Customer Lifetime Value (LTV) Calculator
Customer lifetime value from monthly ARPA, gross margin and churn, with discounted, simple (ARPA × GM ÷ churn) and fixed-horizon LTV side by side.
Customer Lifetime Value Calculator
Background.
Take a subscriber who pays $120 a month. After hosting, support and card fees you keep 80 cents of each dollar, and 3% of customers like this one cancel every month. What is that customer worth to the business? Three answers are in common use — $3,200, $2,452.20 and $1,836.79 — and all three turn up in board decks and investor memos, often with no note of which one is being quoted. They describe the same customer. The highest is 1.74 times the lowest.
The $3,200 is the SaaS rule of thumb from David Skok's SaaS metrics definitions: monthly gross profit of $96 divided by the 3% churn rate. It counts the first month's margin the day the customer signs and never discounts anything. The $2,452.20 is the discounted perpetuity from the marketing-metrics literature — Farris, Bendle, Pfeifer and Reibstein's Marketing Metrics, and Gupta, Lehmann and Stuart's 2004 paper in the Journal of Marketing Research. It values each future month at a 10% annual cost of capital and only books a month's margin if the customer is still there at the end of it. The $1,836.79 is that same discounted stream cut off after 36 months, for a company not yet in a position to promise it will be serving anyone in year ten.
Whichever form you choose, churn moves the result far more than anything else you can type. Halving it from 3% to 1.5% a month lifts the discounted value from $2,452.20 to $4,115.93, a 68% gain. Halving the discount rate from 10% to 5% lifts it only to $2,732.87, about 11%. Gupta and his co-authors found the same asymmetry when they valued Capital One, Amazon, Ameritrade, eBay and E*Trade from public data: a 1% improvement in retention had almost five times the effect on customer value of a 1% improvement in the discount rate.
Two things push a real business away from these figures, in opposite directions. Holding one churn rate constant across a mixed customer base understates its value, because the customers most likely to leave go first and the survivors are stickier — Fader and Hardie showed a single-rate valuation missing 38% of a customer base's worth. And the model holds monthly margin flat, so upsells and price rises are not counted at all. Against that, calculating on revenue instead of gross profit inflates every figure by one over your margin, which is 25% at an 80% margin.
On its own, a lifetime value decides nothing. It becomes useful when you set it against what it costs to win the customer, as an LTV:CAC ratio or a payback period.
What is customer lifetime value calculator?
Customer lifetime value (LTV or CLV) is the present value of the gross profit one customer is expected to generate between signing and leaving. Bessemer Venture Partners puts it as the gross-margin-affected value of a customer over the course of the relationship. It is a forecast, not a measurement: nothing in it has happened yet, and it rests on an assumed churn rate, an assumed margin and an assumed cost of capital. It is not a GAAP figure and no accounting standard defines it, which is why the SEC's 2020 guidance on key performance metrics asks a company that publishes one to give a clear definition and calculation, explain why the metric is useful and how management uses it, and disclose any change in how it is calculated. The closed-form version used here assumes a constant monthly margin, a constant monthly retention probability, customers who never return once they leave, and margin that arrives at the end of each month.
How to use this calculator.
- Choose one cohort before you enter anything. A base that mixes $50-a-month self-serve accounts with $5,000-a-month enterprise contracts has no meaningful average customer; value each segment separately.
- Enter that cohort's monthly ARPA — average recurring revenue per account per month, before any cost of revenue. For annual contracts, divide the annual price by twelve.
- Enter gross margin after hosting, support staff, payment processing and third-party licences. Typical B2B SaaS lands at 70–85%. Enter 100 only if you deliberately want a revenue LTV, and never set that figure against CAC.
- Enter monthly logo churn for the same cohort, measured over several months so one bad month does not dominate. If you only know annual churn, convert it with 1 − (1 − annual)^(1/12) rather than dividing by twelve.
- Set the annual discount rate to your cost of capital (0 switches discounting off) and, if you want the fixed-horizon figure, the number of months to count. The monthly rate actually used is shown with the result.
- Pick the method for the headline figure, then read the simple and discounted comparison figures beneath it: the gap between them shows how much of your LTV is a choice of convention rather than a fact about your customers.
The formula.
Everything starts from monthly gross profit per customer, m = ARPA × gross margin. Monthly churn c gives retention r = 1 − c, the probability a customer present this month is still there next month. The annual discount rate is turned into a monthly effective rate, d = (1 + annual)^(1/12) − 1, so 10% a year becomes 0.7974% a month rather than the 0.8333% you would get by dividing by twelve.
The simple method adds an undiscounted stream that starts immediately: m + mr + mr² + … = m ÷ c. The discounted method adds a stream that starts at the end of month one and discounts every term: mr/(1 + d) + mr²/(1 + d)² + … = m · r ÷ (1 + d − r). Because 1 + d − r is the same as d + c, the denominator stays positive whenever churn is above zero. The fixed-horizon method stops that discounted series after N months: m · k(1 − kᴺ) ÷ (1 − k), with k = r ÷ (1 + d).
The edges show how the three relate. With the discount rate at zero, the discounted figure sits exactly one month's margin below the simple one — $3,104 against $3,200 on the default inputs — because it waits until month end and applies the first month's churn. At 100% churn the discounted value is zero, since nobody survives to month end, while the simple form still credits one month. At very low churn the simple form runs away (0.01% monthly churn gives $960,000) whereas discounting caps the perpetuity near m ÷ d, about $12,039 here. Zero churn is not accepted: a customer who never leaves has an infinite undiscounted value.
