Customer Lifetime Value (LTV) Calculator for E-Commerce and Subscriptions

First, under "Type of calculation", choose store/e-commerce (customers buy again and again) or subscription/SaaS (monthly billing), and whether to calculate LTV or work back from a target LTV. Fill in the fields shown and press "Calculate" to get the LTV, average lifetime and more, with a graph of lifetime against cumulative value.

Type of calculation

Average order value ($)

Purchase frequency (per year)

Customer lifespan (years)

ARPU (monthly revenue per customer, $)

Monthly churn rate (%)

Gross margin (%, optional)

Target LTV ($)

Enter amounts as plain numbers in dollars. For % fields, enter just the number (for 5%, enter "5"). Gross margin is optional. If blank, you get LTV on a revenue basis only; if filled in, you also get LTV on a gross profit basis. When working backward with a gross margin, the target LTV is treated as a gross profit amount.

Result and graph

Choose the type of calculation on the left, enter the values and press "Calculate". The result and a graph of cumulative value over the customer's lifetime will appear here.

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What you can do on this page
What is this calculation used for?
How to Use
Formulas and figures
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Calculates LTV (customer lifetime value) for stores and online shops as "average order value × purchase frequency (per year) × customer lifespan (years)". Enter a gross margin and you also get the LTV on a gross profit basis
Calculates LTV for subscriptions and SaaS as "ARPU (monthly) × gross margin ÷ monthly churn rate", along with the average customer lifetime in months ($100 \div$ churn rate)
It also works backward: "How many years do customers need to stay to reach my target LTV?" and "How low does my monthly churn rate need to be to hit my target LTV?"
A graph shows how the cumulative value of one customer builds up as the months go by
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, LTV is "the total value one customer brings while they stay with you", a simple total that does not discount future money to present value (no discount rate). The subscription formula is an average that assumes the monthly churn rate and monthly price stay the same. Without a gross margin you get LTV on a revenue basis; with one, you also get LTV on a gross profit basis. To find the gross margin itself, use the profit margin calculator page. Comparing LTV with customer acquisition cost (the LTV:CAC ratio) is only covered in the terms section here.

What is this calculation used for?

Deciding how much you can spend on ads (online advertising and marketing)

For a customer who spends $50 per order, 4 times a year, for 3 years on average, the revenue LTV is $50 \times 4 \times 3 = 600$ dollars, and at a 40% gross margin the gross profit LTV is $240. If ads cost $80 to win one new customer, the gross profit LTV is 3 times that, so the ads look worth continuing. LTV gives you the numbers for this kind of decision.
Compare customer acquisition cost (CAC) with the gross profit LTV, not the revenue LTV. If you compare with the $600 of revenue, the business looks profitable before the cost of goods is even paid.

Putting a value on reducing churn (SaaS and apps)

For a $30/month service with an 80% gross margin and a 5% monthly churn rate, the average lifetime is $100 \div 5 = 20$ months and the gross profit LTV is $30 \times 80 \div 5 = 480$ dollars. If a retention program brings churn down to 4%, the average lifetime becomes 25 months and the LTV $600, adding $120 of value per customer.
With 500 new customers a month, that difference is worth $60,000 of LTV every month. This calculation tells you how much staff time and budget a "cut churn by 1 point" program is worth.

Putting a number on your regulars (coffee shops, hair salons and retail)

A regular who comes in twice a month, spends $25 each visit and keeps coming for 5 years buys 24 times a year, so the LTV is $25 \times 24 \times 5 = 3000$ dollars. Each check is only $25, but over the whole relationship this is a $3,000 customer.
It gives you a price yardstick for questions like "how much can we spend per year on perks for regulars (loyalty points, birthday rewards)?" and "how much can we spend on flyers or coupons to bring in one new customer?"

Thinking about retention for a subscription box (e-commerce)

For a $40/month subscription box where 8% of subscribers cancel each month, the average lifetime is $100 \div 8 = 12.5$ months and the revenue LTV is $40 \times 12.5 = 500$ dollars. Even if you give a first-box discount of $60 per customer to win them, at a 50% gross margin the gross profit LTV is $250, so the discount pays for itself.
This calculation, though, is an average that assumes the churn rate is the same every month. In reality, many people cancel after the first box and churn settles down after that, so tracking first-month churn separately makes the estimate more accurate.

