First choose the "Type of calculation", fill in the fields shown and press "Calculate". It calculates the churn rate, retention rate, average lifetime, annual churn and more, and graphs how customers drop month by month.
Enter numbers of customers as plain numbers. For % fields, enter just the number (for 5%, enter "5"). The churn rate period is treated as one month (if you enter weekly or yearly figures as they are, the average lifetime and annual churn will be off).
Result and graph
Choose the type of calculation, enter the values and press "Calculate". The result and a graph of remaining customers over time will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Formula for the monthly churn rate
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Formula for the average customer lifetime (months)
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Formula for the annual churn rate (from the monthly rate)
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Formula for the monthly churn rate (from the annual rate)
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Formula for the customers left after n months
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Formula for the max monthly churn rate (from a target average lifetime)
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Calculates the monthly churn rate and retention rate from the customers at the start of the month and the cancellations during it. New customers added during the period are never counted in the denominator, and the result also shows how another definition (using the average of start and end as the denominator) differs
- From the monthly churn rate, it finds the average customer lifetime (\(100 \div\) churn rate months) and the annual churn rate. The numbers show why "5% a month times 12 = 60% a year" is wrong
- It also works backward: "What is 40% annual churn per month?", "How low must monthly churn be for customers to stay 24 months on average?" and "If 200 customers churn at 5% a month, how many are left after 12 months?"
- A decay graph shows customers dropping month by month, and marks where the average customer lifetime falls
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
On this page, the churn rate is "customers who canceled during the period (one month) as a share of customers at the start of the period" (customer churn, counted by number of customers). New customers who joined during the period are not counted in the denominator. The average lifetime and annual churn are calculated values that assume the monthly churn rate stays the same, and they change with how cancellations really happen (for example, more right after sign-up). To calculate LTV (customer lifetime value) from your churn rate, use the customer lifetime value (LTV) calculator page.
What is this calculation used for?
A regular health check for a subscription or SaaS business (operations)
For a monthly subscription service, the basic routine is to work out the churn rate every month from the customers at the start of the month and the cancellations. With 1,200 at the start and 36 cancellations, it is \(36 \div 1200 \times 100 = 3\)%, and the average lifetime is about \(100 \div 3 \approx 33\) months.
No matter how many new customers you add, if churn stays high, new customers mostly just replace the ones you lose. Tracking "the rate went up or down since last month" gives you numbers for decisions on pricing, product improvements and customer support.
A first step toward estimating LTV (marketing)
LTV, "how much revenue one customer brings", is estimated for a subscription as "monthly price × average lifetime in months" (for gross profit, also multiply by the gross margin). At a 5% monthly churn rate, the average lifetime is 20 months, so for a $30/month plan the LTV is about $600.
With this estimate, you can decide how much you can spend on ads to win one customer. The churn rate is the starting point of that calculation, and the relation "less churn, higher LTV" also comes from the average lifetime being the reciprocal of the churn rate.
Bridging yearly and monthly cancellation rates (membership businesses)
In businesses such as gyms and classes, where people talk about "how many members leave in a year", you need to convert between annual and monthly rates. 40% a year is \((1 - \sqrt[12]{0.6}) \times 100 \approx 4.17\)% a month, which is not the same as 3.33% from simply dividing by 12.
Going the other way, when you put monthly figures into an annual plan, use the share left after 1 year, not "times 12". 5% a month is about 46% a year, very different from 60%, so the way you convert changes how the business looks.
Forecasting how many customers are left after some months (revenue and staffing plans)
"If we have 200 customers now and they cancel at 5% a month, how many are left in a year?" The forecast is \(200 \times 0.95^{12} \approx 108\). Without new customers, you would lose almost half your customers in a year, and the numbers make that visible.
With this forecast you can plan next year's revenue, the size of the support team, and the new customers needed (about 92 new customers a year just to make up for the losses).
Setting an acceptable churn line instead of aiming for zero (goal setting)
You can never stop all cancellations, so in practice you set a churn target by working back from "how many months do customers need to stay on average for the business to pay off". If you need 24 months on average, the max monthly churn rate is \(100 \div 24 \approx 4.17\)%.
