.

All large successful companies have "growth models"--that is to say, key feedback loops that drive sustained customers, acquisition, and business growth.

The concept of a growth model, or growth loop as it's often called, is relatively new, and has been popularized by leaders in the growth community, like Andrew Chen, and programs like Reforge. At its core, the idea is very simple. What are the ways that your business acquires customers? They're called loops because they should be circular and compounding. Some common examples of growth models include paid acquisition, viral invite, two-sided marketplaces, and user-generated SEO content (see image below).

Defining your company's growth using a model helps identify high leverage "inputs" (areas of your business that you have control over) that can amplify compounding growth over time. Additionally, these high impact growth models help you choose which metrics to measure —and set goals against—to get a clear understanding of your growth progress.

We'll dive into four common models and show how to derive a set of high-signal metrics for each one:

User-generated content (e.g., Yelp, Stack Overflow, Genius)

Viral invite loop (e.g., Venmo, Snapchat, Zynga)

Paid acquisition (e.g., Handy, New Relic's campaigns)

Two-sided marketplaces (e.g., Uber, Lyft, Airbnb, Segment)

What is a growth model? 

A growth model is a visual representation of the acquisition model a business uses to grow and sustain its customer base. A business’s growth model will depict the inflow of new customers, the methods used to create this inflow, and the expected growth generated with these methods.

Building a growth model

Before looking at the four growth models, let's quickly walk through the steps to determine the key metrics:

Identify your growth model

Create a mathematical model in a spreadsheet with assumptions

Deduce key metrics by conducting sensitivity analysis on your spreadsheet

Identifying your growth model requires thinking holistically about each cohort of your users and how they can acquire the next cohort of users. This means looking step-by-step at your user journey and mapping them to discrete actions. The final cohort then "becomes" the next base cohort from which the actions in the loop start again.

After identifying the feedback loop, then it's time to mathematically define each step. Note that the final total number of users in the first time period will become the starting number of users in the next time period. We start by keeping things as simple as possible and using percentages in the spreadsheets below.

Lastly, you can deduce key metrics with sensitivity analysis on the mathematical model. Due to the compounding nature of the growth feedback loop, some assumptions have a greater amplifying force on growth over time (e.g., conversion to sign ups vs conversion to paid). We'll illustrate this in our examples below.

1. User-generated SEO content

A user-generated content loop is a popular self-reinforcing growth model used by companies like Yelp , Genius , Stack Overflow , Quora , etc. The step-by-step user story here is:

users sign up

% of the users create new content

Google indexes the content

non-users search and find the content

% of those non-users eventually sign up

Here is a mathematical model in Google sheets to represent the user generated content functions . With this model, we can identify areas of high leverage by adjusting assumptions and seeing their impact on the growth trajectory of the company. For example, we can see if improving the conversion rate of users who generate content or focusing on acquiring new users would generate more money.

The graph above is taken from the aforementioned Google spreadsheet.

The "2x generate content" case assumes the % of users who generate content is twice as much as the base case, whereas the 2x signup case assumes the conversion to sign up is doubled. This model suggests improving the signup conversion has more compounding effects than content generation conversion.

So, if you're running this type of business, the key metrics you should be watching are:

% of existing users who generate content

% of visitors from search who are new

% of sign ups who are new visitors

When we remove ourselves from the mathematical model to do a quick gut check, we can see that these are the key metrics that'll move the needle the most. If we can incentivize users to generate more content or optimize the conversion from visitors to signups, we can see compounded growth over time.

2. Viral invite loop

This is a popular model for many social games or apps (e.g., Snapchat , Venmo ) that asks users to invite friends via importing their address books. Many companies experienced massive growth leveraging this viral loop. When Facebook launched their graph API, users could suddenly ask all their friends to help harvest their Green Wheat in Farmville, and the game took off over night. It's worth noting that the best viral loop examples are almost always found with consumer companies.

The step-by-step user story here is:

user signs up

% of the users invite their friends

% of those friends sign up

Here's a mathematical model in Google sheets to represent this growth model . Again, we use this model to see which assumptions move the needle the most. For example, we can see the impact on growth if we improve each percentage point of number of users who invite their friends.