The average lifetime shown, 1 ÷ c, is a mean. Under constant churn, departures follow a geometric pattern with a long tail, so the median customer leaves sooner: at 3% a month, half are gone by about month 23, while a third are still paying after three years.
A worked example.
Use the default inputs: $120 ARPA, 80% gross margin, 3% monthly churn, a 10% annual discount rate and the discounted method. Monthly gross profit is 120 × 0.80 = $96. Retention is 1 − 0.03 = 0.97. The monthly discount rate is 1.10^(1/12) − 1 = 0.7974%. The denominator of the perpetuity is d + c = 0.007974 + 0.03 = 0.037974, and 0.97 ÷ 0.037974 = 25.54, which is the customer's value expressed in months of gross profit. Multiplying, 96 × 25.54 gives a lifetime value of $2,452.20. Divided by the $120 ARPA, that is 20.43 months of top-line revenue. The comparison figures put the same customer at $3,200.00 on the simple formula (96 ÷ 0.03), 30% above the discounted value, and the expected lifetime at 1 ÷ 0.03 = 33.33 months. Switching to the fixed-horizon method at 36 months returns $1,836.79: three years capture about 75% of the perpetuity's value, because only a third of customers are still paying by then and their later months are discounted. If winning this customer costs $600 in sales and marketing, the discounted LTV is 4.1 times that cost, and the $96 monthly margin earns the $600 back in 6.25 months. Quoting the simple figure instead would have reported 5.3 times — a healthier-looking business built on the same customers.
Frequently asked questions.
Should lifetime value be built on revenue or on gross profit?
Which method should I quote to investors: simple, discounted or fixed horizon?
My churn figure is annual. Can I divide it by twelve?
Why does a 33-month average lifetime feel too long when most customers leave sooner?
How can a single churn rate understate what my customers are worth?
Is it wrong to multiply annual margin by the expected number of years a customer stays?
What LTV to CAC ratio justifies spending more on acquisition?
Does the result include upsells, seat expansion or price increases?
Why do textbooks give slightly different LTVs for the same inputs?
How much does the discount rate I choose actually change the answer?
References& sources.
- [1]Gupta, S., Lehmann, D. R., & Stuart, J. A. (2004). "Valuing Customers." Journal of Marketing Research, 41(1), 7–18. Equation (2) gives LV = Σ m_t r^t/(1+i)^t; footnote 3 works the example m=$100, r=80%, i=12% to $250 and shows the five-year-annuity shortcut ($360) overestimating by about 44%; Table 4 reports retention elasticities of 2.45–6.75. Author copy hosted by Columbia Business School; retrieved 2026-07-29.
- [2]MASB / Common Language Marketing Dictionary — "Customer Lifetime Value," sourced to Farris, P. W., Bendle, N. T., Pfeifer, P. E., & Reibstein, D. J., Marketing Metrics: The Definitive Guide to Measuring Marketing Performance (2nd ed., 2010) and Peppers & Rogers (1997). Gives CLV = Margin × [retention ÷ (1 + discount − retention)] and lists the six assumptions, including "first margin received at end of first period (with retention probability)." Retrieved 2026-07-29.
- [3]Fader, P. S., & Hardie, B. G. S. (2010). "Customer-Base Valuation in a Contractual Setting: The Perils of Ignoring Heterogeneity." Marketing Science, 29(1), 85–93. Shows that a valuation built on a single aggregate retention rate "underestimates the value of the customer base by 38%" on their worked example, because cohort retention rises as high-churn customers leave first. Author copy; retrieved 2026-07-29.
- [4]Skok, D. "SaaS Metrics 2.0 — Detailed Definitions," forEntrepreneurs.com. Source of the simple form, LTV = ARPA × GM% ÷ monthly churn rate, and of the LTV:CAC guideline ("this number should be higher than 3"). Undated revision, current as retrieved 2026-07-29.
- [5]Bessemer Venture Partners — D'Onofrio, M. "Scaling to $100 Million" (updated 2024 edition, PDF). Defines CLTV as "the gross margin-affected value of a customer to a business over the course of its relationship" and recommends investing in acquisition at CLTV/CAC of 3x or better, noting customers are unprofitable below 1x. Retrieved 2026-07-29.
- [6]U.S. Securities and Exchange Commission — "Commission Guidance on Management's Discussion and Analysis of Financial Condition and Results of Operations," Release Nos. 33-10751; 34-88094; FR-87, issued 30 January 2020. Requires a company disclosing a metric to give a clear definition and calculation, the reasons it is useful, how management uses it, and any change in the method of calculation. Federal Register text via GovInfo; retrieved 2026-07-29.
How this page was produced
- Published by
- Quanta Calculator
- Overseen by
- Daniel, Quanta Calculator Researcher
- Primary sources
- 6 cited below
- Method
- LTV = m · r ⁄ (1 + d − r) · LTV_simple = m ⁄ c · LTV_N = m · k(1 − kᴺ) ⁄ (1 − k)
- Published
- Last verified
Built with AI assistance and verified by automated tests against the cited sources — every worked example on this page is computed by the same code that runs the calculator. How we build and check calculators.
In this category
Embed
Quanta Pro
Paid features are coming later.
- All 1560 calculators remain free
- No billing is enabled