With the target as a number, results turn into concrete action, such as "this month was 4.5%, so we need to improve". The basis is a simple formula, "the reciprocal of the churn rate = average lifetime", which also makes it easy to share with the team.
Formulas and figures
Formula for the monthly churn rate
Standard notation
(the usual math form)
\(c\)
\(=\)
\(D\)
\(\div\)
\(N_{0}\)
\(\times\)
\(100\)
In words
(symbols replaced with words)
④
\(c\): monthly churn rate (%)
\(=\)
①
\(D\): cancellations during the period
\(\div\)
②
\(N_{0}\): customers at the start
\(\times\)
③
\(100\): percent base
The formula in words
①
Take the
\(D\): cancellations during the period
②
divide it by the
\(N_{0}\): customers at the start
,
③
multiply by the
\(100\): percent base
to turn it into a percentage, and you get the
④
\(c\): monthly churn rate (%)
Quick example
If you have 200 members at the start of the month and 10 of them cancel during the month, the monthly churn rate is
monthly churn rate \(c\) (%)
\(=\)
cancellations (10)
\(\div\)
customers at the start (200)
\(\times\)
\(100\)
\(10 \div 200 \times 100 = 5\ \ (5\%)\)
Key idea
The denominator is the number of customers at the start of the month. Customers who join during the month have not had a chance to cancel yet (they just arrived), so they are not counted. For example, with 200 at the start, 10 cancellations and 30 new customers, you end with 220, but the churn rate is \(10 \div 200 = 5\)%. Calculating \(10 \div 220\) or \(10 \div 230\) is wrong.
Some companies, however, use another definition that divides by the average of the start and end counts. In the example above that gives \(10 \div [(200 + 220) \div 2] \times 100 \approx 4.76\)%, which comes out smaller the more new customers you add. When you compare with other companies' numbers or reports, always check which definition they use. If you enter new customers, this calculator also shows this other definition for reference.
Subtract the churn rate from 100 and you get the retention rate (\(r = 100 - c\); 95% at 5% churn). It is the share of customers who did not cancel, so the two add up to exactly 100%.
Formula for the average customer lifetime (months)
Figure
Standard notation
(the usual math form)
\(L\)
\(=\)
\(100\)
\(\div\)
\(c\)
In words
(symbols replaced with words)
③
\(L\): average lifetime (months)
\(=\)
①
\(100\): percent base
\(\div\)
②
\(c\): monthly churn rate (%)
The formula in words
①
Take the
\(100\): percent base
②
divide it by the
\(c\): monthly churn rate (%)
(that is, take the reciprocal of the churn rate), and you get the
③
\(L\): average lifetime (months)
Quick example
For a service with a monthly churn rate of 5%, the number of months one customer stays on average is
average lifetime \(L\)
\(=\)
\(100\)
\(\div\)
monthly churn rate (5%)
\(100 \div 5 = 20\)
Key idea
If "5% leave every month", one customer stays 20 months on average. This is the relation "average lifetime is the reciprocal of the churn rate". As the figure shows, the total area of the bars for 200 customers shrinking by 5% every month (the total customer-months) is exactly the area of a rectangle of "200 customers × 20 months". Per customer, that is 20 months.
This formula is an expected value (average) that assumes the monthly churn rate stays the same forever. In reality, many customers cancel right after signing up, and those who have stayed a long time tend to stay even longer, so use it as a guide. With a churn rate of 0%, the division cannot be done (no one cancels, so the average lifetime is infinite).
To go the other way, from a goal such as "we want customers to stay 24 months on average" to the churn rate you can allow, flip this formula over: \(c = 100 \div L\) (the sixth formula).