The second "Double any key assumption" is the case where either the % of users invited or the % of invited users sign up are doubled. The math happens to work out that way.

For this model, "amplifying" metrics are:

% of users who invite friends

% of sign ups per invitee

It makes sense that these are the metrics that can significantly add growth over time. If users were more incentivized to invite their friends, then that leads to a greater pool of users who can convert to registration. Seeing that these areas are higher leverage, it makes sense to optimize for those metrics so you can reap the growth benefits later.

3. Paid acquisition

The paid acquisition growth model is slightly less exciting, but it's how many companies scale efficiently. Existing users don't directly help you acquire new users, but they generate revenue that you can to reinvest in paid marketing. For example, for a company that earns $100 reinvests that money into new acquiring new users. From that cohort, the company makes $80 to reinvest again. This model assumes that the cost of acquiring the user is less than the lifetime value of each user (most VC's and founders say that the acquisition cost should be ⅓ of the lifetime value).

company uses money to get X users

% of X users upgrade and pay total of $Y

company reinvests $Y to get next cohort of users

Here is a template mathematical model for the paid acquisition growth model .

Graph above is taken from the aforementioned Google spreadsheet.

We see that doubling the conversion rate to paid has a higher impact than doubling "margin" (calculated as LTV - CAC).

You can see in the model that the main assumptions for this are:

% of customers convert to paying

CAC: Customer Acquisition Cost

LTV: Customer Lifetime Value

It's not trivial to optimize any of these three metrics (it probably will take resources across several teams within a company). However, each KPI can significantly improve the effectiveness of a single marketing dollar spent. Higher LTVs and lower CACs can make the dollar work for acquiring more users, and a higher percent of paying customers leads to a larger marketing budget.

4. Two-sided marketplaces

The two-sided marketplace model has become more and more popular, as technology helps buyers and sellers transact more easily with one another. For example, Uber , Etsy , Segment , and Grubhub all represent marketplaces.

Growth in a two-sided marketplace relies heavily on the increasing value one side gets from the other. What value do drivers get from more riders and riders from more drivers? Each network effect can be modeled out. If you want to dive deeper in how we do marketplace growth analysis at Segment, check out our post on modeling two-sided marketplaces .

To illustrate the reinforcing nature of growth for two-sided marketplaces, here is the set of the six key growth dynamics (ideas heavily borrowed from this HBR article ):

Buyer-to-seller cross-side : Prospective buyers tell prospective sellers that they prefer to do business on the platform. "It was hard to find your place. How come you don't list on Airbnb?"

Seller-to-buyer cross-side : Prospective sellers expose prospective buyers to the platform. "Buy my adorable elephant mittens on Etsy."

Buyer same-side : Buyers love the new transaction experience, and tell other prospective buyers to use the platform. "Why would you use a taxi? You should check out Lyft."

Seller same-side : Sellers love the new transaction experience, and tell other prospective sellers to use the platform. "I made a good chunk of change while I was on vacation, renting my place on Airbnb. You should try it out!"

Direct to buyers : The marketplace tells buyers about itself directly. "Wow, Uber has a lot of billboards here."

Direct to sellers : The marketplace tells sellers about itself directly. "I searched for jobs in Cincinnati and found Lyft."

Here's a sample mathematical model that we used for two-sided marketplaces . Note that this example is a little more involved than the previous ones—the template is a fictitious Segment, with one side being "customers" and the other being integration "partners."

For more information, we kindly direct you to this section of "How we model growth for two-sided marketplaces," where we look at tinkering with a single assumption to project growth.

You have a few more metrics to focus on in this model:

direct acquisition of buyers

direct acquisition of vendors

average # of buyer signups driven by each new vendor

average # vendor signups driven by each new buyer

Often the highest contributors to growth depend on your company's stage. For example, if it's too early for any of the cross-side or same-side marketplace growth dynamics to be a major contributor to growth, then you should focus on growing one side of the marketplace. For example, at Segment, we started by building up our catalog of integrations partners ourselves to attract customers. Then, as we gained more traction and had a critical mass of integrations, we started to think about how we could better work with our partners to drive more customers to Segment.

