Cohort LTV Calculator | Retention Curves, Revenue Waterfall & Power-Law Fit
Analyze customer cohort retention and lifetime value with up to 12 monthly cohorts. Input cohort sizes and period-by-period retention, fit power-law decay curves, and visualize a cumulative revenue waterfall. Compare LTV at 1, 3, 6, and 12 months across cohorts.
Cohort Inputs
| Cohort Name | Initial Size | Rev/User M1 ($) | Ret M1 (%) | Ret M2 (%) | Ret M3 (%) | Ret M6 (%) | Ret M12 (%) |
|---|---|---|---|---|---|---|---|
LTV Comparison Table
| Cohort | Size | M1 LTV | M3 LTV | M6 LTV | M12 LTV | M24 LTV | Ret @ M6 | Curve |
|---|---|---|---|---|---|---|---|---|
| Jan 2024 | 1,000 | $45.0K | $102.2K | $156.0K | $226.6K | $317.6K | 34.8% | R(t)=113.9×t^(-0.66) |
| Apr 2024 | 1,200 | $62.4K | $138.7K | $215.9K | $324.1K ★ | $473.4K | 36.8% | R(t)=100.1×t^(-0.56) |
| Jul 2024 | 800 | $48.8K | $114.7K | $181.8K | $276.4K | $407.6K | 41.0% | R(t)=109.8×t^(-0.55) |
Retention Curves (24-month projection)
Revenue Waterfall (Monthly by Cohort)
What Is the Cohort LTV Calculator | Retention Curves, Revenue Waterfall & Power-Law Fit?
Cohort analysis groups customers by acquisition period and tracks their behavior over time. Unlike aggregate metrics, cohorts reveal whether retention is improving or declining across successive acquisition waves — the single most important leading indicator of sustainable growth. A business where each new cohort retains better than the last is building compounding value; one where cohorts are degrading has a structural problem.
- ▸Power-law curve fitting: Enter retention data at months 1, 2, 3, 6, and 12. The calculator fits R(t) = a × t^(−b) and extrapolates to 24 months, so you can estimate LTV well beyond your observation window.
- ▸Multi-cohort comparison: Enter up to 6 cohorts side by side. The LTV table highlights the best-performing cohort in green and the worst in a muted tone.
- ▸Revenue waterfall: See how each cohort's monthly revenue contribution stacks at months 1, 3, 6, 12, 18, and 24, revealing the revenue mix as older cohorts age.
- ▸Retention curve visualization: SVG-based curves show the shape of each cohort's retention decay over 24 months.
Formula
Cohort LTV analysis uses historical retention data to fit a mathematical decay curve, then extrapolates future revenue per cohort. The power-law model R(t) = a × t^(−b) is the industry standard for subscription and SaaS retention because it captures the characteristic "fast early drop, slow long-term plateau" pattern.
R(t) = a × t^(−b) b = −log(R₂/R₁) / log(t₂/t₁) a = R₁ × t₁^b
Fit from any two retention data points. b is the decay exponent — higher b = faster churn. a ≈ month-1 retention (normalized to 100).
LTV(N) = Size × RevM1 × Σ(t=1 to N) R(t)/100 R(1) = 100% by definition
Summing retention at each month gives expected user-months. Multiply by revenue per user per month to get total cohort revenue.
Revenue(t) = Size × R(t)/100 × RevM1
At any given month, remaining active users × revenue per user. Aggregated across cohorts gives total monthly recurring revenue.
LTV ratio = Best cohort M12 LTV / Worst cohort M12 LTV
A ratio >2× between cohorts signals meaningful differences in product-market fit or acquisition channel quality worth investigating.
How to Use
- 1
Pull cohort retention data from your analytics platform (Mixpanel, Amplitude, or your own SQL query).
- 2
Organize by acquisition period (monthly or quarterly).
- 3
Enter cohort name, initial size, and first-month ARPU (average revenue per user).
- 4
Enter retention percentages at months 2, 3, 6, and 12 — retention is cumulative from month 1, not month-over-month.
- 5
Review the fitted power-law curve equation R(t) = a × t^(-b) — the b exponent tells you the decay rate.
- 6
Check the LTV comparison table: find the best-performing cohort (highlighted in green) and investigate what made that acquisition period different.
- 7
Use the 24-month LTV to set your customer acquisition cost (CAC) ceiling: CAC should be below M24 LTV × gross margin.
- 8
Review the revenue waterfall to see how much of current MRR comes from each historical cohort.
- 1
Name each cohort
Use the acquisition month/quarter. Clear naming helps compare seasonal or channel-specific cohorts.
- 2
Enter initial cohort size
The number of customers acquired in that period. This is the "100%" denominator for retention calculations.