Formula for the annual churn rate (from the monthly rate)
Figure
Standard notation
(the usual math form)
\(R_{\mathrm{y}}\)
\(=\)
\(\left(1 - \dfrac{c}{100}\right)\)
\(12\)
\(c_{\mathrm{y}}\)
\(=\)
\((\)
\(1 -\)
\(R_{\mathrm{y}}\)
\()\)
\(\times\)
\(100\)
In words
(symbols replaced with words)
③
\(R_{\mathrm{y}}\): share left after 1 year
\(=\)
①
\(1 -\) monthly churn rate \(c \div 100\)
②
12 months
⑥
\(c_{\mathrm{y}}\): annual churn rate (%)
\(=\)
\((\)
\(1 -\)
④
\(R_{\mathrm{y}}\): share left after 1 year
\()\)
\(\times\)
⑤
\(100\): percent base
The formula in words
①
Multiply
\(1 -\) monthly churn rate \(c \div 100\)
(the share left after 1 month) by itself
②
once for each of the
12 months
, and you get the
③
\(R_{\mathrm{y}}\): share left after 1 year
. Subtract the
④
\(R_{\mathrm{y}}\): share left after 1 year
from 1,
⑤
multiply by the
\(100\): percent base
to turn it into a percentage, and you get the
⑥
\(c_{\mathrm{y}}\): annual churn rate (%)
Quick example
With a monthly churn rate of 5%, the churn rate converted to an annual rate is
share left after 1 year \(R_{\mathrm{y}}\)
\(=\)
\(1 - 5 \div 100\)
12 months
annual churn rate \(c_{\mathrm{y}}\) (%)
\(=\)
\((\)
\(1 -\)
\(R_{\mathrm{y}}\)
\()\)
\(\times\)
\(100\)
\(R_{\mathrm{y}} = 0.95^{12} \approx 0.5404\)
\((1 - 0.5404) \times 100 \approx 45.96\ \ (45.96\%)\)
Key idea
Taking 5% a month and "multiplying by 12 to get 60% a year" is a mistake. Each month, the people who cancel are 5% of those still left at that point, so the denominator shrinks month by month and so does the number of cancellations. Start with 100 people: after 1 month 95 are left, after 2 months \(95 \times 0.95 \approx 90.25\), and so on, until after 12 months \(100 \times 0.95^{12} \approx 54.04\) remain. About 45.96 people left during the year, so the annual churn rate is about 45.96%, less than the 60% you get by multiplying by 12.
"Multiply the share left after 1 month 12 times" has the same form as compound interest (applying the interest rate 12 times). To go the other way, from an annual rate to a monthly rate, use the fourth formula (the 12th root). Simply dividing by 12 is wrong for the same reason.
Formula for the monthly churn rate (from the annual rate)
Standard notation
(the usual math form)
\(c\)
\(=\)
\((\)
\(1 -\)
\(\sqrt[12]{1 - \dfrac{c_{\mathrm{y}}}{100}}\)
\()\)
\(\times\)
\(100\)
In words
(symbols replaced with words)
③
\(c\): monthly churn rate (%)
\(=\)
\((\)
\(1 -\)
①
12th root of (\(1 -\) annual rate \(c_{\mathrm{y}} \div 100\))
\()\)
\(\times\)
②
\(100\): percent base
The formula in words
①
Divide the annual churn rate \(c_{\mathrm{y}}\) by 100 and subtract it from 1 to get the share left after 1 year. Its
12th root of (\(1 -\) annual rate \(c_{\mathrm{y}} \div 100\))
is the share left after 1 month, so subtract it from 1,
②
multiply by the
\(100\): percent base
to turn it into a percentage, and you get the
③
\(c\): monthly churn rate (%)
Quick example
With an annual churn rate of 40% (40% of members leave within a year), the monthly churn rate is
monthly churn rate \(c\) (%)
\(=\)
\((\)
\(1 -\)
12th root of (\(1 - 40 \div 100\))
\()\)
\(\times\)
\(100\)
\(\sqrt[12]{0.6} \approx 0.9583\)
\((1 - 0.9583) \times 100 \approx 4.17\ \ (4.17\%)\)
Key idea
The "12th root" is the number that gives this number when multiplied by itself 12 times. If the share left after 1 year is 0.6, then since \(0.9583^{12} \approx 0.6\), customers remain at 0.9583 times each month (about 4.17% cancel each month). This formula traces the third formula (monthly to annual) exactly backward.