Measuring and hitting the right metrics

Using a growth model makes it easier to derive a set of metrics to track and set goals against. The model, when represented mathematically in a spreadsheet, enables you to easily adjust the assumptions to determine which focus area can lead to the most compounded growth.

And remember, this model is not for financial planning and projections about what will happen. They're to be used as strategic tools to understand what the business could do so you can see the bounds of what strategy you can invest in.

That being said, once you identify the set of metrics that are most impactful, it's a matter of holding teams accountable to one or two metrics and really focusing on tasks and experiments that can move these numbers. What we've found to be most effective is to hold each team accountable to one (or two, max) of these metrics, then prioritize experiments that can improve those metrics .

While we covered four common growth models in this lesson, there are many others! If you have any ideas, please share them by tweeting at us!

Frequently asked questions

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Guide to Greiner’s Growth Model

Where do you sit on the growth curve and what risks do you face…🌱

Table of Contents

Growing your company is exciting, stressful, at times tiring, but always fun! During the growth you’ll encounter numerous crises that will jeopardise the success. As with most of life’s business problems, there’s a framework to explain or help map out this scenario…

So, let’s take a look at Greiner’s Growth Model.

What is Greiner’s Growth Model?

Greiner’s Growth Model is a framework that shows the different phases a company goes through to achieve growth and the different types of crisis that may occur during those milestones.

The graph shows time on the X axis and size of the business on the Y axis, with both increasing as the company goes through the different phases.

The model is helpful in showing companies the different approaches to growth, as well as highlighting the different challenges. It is commonly used by businesses to self-identify obstacles they are facing that will hamper their efforts to achieve their full potential.

What are the phases of growth in the Greiner’s Growth Model?

Let’s firstly look at the different phases a company goes through based on this model.

Growth Through Creativity

All businesses start from a spark of an idea, one that is fostered and developed over time. It’s a truly creative stage of a company’s life as they attempt to develop a new product or service, pull together a team, a route to customers, and get that sometimes elusive ‘product-market fit’.

There are some common traits of companies at this stage:

• They are small, responsive and agile
• They are creative and working to find their product-market fit
• They’re informally structured with strong communication between teams

Growth Through Direction

At this point in a company’s life the owner/founders begin to hire managers, releasing some of the control of the resources and direction of the business. This is normally a ‘growing up’ period of a company’s life, when processes become slightly more formal, departments may be developed, and a culture is set within the business. That’s not to say the founders/owners aren’t still actively involved, they are indeed ultimately running the company, but it’s a collaboration of managers that drive the direction.

A company can be considered in the Growth Through Direction phase if:

• They have recently hired managers as the team grows
• Decisions are no longer solely made by the founder/owners
• Processes have started to be created within the company (e.g. HR, operations)
• A culture is embedded within the company
• Things are getting bigger and more complicated!

Growth Through Delegation

The Delegation phase of growth occurs when key staff members are given accountability and responsibility to deliver in areas where they are better equipped to than the manager. At this point in a company life there will be specialist employees, focused on specific roles.

Delegating jobs to more specialist, skilled employees means you’ll get a better result, with the added benefit that the executive team have time to focus on the market data, their strategic decisions, and business planning.

A company may be in this phase if:

• Specialist skilled employees are increasingly being hired
• Accountability for key tasks is shared down the company
• Leadership teams spend less time doing jobs they aren’t good at or don’t like

Growth Through Coordination

This is now a mature stage of growth, one that focuses on the company core competencies and all departments working in line with each other to output a product or service. Growth comes from the whole business being greater than the sum of its parts.

• They are mature in a marketplace
• Teams work with each other internally for the best outcome
• There are set processes and functions within the business
• Workflows and communication tools are present within the business
• Roles and responsibilities are clearly defined

Growth Through Collaboration

The final stage of growth in this model is deemed to be Collaboration. This is an evolution of Coordination, one where all parts of the company work together in a trusted, effective manner. Systems are simplified for efficiency, learning and development is prominent, and all aspects of the business contribute towards ways to continue success.

