This is the first post in a series on SaaS metrics where I plan to develop a variety of SaaS financial metric models using simple mathematical heuristics. In the process, I hope to highlight important relationships between key SaaS metrics and develop a short list of valuable SaaS Metrics Rules-of-Thumb.

### SaaS Metrics Rule-of-Thumb #1 – SaaS Churn Kills SaaS Company Growth

Consider a SaaS company that acquires new customers at the *constant* rate of “b” (for bookings), and has a percentage churn rate of “a” (for attrition). The number of customers after n periods of time “C_{n}” is given by the following formula:

C_{n+1} = b + ( 1 – a ) x C_{n}

C_{n} = b + b (1-a) + b (1-a)^{2} + b (1-a)^{3} … + b(1-a)^{n-2} + b(1-a)^{n-1}

C_{n} = b⁄a x ( 1 – ( 1 -a )^{n} )

This formula can be approximated at the two extremes of early growth and maturity.

Early Growth | C_{n} = b x n |
acquisition rate x time | (n x a << 1) |

Maturity Limit | C_{limit} = b ÷ a |
acquisition rate ÷ % churn rate | (n x a >> 1) |

These two boundaries are shown in the chart below along with the blue curve representing total customers over time.

*As a SaaS company grows, absolute churn increases with the total number of existing customers and will limit growth if new customers are not added at a faster and faster rate.*

In the early days, churn is small and the customer base grows unimpeded at the customer acquisition rate. As the customer base grows, the absolute value of churn increases and soon overwhelms new customer acquistion. When the customer acquisition rate, b, equals churn, a x C, then the number of customers coming in the door is exactly equal to the number leaving. At this point further growth is impossible, limiting the total customer base size to the new customer acquisition rate divided by the percentage churn rate. This limit might be more than satisfying if you run a bootstrapped, private SaaS business as your primary means of personal income. But, it is unlikely to satisfy investors if you are a VC-backed SaaS startup, bringing us to…

### SaaS Metrics Rule-of-Thumb #2 – New Customer Acquisition Growth Must Outpace Churn

The bad news is that if you want to grow your SaaS company without limits, you can’t just sit back and book a hundred new customers per year and expect recurring revenue to accumulate, because sooner or later churn catches up with you. You must not only acquire new customers, but *you must acquire them at an increasing rate* that outpaces your increasing churn.

*SaaS churn scales with the customer acquisition rate.*

The good news is that the lower your percentage churn rate, the longer you have to figure it out, because churn lags behind customer acquisition for a time equal to one divided by the percentage churn rate. But, the reality of this SaaS metric rule-of-thumb is that churn relentlessly chases the new customer acquisition rate, and if customer acquisition growth doesn’t outpace churn, overall growth will slow and eventually stop.

In the next post in this SaaS Metrics series, I’ll explore how *viral growth* is the surest path (albeit not the only path) to achieve the goal of SaaS Metrics Rule-of-Thumb #2 above and break the chains of SaaS churn.

**SaaS Metrics Math Notes**

This relationship between SaaS churn and SaaS growth can also be derived (somewhat more cleanly) using a continuous model as a function of time, “t”, rather than a discrete model as a function of the number of periods, n. For those that remember their college calculus, the model is represented by the linear first order differential equation: C'(t) = b – a C(t) with the solution: C(t) = b⁄a ( 1 – e^{-at} ). The first graph above is plotted using this continuous solution.

The second SaaS metric rule of thumb above can be shown using asymptotic methods, such that even for increasing customer acquisition b(t), the total SaaS churn rate a C(t) approaches b(t) over time, i.e., SaaS churn chases the acquisition rate.

It is also worth mentioning that this SaaS metrics model applies not only to SaaS, but to any subscription-based business.

### Check out the rest of the SaaS Metrics Rules-of-Thumb

- SaaS Metrics Rule-of-Thumb #1 – SaaS Churn Kills SaaS Company Growth
- SaaS Metrics Rule-of-Thumb #2 – New Customer Acquisition Growth Must Outpace Churn
- SaaS Metrics Rule-of-Thumb #3 – Viral Growth Trumps SaaS Churn
- SaaS Metrics Rule-of-Thumb #4 – Company Time to Profit Follows Customer Break-Even
- SaaS Metrics Rule-of-Thumb #5 – Best Case Time to Profit is Simple Break-Even
- SaaS Metrics Rule-of-Thumb #6 – Growth Creates Pressure to Reduce Total Cost of Service
- SaaS Metrics Rule-of-Thumb #7 – Churn Creates Pressure to Reduce Total Cost of Service
- SaaS Metrics Rule-of-Thumb #8 – Upselling and Upgrades Accelerate SaaS Profitability
- SaaS Metrics Rule-of-Thumb #9 – Joel’s SaaS Magic Number
- SaaS Metrics Rule-of-Thumb #10 – SaaS Customer Lifetime Value Drives SaaS Company Value

[…] is the lifeblood of any SaaS model. SaaS Churn is discussed from a mathematical stance by Joel York in a recent post on his must-read Chaotic Flow […]

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[…] SaaS Metrics Rule-of-Thumb #2 – New Customer Acquisition Growth Must Outpace Churn […]

So what you’re saying is that you need to get customers faster than you lose them or you won’t grow. Genius.

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These rules of thumb are great, for those of us who have poor excel skill any chances of downloading a template?

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[…] no point filling the bucket if it’s full of holes. This topic has been covered over, and over, and over again. Read these articles and digest them. Investors will be heavily focused on this […]

[…] Joel York explains here, subscription revenue growth must continually outpace the churn rate. When the latter overtakes […]

[…] experts. But for all the time we spend on churn, we think about retention even more. Churn kills momentum for businesses but it’s also a tricky problem to solve. Let’s dive into a quick […]

[…] since first getting introduced to his SaaS Rules of Thumb mathematics a few years ago. Start with SaaS Metrics Rule-of-Thumb #1 and read all 10 rules. It gets a little deep, but be sure to at least come away with the concepts […]

[…] since first getting introduced to his SaaS Rules of Thumb mathematics a few years ago. Start with SaaS Metrics Rule-of-Thumb #1 and read all 10 rules. It gets a little deep, but be sure to at least come away with the concepts […]

[…] Source […]

Thanks for writing this article.

The above formula is based on assumption that we will have a constant rate of acquisition and that the churn rate is also constant across periods.

Since in reality the above will not be true, how would you suggest that the above formula look like.

Unless the above values of B & A are aggregated somehow across time periods, in that case would love to hear how did we aggregate it.

thanks in advance for your help.

Zenith

[…] impact of churn is clear, as explained in this image by Chaotic Flow. Even if acquisitions is greater than churn, it can still severely handicap your […]

[…] Source: Chaotic Flow […]