Simply dividing 40% a year by 12 gives about 3.33%, but the correct monthly rate is about 4.17%, larger than dividing by 12. "Times 12 is too big" and "divided by 12 is too small" have the same cause: both ignore that the denominator of cancellations shrinks each month.
In Excel and Google Sheets, calculate the 12th root with \(\wedge(1/12)\) (the 1/12 power).
Formula for the customers left after n months
Figure
Standard notation
(the usual math form)
\(N_{n}\)
\(=\)
\(N_{0}\)
\(\times\)
\(\left(1 - \dfrac{c}{100}\right)\)
\(n\)
In words
(symbols replaced with words)
④
\(N_{n}\): customers left after \(n\) months
\(=\)
①
\(N_{0}\): customers at the start
\(\times\)
②
\(1 -\) monthly churn rate \(c \div 100\)
③
\(n\): months elapsed
The formula in words
①
Take the
\(N_{0}\): customers at the start
and multiply by
②
\(1 -\) monthly churn rate \(c \div 100\)
(the share left after 1 month)
③
once for each of the
\(n\): months elapsed
, and you get the
④
\(N_{n}\): customers left after \(n\) months
Quick example
If 200 customers cancel at a monthly churn rate of 5%, the number left after 12 months is
customers left after 12 months \(N_{12}\)
\(=\)
customers at the start (200)
\(\times\)
\(1 - 5 \div 100\)
12 months
\(200 \times 0.95^{12} \approx 200 \times 0.54036 \approx 108.07\)
Key idea
This formula assumes no new customers come in, and shows how only the customers at the start shrink over time (how one cohort, a group that started at the same time, holds up). The answer of 108.07 customers is an average forecast; in reality the count is a whole number.
Because you multiply by "the share left after 1 month" \(n\) times, the drop slows down as the months go by, and the graph is a downward curve (exponential decay). It is exactly the same form as the half-life of a radioactive substance or compound interest. The third formula (annual churn) is the special case of this formula with \(n = 12\) and \(N_{0} = 100\).
To see the monthly customer count when new customers keep joining, add each month's new customers to the result of this formula.
Formula for the max monthly churn rate (from a target average lifetime)
Standard notation
(the usual math form)
\(c\)
\(=\)
\(100\)
\(\div\)
\(L\)
In words
(symbols replaced with words)
③
\(c\): max monthly churn rate (%)
\(=\)
①
\(100\): percent base
\(\div\)
②
\(L\): target average lifetime (months)
The formula in words
①
Take the
\(100\): percent base
②
divide it by the
\(L\): target average lifetime (months)
, and you get the
③
\(c\): max monthly churn rate (%)
Quick example
If you want customers to stay 24 months (2 years) on average, the max monthly churn rate is
max monthly churn rate \(c\) (%)
\(=\)
\(100\)
\(\div\)
target average lifetime (24 months)
\(100 \div 24 \approx 4.17\ \ (4.17\%)\)
Key idea
This is just the second formula, \(L = 100 \div c\), flipped over to solve for the churn rate \(c\). The answer, about 4.17%, is the dividing line: "above this, customers do not reach 24 months on average", so in practice keep churn below it.
If the target average lifetime is under 1 month, the churn rate needed would be over 100%, which has no meaning (even if everyone cancels within 1 month, the average lifetime is 1 month).
The flow of finding the lifetime needed from an LTV (customer lifetime value) target and then the max churn rate from it is covered on the customer lifetime value (LTV) calculator page.
The churn rate is "cancellations ÷ customers at the start × 100" (new customers are not in the denominator), and the average lifetime is its reciprocal, "100 ÷ churn rate" months. To convert to an annual rate, do not multiply by 12; use the share left after 1 year, \((1 - c \div 100)^{12}\). Working backward, "100 ÷ target average lifetime in months" gives the max churn rate, and "customers at the start × the share left to the \(n\)th power" gives the customers left after \(n\) months.