• They are a mature company
• There is a positive culture around problem solving
• There’s little ‘red tape’
• Reward is shared on the basis of team performance
• Processes are simple and teamwork is good
• Employees feel they can contribute ideas for growth
• Everyone knows how they impact the company with the work they do

Growth Through Alliances

The final stage of growth is a new one introduced more recently to the curve, and it focuses on strategic alliances. The idea being that companies may merge, acquire, partner or work with other companies in order to grow themselves.

Are the phases of growth linear in the Greiner’s Growth Model?

The model suggests that is the case, but in real life it is not necessarily always linear. For example, a start-up company focused on Direction may also embark on Strategic Alliances. It’s important to note the real importance and value of this model lies in the crises that may impact a company at the different stages… so let’s take a look at those.

What are the crises in the Greiner’s Growth Model?

Each phase in the Growth Model has an associated potential crisis that may disrupt the trajectory of growth.

Crisis of Leadership occurring during Creativity

This is a common issue for start-ups and young companies that find themselves growing via creativity and innovation. Initially with a small and informal team it’s possible for founders to manage the business in a relaxed manner, but over time this becomes a challenge.

Growth will lead to increasing difficultly around coordinating processes, communicating and motivating the team, or driving the company forward. This can be fatal for a business as it can result in key people departing (remember, people leave managers as much as they leave jobs) and founders becoming increasingly frustrated.

At this point a more defined management style is required in the company to take it to the next level.

Crisis of Autonomy occurring during Direction

This is a really interesting crisis. As a company develops in direction then managers may become more interested in their own unit than the business as a whole. This can result in conflict between management where a decision may be good for one department or area but bad for another.

The balance to strike is giving managers and employees autonomy but ensuring everyone is on the same page around decision that are best for the business as a whole. Ensuring everyone is on the same page around their strategy is key in that balance.

Crisis of Control occurring during Delegation

The crisis around the Delegation phase can be summed up with two factors:

• Founders and managers can find it difficult to let go and give others full control over certain aspects of the business.
• Communication may be difficult. At this point in a company’s life there can be problems between management or employees about what is trying to be achieved in each job and how to get the best result.

The latter can sometimes be a reason to reinforce the behaviour of the former, with founders citing concerns that if they do not do something it won’t be done well. It ultimately will result in a sub-par outcome though, with founders struggling to ‘do everything’ and teams feeling unmotivated.

Crisis of Red Tape occurring during Coordination

Another very relatable crisis within the life of a company is that of ‘Red Tape’ or bureaucracy. The addition of extra reports, processes, functions, all of which contribute to additional work for employees and can risk the wider culture of the business.

This can slow down decision making, resulting in a less agile company that cannot respond to market changes while also suffering a wider loss of efficiency/reduced margins.

Of course, this is a risk at all points in a company life, but it has more chance of arising when coordination is required and thus processes are needed within a company.

Crisis of Growth occurring during Collaboration or Alliances

The final crisis is one of how to grow. In the framework we’ve moved through each phase, so the company is now successful and mature. The question becomes how does it continue to grow, given the success?

If you’re in Collaboration, then perhaps Alliances are your way forward. If you are already developing partnerships then perhaps diversification is the route to growth? There are lots of potential options here, it’s a good point to evaluate your industry and develop a new strategy.

What are the advantages of Greiner’s Growth Model?

There are lots of advantages to this model including:

• It provides a number of identifiable challenges companies may face
• It’s simple to understand and shows a way forward for growth
• Different phases for a company to identify their current position are highlighted
• It provides a good discussion piece for management teams
• It reinforces change is needed for growth

What are the disadvantages of Greiner’s Growth Model?

The few limitations of this model include:

• It’s simple and in real life the lines blur between phases
• Not all companies follow the curve in a linear way
• The crises may not always occur in each phase

What frameworks go well with Greiner’s Growth Model?

As a company using Greiner’s Growth Model you may also want to use a SWOT Analysis, which should include strengths & weaknesses from this model.

Who invented Greiner’s Growth Model?

The Greiner’s Growth Model was invented by Larry E. Greiner in 1972 with the five phases of growth. In 1998 he updated the model to add the sixth phase around Alliances.

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What Is a Growth Curve?

Understanding a growth curve.

