Cohort Analysis Calculator
Analyze user cohort retention over time. Calculate monthly retention rates, churn rates, estimated customer lifetime value (LTV), and total cohort revenue.
About this calculator
This calculator tracks a single cohort's retention across three months, computing each month's retention rate as that month's retained users divided by Initial Users, times 100 (lines 10-12). Initial Users and each month's own Retained count have closely matched effects on that month's retention rate — both are real, verified drivers, with Initial Users showing a marginally larger measured effect purely from the mild convexity of dividing by a changing denominator, not from the formula weighing it more heavily. Initial Users, however, clearly dominates Average Retention Rate, since it sits in the denominator of all three monthly retention terms at once, while each month's Retained count only affects its own single term.
Average Revenue per User has no effect at all on any retention or churn rate — it only enters Estimated LTV and Observed Cohort Revenue, both of which it dominates, since it's a flat multiplier applied to the whole cohort at once rather than to any single month's user count. Estimated LTV assumes a constant average monthly churn rate projected forward indefinitely, capped at 36 months when churn computes to 0 (line 30) — this calculator does not account for a retention curve that flattens out or declines non-linearly over a customer's lifetime, which real cohorts very often do after the first few months.
Inputs
Results
Month 1 Retention
40%
Estimated LTV
$59.76
How to Use This Calculator
- Enter the cohort size at acquisition and retention counts at each time period.
- Enter the average revenue per user (ARPU) used to estimate lifetime value.
- Review retention rate and churn rate at each period.
- Identify which cohorts show higher retention to trace back to acquisition channel or product change.
- Use the lifetime value output to set customer acquisition cost targets.
How the result changes with Initial Users (Month 0)
| Initial Users (Month 0) | Month 1 Retention | Estimated LTV |
|---|---|---|
| 500 | 80% | $87.72 |
| 750 | 53.33% | $66.86 |
| 1,500 | 26.67% | $54.02 |
| 2,500 | 16% | $50.17 |
What each input means
- Initial Users (Month 0)
- Number of users who joined in the cohort's starting month.
- Month 1 Retained
- Number of original cohort users still active in month 1.
- Month 2 Retained
- Number of original cohort users still active in month 2.
- Month 3 Retained
- Number of original cohort users still active in month 3.
- Avg Revenue per User ($)
- Average monthly revenue generated per active user (ARPU).
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersInitial Users (Month 0) = 1000, Month 1 Retained = 400, Month 2 Retained = 250, Month 3 Retained = 180 = 5 input(s) provided
- Calculate Month 1 RetentionMonth 1 Retention40 = 40
- Calculate Estimated LTVEstimated LTV59.76 = $59.76
- Calculate Month 2 RetentionMonth 2 Retention25 = 25
- Calculate Month 3 RetentionMonth 3 Retention18 = 18
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Does Initial Users really move Month 1 Retention more than Month 1 Retained does?
Only very slightly, and not because the formula favors one over the other — Month 1 Retention is simply Month 1 Retained divided by Initial Users (line 10). The tiny extra sensitivity to Initial Users comes from the mild curvature of dividing by a changing denominator, not from any difference in how the formula treats the two inputs.
Why does Initial Users have such a large effect on Average Retention Rate specifically?
Because it appears in the denominator of all three monthly retention calculations at once (lines 10-12, 24), so a change to Initial Users moves every term in the average simultaneously — whereas each month's Retained count only ever affects its own single term.
Does Average Revenue per User affect the retention or churn percentages?
No — none of the retention or churn formulas (lines 10-21) reference Average Revenue per User at all. It only feeds into Estimated LTV and Observed Cohort Revenue, where it acts as a flat multiplier on numbers built entirely from the user counts.
How does Estimated LTV handle a cohort with zero measured churn?
If the average monthly churn rate computes to exactly 0, the formula switches to a flat 36-month cap — Average Revenue per User times 36 (line 30) — rather than dividing by a zero churn rate, which would otherwise produce an undefined result.
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