Symbols and terms
Symbols
| \(c\) | see | Monthly churn rate (%), from the first letter of "churn" (customers leaving). The share of customers who cancel during one month. In the reverse formula, it is the highest churn rate you can allow. |
| \(r\) | ar | Monthly retention rate (%), from the first letter of "retention". The share of customers still subscribed after 1 month: \(r = 100 - c\). |
| \(N_{0}\) | N sub zero (N naught) | Customers at the start (of the month). \(N\) is the first letter of "number", and the subscript \(0\) stands for month 0, the starting point. (Example - with 200 at the start of the month, \(N_{0} = 200\)) |
| \(D\) | dee | Cancellations during the period (one month): how many of the customers at the start canceled that month. There is no standard one-letter symbol, so this page uses \(D\), for "drop-offs". |
| \(L\) | el | Average lifetime in months, from the first letter of "lifetime". How many months one customer stays subscribed on average: \(L = 100 \div c\). In the reverse formula, it is the target average lifetime. |
| \(c_{\mathrm{y}}\) | C sub y | Annual churn rate (%). The subscript \(\mathrm{y}\) is the first letter of "year". The share of customers who cancel during one year. |
| \(R_{\mathrm{y}}\) | R sub y | Share left after 1 year (as a decimal). \(R\) for retention with \(\mathrm{y}\) for year: \(R_{\mathrm{y}} = (1 - c \div 100)^{12}\). Times 100, it is the annual retention rate (%). |
| \(N_{n}\) | N sub n | Customers left after \(n\) months. The subscript \(n\) is the number of months elapsed; it is the count after starting from \(N_{0}\) and shrinking month by month. |
| \(n\) | en | Months elapsed, from the first letter of "number". A whole number for "how many months later". In the formula, it is how many times you multiply by the share left after 1 month (the exponent). |
| \(\sqrt[12]{\ }\) | twelfth root | The 12th root. The symbol for the number that gives this number when multiplied by itself 12 times. Used to get the monthly share left from the yearly share left. |
| \(100\) | one hundred | The base for percentages. Divide a percentage by 100 to get back a decimal (\(5\% \div 100 = 0.05\)). This conversion is also why the reciprocal of the churn rate, \(100 \div c\), is the average lifetime in months. |
Terms
| churn rate | The share of customers who cancel in a given period (one month on this page). The word comes from "churn", to stir, describing customers turning over. On this page it is defined as cancellations during the period divided by customers at the start. In subscriptions and SaaS it is one of the most important metrics, because it directly decides how fast revenue shrinks. |
| retention rate | The share of customers at the start who are still subscribed at the end. Added to the churn rate, it makes exactly 100% (retention rate = 100 − churn rate). For apps, retention for a set number of days, such as "day-1 retention" or "day-30 retention", is common. |
| customer churn | Churn counted by the number of customers (accounts), also called logo churn. This is the churn rate on this page. When a report just says "churn rate", check whether it is based on customers or on revenue (revenue churn). |
| revenue churn | Churn measured as the share of monthly recurring revenue (MRR) lost to cancellations and downgrades, also called MRR churn. When customers on expensive plans leave, it comes out larger than customer churn. When a report just says "churn rate", check whether it is based on customers or on revenue. |
| start of the period | The beginning of the period you measure. For monthly figures, the start of the month. The denominator of the churn rate is the customers at the start of the period. |
| end of the period | The end of the period you measure. For monthly figures, the end of the month. Customers at the end = start − cancellations + new. |
| churn rate using the average customers | Another definition of the churn rate that uses the average of the start and end counts as the denominator. In a growth phase with many new customers, the denominator gets bigger, so it comes out smaller than the value based on the start count. Neither is "right"; they are different counting rules, so match the definitions before comparing. |