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Growth Curve: Definition, How They're Used, and Example

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

A growth curve is a graphical representation that shows the course of a phenomenon over time. An example of a growth curve might be a chart showing a country's population increase over time.

Growth curves are widely used in statistics to determine patterns of growth over time of a quantity—be it linear, exponential, or cubic. Businesses use growth curves to track or predict many factors, including future sales .

Key Takeaways

• A growth curve shows the direction of some phenomena over time, in the past or into the future, or both.
• Growth curves are typically displayed on a set of axes where the x-axis is time and the y-axis shows an amount of growth.
• Growth curves are used in a variety of applications from population biology and ecology to finance and economics.
• Growth curves allow for the monitoring of change over time and what variables may cause this change. Businesses and investors can adjust strategies depending on the growth curve.

The shape of a growth curve can make a big difference when a business determines whether to launch a new product or enter a new market . Slow growth markets are less likely to be appealing because there is less room for profit. Exponential growth is generally positive but it also could mean that the market could see a lot of competitors.

Growth curves were initially used in the physical sciences such as biology. Today, they're a common component of social sciences as well.

Digital Enhancements

Advancements in digital technologies and business models now require analysts to account for growth patterns unique to the modern economy. For example, the winner-take-all phenomenon is a fairly recent development brought on by companies such as Amazon, Google, and Apple . Researchers are scrambling to make sense of growth curves that are unique to new business models and platforms.

Growth curves are often associated with biology, allowing biologists to study organisms and how these organisms behave in a specific environment and the changes to that environment in a controlled setting. This is used to help with medical treatments.

Shifts in demographics, the nature of work, and artificial intelligence will further strain conventional ways of analyzing growth curves or trends.

Analysis of growth curves plays an essential role in determining the future success of products, markets, and societies, both at the micro and macro levels.

Example of a Growth Curve

In the image below, the growth curve displayed represents the growth of a population in millions over a span of decades. The shape of this growth curve indicates exponential growth. That is, the growth curve starts slowly, remains nearly flat for some time, and then curves sharply upwards, appearing almost vertical.

This curve follows the general formula: V = S * (1 + R) t

The current value, V, of an initial starting point subject to exponential growth, can be determined by multiplying the starting value, S, by the sum of one plus the rate of interest, R, raised to the power of t, or the number of periods that have elapsed.

In finance, exponential growth appears most commonly in the context of compound interest.

The power of compounding is one of the most powerful forces in finance. This concept allows investors to create large sums with little initial capital. Savings accounts that carry a compounding interest rate are common examples.

What Are the 2 Types of Growth Curves?

The two types of growth curves are exponential growth curves and logarithmic growth curves. In an exponential growth curve, the slope grows greater and greater as time moves along. In a logarithmic growth curve, the slope grows sharply, and then over time the slope declines until it becomes flat.

Why Use a Growth Curve?

Growth curves are a helpful visual representation of change over time. Growth curves can be used to understand a variety of changes over time, such as developmental and economic. They allow for the understanding of the effect of policies or treatments.

What Is a Business Growth Model?

A business growth model provides a visual representation for businesses to track various metrics and key drivers, allowing businesses to map out growth and adjust the businesses accordingly to foster these metrics.

Curran, Patrick J., Obeidat, Khawla, and Losardo, Diane. " Twelve Frequently Asked Questions About Growth Curve Modeling: Abstract ." Journal of Cognition and Development , vol. 11, no. 2, 2010.

Sigirli, Deniz and Ercan, Ilker. " Examining Growth with Statistical Shape Analysis and Comparison of Growth Models ." Journal of Modern Applied Statistical Methods , vol. 11, no. 2, November 2012, pp. 1.

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Growth Curve - Explained

What is the Growth Curve?

Written by Jason Gordon

Updated at March 10th, 2022

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Table of Contents

What is a growth curve.

A growth curve is a graphical representation of the increase in a particular quantity over time. 

Growth curves can be typically classified into two types -

• Exponential growth curve, or, J Curve.
• Logistic growth curve, or S Curve.

A growth curve has different applications in different fields of study. Growth curves are extensively used in finance, especially by businesses, in order to create a mathematical model to analyze the growth in sales or profits, and also to predict future sales.