- 3
Enter revenue per user in month 1
Average monthly revenue per customer in their first month. If you have expansion revenue, use an average across months instead.
- 4
Fill in retention percentages
Enter retention at months 2, 3, 6, and 12 as percentages of the original cohort (not previous month). Month 1 is always 100%.
- 5
Review the power-law curve equation
The Curve column in the results table shows R(t) = a × t^(−b). A lower b value means slower decay and better long-term retention.
- 6
Compare LTV at key milestones
Use the M12 LTV column as the primary comparison point. The highlighted best performer shows which acquisition channel or time period to double down on.
Example Calculation
Example | Three SaaS cohorts with different retention profiles
The Jul 2024 cohort costs more per user to acquire but delivers better LTV. This justifies a higher CAC ceiling for the channel that sourced that cohort.
Understanding Cohort LTV | Retention Curves, Revenue Waterfall & Power-Law Fit
Retention Benchmarks by Business Model
| Business Type | M3 Retention | M6 Retention | M12 Retention | Typical b exponent |
|---|---|---|---|---|
| Enterprise SaaS | 85–95% | 75–88% | 65–82% | 0.15–0.25 |
| SMB SaaS | 65–80% | 52–70% | 40–60% | 0.25–0.40 |
| Consumer subscription | 40–60% | 28–45% | 18–32% | 0.40–0.65 |
| Mobile gaming | 20–35% | 12–22% | 7–15% | 0.65–0.90 |
| E-commerce (repeat purchase) | 30–50% | 22–38% | 15–28% | 0.40–0.60 |
| Media / news | 50–70% | 38–58% | 28–45% | 0.30–0.50 |
Reading the Revenue Waterfall
The revenue waterfall shows how total monthly cohort revenue evolves over time. In a healthy growing business, the revenue at month 24 should be higher than month 1 because new cohorts are added faster than old ones decay. A business where month 24 revenue is lower than month 6 is losing ground — the decay rate of existing cohorts exceeds the acquisition rate of new ones.
- ▸Rising waterfall: Each bar is taller than the last. New cohort additions outpace retention losses. Healthy growth trajectory.
- ▸Flat waterfall: Monthly revenue stays constant. You are running to stand still — new customers exactly replace churned ones. Not a crisis but growth is stalled.
- ▸Falling waterfall: Each bar is shorter. Churn exceeds new customer acquisition. Requires immediate attention to either reduce churn or accelerate acquisition.
- ▸Cohort dominance shift: Later cohorts represent an increasing share of each bar. Good sign if new cohorts have better unit economics; a concern if early cohorts were unusually strong and the business is regressing.
Frequently Asked Questions
Why use a power-law model for retention rather than exponential decay?
Exponential decay (R(t) = e^(−λt)) assumes a constant churn probability at every period, which leads to unrealistically low long-term retention predictions. Empirically, subscriber churn is highest in early months and then slows as the churnable population shrinks. The power-law model R(t) = a × t^(−b) captures this pattern: fast initial decay that flattens over time, fitting observed SaaS and subscription data far better than exponential models.
What is a healthy retention curve for SaaS?
For B2B SaaS, healthy retention looks like: M3 ≥ 75%, M6 ≥ 60%, M12 ≥ 45%. Consumer subscription apps typically see: M3 40–60%, M6 25–40%, M12 15–25%. If your M12 retention exceeds your M3 by less than a 30% relative drop, you have a strong "flattening" curve indicating a loyal core. If M12 retention is below 50% of M3, churn is still accelerating and product-market fit may be weak.
How should I use LTV to set my CAC target?
The industry-standard LTV:CAC ratio target is 3:1 to 5:1. At 3:1, you recover acquisition cost in about 12–16 months. At 5:1, you have significant headroom for investment. Adjust by gross margin: if your LTV is $1,200 and gross margin is 70%, the LTV in profit terms is $840 — your CAC should be below $280 (3:1) to $168 (5:1). Use your M24 LTV, not M12, for companies with slow revenue build-up.
What does a high b exponent mean?
In R(t) = a × t^(−b), b is the decay rate. A higher b means faster churn — retention drops steeply in the early months. A b of 0.2–0.3 indicates stable, slowly-decaying retention typical of high-value B2B products. A b of 0.5–0.8 is common for consumer apps with lots of casual users. B values above 1.0 suggest severe early-period churn that may indicate onboarding or product-fit issues.
Can I use this calculator for e-commerce cohorts?
Yes, with adjustments. For e-commerce, "retention at month N" means the percentage of customers who made at least one repeat purchase by month N. ARPU becomes average monthly revenue per active customer. The power-law model still applies since repeat purchase frequency declines over time in a similar pattern. You may want to use a shorter time horizon (12 months) and lower retention figures than subscription businesses.
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