| average customer lifetime | How many months (or years) one customer stays subscribed on average. When customers cancel at a steady monthly churn rate, it is the reciprocal of the churn rate (100 ÷ churn rate). It is the basis for estimating LTV (customer lifetime value) as "monthly price × average lifetime in months". |
| annualizing | Converting a monthly rate into "what it comes to over a year". For something like churn, where each month's rate applies only to those still left, convert by "multiply the share left after 1 month 12 times and subtract from 1", not by multiplying by 12. It is the same idea as converting a monthly interest rate to an annual rate. |
| cohort | A group of people who started at the same time, such as "customers who signed up in the same month". Following each cohort month by month shows whether cancellations happen mostly right after sign-up or at a steady pace. The formula for customers left on this page shows one cohort shrinking. |
| reciprocal | The number that gives 1 when multiplied. The reciprocal of 5 is \(\dfrac{1}{5}\) (= 0.2). The reciprocal of a 5% churn rate (0.05 as a decimal) is \(1 \div 0.05 = 20\), the average lifetime in months (with the percentage as is, calculate 100 ÷ 5). |
| power (exponent) | Multiplying the same number by itself several times. \(0.95^{12}\) is 0.95 multiplied 12 times, the share left after 1 year built from 12 months of "share left after 1 month". |
| 12th root | The number that gives this number when multiplied by itself 12 times. \(\sqrt[12]{0.6} \approx 0.9583\) says "0.9583 multiplied 12 times is about 0.6". It undoes a power, and in Excel you write it as \(\wedge(1/12)\). |
| exponential decay | A kind of decline where a fixed share of what is left disappears each period. The drop is largest at first and then gets smaller, so the graph is a downward curve. Radioactive half-life and how a drug's level in the blood falls have the same form. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
If you get stuck, going back over these topics is the quickest way forward.
| Percents (Grades 6–7) |
|
| Reciprocals (Grade 6) |
|
| Exponents (Grade 8 and Algebra 1) |
|
| Roots and rational exponents (Algebra 2) |
|
| Compound interest (Algebra 2 and personal finance) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the monthly churn rate
| Cancellations during the period D | 10 |
| Customers at the start N0 | 200 |
| Monthly churn rate c (%) | =B1/B2*100 |
Table to find the average lifetime in months
| Monthly churn rate c (%) | 5 |
| Average lifetime L (months) | =100/B1 |
Table to find the annual churn rate
| Monthly churn rate c (%) | 5 |
| Share left after 1 year Ry | =(1-B1/100)^12 |
| Annual churn rate cy (%) | =(1-B2)*100 |
Table to find the monthly churn rate (from the annual rate)
| Annual churn rate cy (%) | 40 |
| Monthly churn rate c (%) | =(1-(1-B1/100)^(1/12))*100 |
Table to find the customers left after n months
| Customers at the start N0 | 200 |
| Monthly churn rate c (%) | 5 |
| Months elapsed n | 12 |
| Customers left after n months Nn | =B1*(1-B2/100)^B3 |
Table to find the max monthly churn rate (from a target average lifetime)
| Target average lifetime L (months) | 24 |
| Max monthly churn rate c (%) | =100/B1 |
After pasting, the upper rows of column B are your inputs and the bottom row is calculated automatically.
For example, B3 of the first table shows 5 (churn rate 5%), B2 of the second shows 20 (20 months on average), B3 of the third shows about 45.96 (annual 45.96%), B2 of the fourth shows about 4.17 (monthly 4.17%), B4 of the fifth shows about 108.07 (about 108 customers after 12 months), and B2 of the sixth shows about 4.17 (max churn rate 4.17%).
"^" is a power (how many times to multiply), and "^(1/12)" is the 12th root. Just replace the inputs with your own numbers.
For example, B3 of the first table shows 5 (churn rate 5%), B2 of the second shows 20 (20 months on average), B3 of the third shows about 45.96 (annual 45.96%), B2 of the fourth shows about 4.17 (monthly 4.17%), B4 of the fifth shows about 108.07 (about 108 customers after 12 months), and B2 of the sixth shows about 4.17 (max churn rate 4.17%).