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What is an Exponential growth curve ?

Exponential growth, also referred to as unrestricted growth, usually occurs in an ideal environment with unlimited resources. The growth is slow in the beginning but increases rapidly with the passage of time. 

Exponential growth curves are most commonly used to denote population growth, growth of wealth and investments, business growth, and growth in website traffic as well as followers on social media. 

A great example to illustrate exponential growth would be that of living bacteria in a petri dish in a laboratory under ideal conditions, the bacteria will reproduce by binary fission, i.e by splitting in half, roughly once every hour. Now assuming that the petri dish originally contained 1 million bacteria cells, it would end up with 2 million cells after an hour. After two hours, there would be 4 million bacteria cells. The number of bacteria cells in the petri dish would increase to 8 million cells after the passage of three hours, and so on. However, it should be borne in mind that it is usually not possible to sustain exponential growth over long periods of time since there is a limit to the availability of resources in the real world. 

What is a Logistic growth curve ? 

Logistic growth, or restricted growth, occurs when the numbers begin to approach a finite carrying capacity. The growth is typically fast in the initial stage but drastically slows down with the passage of time. 

Logistic growth patterns are most prominent in graphical representations of increase in literary skills or language proficiency, weight loss regimes and musical skills. Logistic growth also occurs in populations that begin to experience environmental resistance while approaching the carrying capacity. 

A good example of logistic growth would be that of a person partaking in mass building or strength training at the gym the initial muscle or strength gains will be quick and fairly noticeable. However, once the individual attains a certain degree of fitness, the gain will typically slow down and become much less noticeable as time passes. In business, the shape of the growth curve essentially determines the direction that the company will be required to take in the market. For many businesses, logistic growth markets are not the most desirable places for product launches because such saturated markets do not leave much room for profits. On the other hand, exponential growth markets do provide opportunities for fast growth and handsome profits, but they also typically lure in a lot of competitors.

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The Greiner Curve

Understanding and overcoming the crises of growth.

By the Mind Tools Content Team

Fast-growing companies can often be chaotic places to work.

As workloads increase exponentially, approaches which have worked well in the past start failing. Teams and people get overwhelmed with work. Previously-effective managers start making mistakes as their span of control expands. And systems start to buckle under increased load.

While growth is fun when things are going well, when things go wrong, this chaos can be intensely stressful. More than this, these problems can be damaging (or even fatal) to the organization.

Growth can be painful but you can make it easier by preparing. Learn how with our video and transcript .

The "Greiner Curve" is a useful way of thinking about the crises that organizations experience as they grow.

In this article, we'll learn more about the Greiner Curve, and how you can use it to understand the root cause of the problems you're likely to experience in a fast-growing business, as well as how to prevent them.

What Is the Greiner Curve?

The Greiner Curve (shown in figure 1, below) describes the different phases that organizations go through as they grow. All kinds of organizations – from design shops to manufacturers, construction companies to professional service firms – experience these.

Each growth phase is made up of a period of relatively stable growth, followed by a "crisis" when major organizational change is needed if the company is to carry on growing.

Figure 1. The Greiner Growth Model

Reprinted by permission of Harvard Business Review . From " Evolution and Revolution as Organizations Grow " by Larry E. Greiner, May 1998. Copyright © 1998 by the Harvard Business School Publishing Corporation; all rights reserved.

Although the word "crisis" is often linked to a state of panic, it can also mean "turning point." While companies certainly have to change at each of these points, if they properly plan ahead, there is no need for panic, and so we will call them "transitions."

The Six Phases of Growth

Larry E. Greiner originally proposed the Greiner Curve (also known as the Greiner Growth Model) in 1972 with five phases of growth. In 1998, he added a sixth phase in an updated version of his original article. [1]

The six growth phases are described below:

Phase 1: Growth Through Creativity

Here, the entrepreneurs who founded the firm are busy creating products and opening up markets. There aren't many staff, so informal communication works fine, and rewards for long hours are probably through profit share or stock options.

However, as more staff join, production expands and capital is injected, there's a need for more formal communication .

This phase ends with a Leadership Crisis , where professional management is needed. The founders may change their style and take on this role, but often someone new will be brought in.