"^" is a power (how many times to multiply), and "^(1/12)" is the 12th root. Just replace the inputs with your own numbers.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the monthly churn rate
| Cancellations during the period D | 10 |
| Customers at the start N0 | 200 |
| Monthly churn rate c (%) | =B1/B2*100 |
Table to find the average lifetime in months
| Monthly churn rate c (%) | 5 |
| Average lifetime L (months) | =100/B1 |
Table to find the annual churn rate
| Monthly churn rate c (%) | 5 |
| Share left after 1 year Ry | =(1-B1/100)^12 |
| Annual churn rate cy (%) | =(1-B2)*100 |
Table to find the monthly churn rate (from the annual rate)
| Annual churn rate cy (%) | 40 |
| Monthly churn rate c (%) | =(1-(1-B1/100)^(1/12))*100 |
Table to find the customers left after n months
| Customers at the start N0 | 200 |
| Monthly churn rate c (%) | 5 |
| Months elapsed n | 12 |
| Customers left after n months Nn | =B1*(1-B2/100)^B3 |
Table to find the max monthly churn rate (from a target average lifetime)
| Target average lifetime L (months) | 24 |
| Max monthly churn rate c (%) | =100/B1 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the inputs with your own numbers.
How to calculate it in Python
customers_start = 200 # customers at the start (of the month)
churned = 10 # cancellations during the period
churn_rate = churned / customers_start * 100 # monthly churn rate (%)
retention_rate = 100 - churn_rate # monthly retention rate (%)
avg_months = 100 / churn_rate # average lifetime (months)
annual_retention = (1 - churn_rate / 100) ** 12 # share left after 1 year
annual_churn = (1 - annual_retention) * 100 # annual churn rate (%)
print(f"Monthly churn rate: {churn_rate}%")
print(f"Monthly retention rate: {retention_rate}%")
print(f"Average lifetime: {avg_months} months")
print(f"Annual churn rate: {annual_churn:.4f}% (simply times 12: {churn_rate * 12}%)")
# Reverse 1: monthly churn rate from an annual churn rate (12th root)
annual_rate = 40
monthly_from_annual = (1 - (1 - annual_rate / 100) ** (1 / 12)) * 100
print(f"Monthly churn rate for {annual_rate}% a year: {monthly_from_annual:.4f}%")
# Reverse 2: max monthly churn rate from a target average lifetime
target_months = 24
print(f"Monthly churn rate needed for {target_months} months on average: {100 / target_months:.4f}% or less")
# Reverse 3: customers left after n months
months = 12
remaining = customers_start * (1 - churn_rate / 100) ** months
print(f"Customers left after {months} months: {remaining:.2f}")
Runs with the standard library only. In this example, the monthly churn rate is 5.0%, the retention rate is 95.0%, the average lifetime is 20.0 months, the annual churn rate is about 45.9640%, 40% a year converts to about 4.1675% a month, the churn rate needed for 24 months on average is about 4.1667%, and about 108.07 customers are left after 12 months. Change the customer count and cancellations at the top and run it.
How to write it in LaTeX and other math languages (copy and paste)
Formula for the monthly churn rate
c = D ÷ N₀ × 100
c = \dfrac{D}{N_{0}} \times 100
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac><mi>D</mi><msub><mi>N</mi><mn>0</mn></msub></mfrac>
<mo>×</mo>
<mn>100</mn>
</mrow>
</math>
c = D/N_0 xx 100
d/n0*100
c := d/n0*100;
c = d/n0*100;
c = D/N_0 × 100
Formula for the average customer lifetime (months)
L = 100 ÷ c
L = \dfrac{100}{c}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>L</mi>
<mo>=</mo>
<mfrac><mn>100</mn><mi>c</mi></mfrac>
</mrow>
</math>
L = 100/c
100/c
L := 100/c;
L = 100/c;
L = 100/c
Formula for the annual churn rate (from the monthly rate)
cy = (1 − (1 − c/100)¹²) × 100
c_{\mathrm{y}} = \left[1 - \left(1 - \dfrac{c}{100}\right)^{12}\right] \times 100
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>c</mi><mi mathvariant="normal">y</mi></msub>
<mo>=</mo>
<mrow>
<mo>[</mo>
<mn>1</mn><mo>−</mo>
<msup>
<mrow><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mi>c</mi><mn>100</mn></mfrac><mo>)</mo></mrow>
<mn>12</mn>
</msup>
<mo>]</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</mrow>
</math>
c_y = (1 - (1 - c/100)^12) xx 100
(1 - (1 - c/100)^12)*100
cy := (1 - (1 - c/100)^12)*100;
cy = (1 - (1 - c/100)^12)*100;
c_y = (1 - (1 - c/100)^12) × 100
Formula for the monthly churn rate (from the annual rate)
c = (1 − (1 − cy/100)^(1/12)) × 100
c = \left(1 - \sqrt[12]{1 - \dfrac{c_{\mathrm{y}}}{100}}\right) \times 100
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>c</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn><mo>−</mo>
<mroot>
<mrow><mn>1</mn><mo>−</mo><mfrac><msub><mi>c</mi><mi mathvariant="normal">y</mi></msub><mn>100</mn></mfrac></mrow>
<mn>12</mn>
</mroot>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</mrow>
</math>
c = (1 - root(12)(1 - c_y/100)) xx 100
(1 - (1 - cy/100)^(1/12))*100
c := (1 - (1 - cy/100)^(1/12))*100;
c = (1 - (1 - cy/100)^(1/12))*100;
c = (1 - (1 - c_y/100)^(1/12)) × 100
Formula for the customers left after n months
Nₙ = N₀ × (1 − c/100)ⁿ
N_{n} = N_{0} \left(1 - \dfrac{c}{100}\right)^{n}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>N</mi><mi>n</mi></msub>
<mo>=</mo>
<msub><mi>N</mi><mn>0</mn></msub>
<msup>
<mrow><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mi>c</mi><mn>100</mn></mfrac><mo>)</mo></mrow>
<mi>n</mi>
</msup>
</mrow>
</math>
N_n = N_0 (1 - c/100)^n
n0*(1 - c/100)^n
Nn := N0*(1 - c/100)^n;
Nn = N0*(1 - c/100)^n;
N_n = N_0 (1 - c/100)^n
Formula for the max monthly churn rate (from a target average lifetime)
c = 100 ÷ L
c = \dfrac{100}{L}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>c</mi>
<mo>=</mo>
<mfrac><mn>100</mn><mi>L</mi></mfrac>
</mrow>
</math>
c = 100/L
100/l
c := 100/L;
c = 100/L;
c = 100/L
How to have ChatGPT do the calculation
You are a calculation assistant for subscription business metrics. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). There were 200 customers at the start of the month, and 10 of them canceled during the month (new customers are not included in the denominator). Find each of the following: 1. Monthly churn rate (cancellations ÷ customers at the start × 100, as a %) 2. Monthly retention rate (100 − churn rate, as a %) 3. Average lifetime in months (100 ÷ churn rate) 4. Annual churn rate ((1 − (1 − churn rate/100)^12) × 100, as a %). Also show how it differs from simply multiplying by 12 5. A separate question: with an annual churn rate of 40%, the monthly churn rate ((1 − (1 − 40/100)^(1/12)) × 100, as a %) 6. A separate question: for an average lifetime of 24 months, the max monthly churn rate (100 ÷ 24, as a %) 7. If 200 customers cancel at 5% a month, the customers left after 12 months (200 × (1 − 5/100)^12) Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Related Features
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Calculates the cost of winning one customer and compares it with LTV. Helps you decide between raising LTV by reducing churn and lowering acquisition cost
Half-Life Calculator (Initial Amount, Remaining Amount, Time, Half-Life)
Uses the same "shrinks by a fixed share each period" formula, but for how long it takes an amount of a substance, not customers, to halve. A cousin of the decay formula
Percentage Change Calculator (Increase and Decrease)
For month-over-month questions like "by what % did customers go up or down since last month?". Churn rate is the share of people who cancel, a different metric
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