Phase 2: Growth Through Direction

Growth continues in an environment of more formal communications, budgets and focus on separate activities like marketing and production. Incentive schemes replace stock as a financial reward.

However, there comes a point when the products and processes become so numerous that there are not enough hours in the day for one person to manage them all, and they can't possibly know as much about all these products or services as those lower down the hierarchy.

This phase ends with an Autonomy Crisis in which new structures based on delegation are needed.

Phase 3: Growth Through Delegation

With mid-level managers freed up to react faster to opportunities for new products or new markets, the organization continues to grow. Meanwhile, top management focuses its efforts on monitoring and dealing with the big issues (perhaps starting to look at merger or acquisition opportunities).

Many businesses flounder at this stage because the manager whose directive approach solved the problems at the end of Phase 1 finds it hard to let go of the control they've assumed. This can mean that the mid-level managers begin to struggle with their roles.

This phase ends with a Control Crisis . A much more sophisticated organizational design is required, so the separate parts of the business can work together more effectively.

Phase 4: Growth Through Coordination and Monitoring

Growth continues with the previously isolated business units re-organized into product groups or service practices. Investment finance is allocated centrally and managed according to Return on Investment (ROI) and not just profits. Incentives are shared through company-wide profit share schemes aligned to corporate goals.

Eventually, though, work becomes submerged under increasing amounts of bureaucracy, and growth is stifled as a result.

This phase ends on a Red-Tape Crisis: a new culture and structure must be introduced.

Phase 5: Growth Through Collaboration

The formal controls of Phases 2-4 are replaced by professional good sense, as staff group and re-group flexibly in teams to deliver projects in a matrix structure which is supported by sophisticated information systems and team-based financial rewards.

This phase ends with a crisis of Internal Growth: further growth can only come by developing partnerships with external, complementary organizations.

Phase 6: Growth Through Extra-Organizational Solutions

Greiner's recently added sixth phase suggests that growth may continue through mergers, outsourcing, networks, and other solutions involving external companies.

Growth rates will vary between and even within phases. The duration of each phase depends almost totally on the rate of growth of the market in which the organization operates. The longer a phase lasts, though, the harder it will be to transition to the next phase of growth.

This is a useful model, however not all businesses will go through these crises in this order. Use this as a starting point for thinking about business growth, and adapt it to your circumstances.

Applying the Greiner Curve

The Greiner Growth Model helps you to think about your own organization's growth trajectory, and plan ahead so you can overcome each growth crises that affects it.

To apply this model, use the following five steps:

• Based on the descriptions above, think about where your organization is now.
• People feel that managers and company procedures are getting in the way of them doing their jobs.
• People feel that they are not fairly rewarded for the effort that they put in.
• People seem unhappy, and there is a higher staff turnover than usual.
• Delegate more?
• Take on more responsibilities?
• Specialize more in a specific product or market?
• Change the way you communicate with others?
• Incentivize and reward your team differently?

By thinking this through, you can start to plan and prepare yourself for the inevitable changes, and perhaps help others to do the same.

• Plan and take preparatory actions that will make the transition as smooth as possible for you and your team.
• Revisit Greiner's model for growth again every 6-12 months, and think about how your organization's current stage of growth is affecting you and others around you.

The Greiner Curve (also known as Greiner's Growth Model) was first developed by Larry E. Greiner. It illustrates six key phases of growth that organizations typically go through – from start-up phase to multinational corporation.

After each stage of growth, organizations tend to hit a crisis, which they must adapt and overcome to in order to continue to grow.

The six phases of growth are:

• Growth Through Creativity – ends in a Leadership Crisis.
• Growth Through Direction – ends in an Autonomy Crisis.
• Growth Through Delegation – ends in a Control Crisis.
• Growth Through Coordination and Monitoring – ends in a Red-Tape Crisis.
• Growth Through Collaboration – ends in a crisis of Internal Growth.
• Growth Through Extra-Organizational Solutions .

The Greiner Curve can help organizations to understand their own personal trajectory of growth, and to plan ahead more effectively, so that when they reach a growth crisis, they are in a better position to overcome it and continue to grow.

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