Working back from a goal to "how many years" or "how low churn must be" (business planning)

Suppose you spend $200 to win a customer and want $600 of gross profit back. At $50 per order, 4 times a year and a 40% gross margin, the gross profit per year is $50 \times 4 \times 40 \div 100 = 80$ dollars, so the lifespan needed is $600 \div 80 = 7.5$ years. If 7.5 years is too long, you know you need to raise the order value or the purchase frequency.
For a subscription at $30/month with a 40% gross margin, keeping the gross profit LTV at $240 or more requires a monthly churn rate of $30 \times 40 \div 240 = 5$% or less. In business planning, the goal comes first and you work back to the conditions.

Formulas and figures

Formula for store/e-commerce LTV (revenue basis)

Figure

Standard notation (the usual math form)

$\mathrm{LTV}$ $=$ $P$ $\times$ $F$ $\times$ $T$

In words (symbols replaced with words)

④ $\mathrm{LTV}$: customer lifetime value $=$ ① $P$: average order value $\times$ ② $F$: purchase frequency (per year) $\times$ ③ $T$: customer lifespan (years)

The formula in words

① Take the $P$: average order value ,

② multiply it by the $F$: purchase frequency (per year) to get the spending per year, then multiply that by the

③ $T$: customer lifespan (years) , and you get the

④ $\mathrm{LTV}$: customer lifetime value

Quick example

For a customer whose average order is $50, who buys 4 times a year and stays for 3 years on average, the LTV (revenue basis) is

customer lifetime value $\mathrm{LTV}$ $=$ average order value ($50) $\times$ purchase frequency (4 per year) $\times$ lifespan (3 years)

$50 \times 4 = 200$

$200 \times 3 = 600$

Key idea

LTV (customer lifetime value) is "how much one customer pays you in total for as long as they stay with you". This formula just multiplies the spending per year (order value × number of orders) by the number of years, so the order of multiplication does not change the answer. Raise any one of the three numbers and LTV grows by the same factor. The shape of the formula shows the three ways to grow LTV: raise the order value, get customers to buy more often, and keep them longer. What we found here is LTV on a revenue basis; the cost of goods has not been subtracted. To think in terms of gross profit after the cost of goods, convert it with the gross profit formula below. Future revenue is also not discounted to present value (no discount rate). For LTV over a few years, a simple undiscounted total is the usual approach. If you need a discounted value, combine this with the ideas on the compound interest calculator page.

Formula for the average customer lifetime of a subscription (from the churn rate)

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 (%) (the same as the reciprocal of $c \div 100$, the churn rate as a decimal), and you get the

③ $L$: average lifetime (months)

Quick example

For a subscription where 5% of customers cancel each month, the average lifetime per customer is

average lifetime $L$ $=$ $100$ $\div$ monthly churn rate (5%)

$100 \div 5 = 20$

Key idea

If "5% cancel every month", 100 customers lose 5 in month 1, then 5% of the remaining 95 (4.75) in month 2, and so on. They do not all disappear after 20 months. Even so, if you work out "how many months one customer stays on average", the answer is exactly $100 \div 5 = 20$ months. The reason: when something happens with a chance of $c\%$ each month, the average month in which it first happens is $100 \div c$ (the expected value of a geometric distribution). So the average lifetime is the reciprocal of the churn rate. Halve the churn rate and the average lifetime doubles; this inverse relationship is what the formula says. The churn rate is usually calculated as "customers who canceled during the month ÷ customers at the start of the month".

Formula for subscription LTV (revenue basis)

Figure

Standard notation (the usual math form)

$\mathrm{LTV}$ $=$ $A$ $\times$ $L$

In words (symbols replaced with words)

③ $\mathrm{LTV}$: customer lifetime value $=$ ① $A$: ARPU (monthly revenue per customer) $\times$ ② $L$: average lifetime (months)

The formula in words

① Take the $A$: ARPU (monthly revenue per customer) ,

② multiply it by the $L$: average lifetime (months) , and you get the

③ $\mathrm{LTV}$: customer lifetime value

Quick example

For a subscription with $30 of monthly revenue per customer and an average lifetime of 20 months (5% monthly churn), the LTV (revenue basis) is

customer lifetime value $\mathrm{LTV}$ $=$ ARPU ($30) $\times$ average lifetime (20 months)

$30 \times 20 = 600$

Key idea

"Monthly price × average lifetime in months" is the same idea as "order value × frequency × lifespan" for a store. A subscription bills once every month, so the frequency is fixed at once a month and the period becomes the average lifetime $L$. As the figure shows, the revenue from 100 customers is a row of bars that shrinks by $c\%$ every month. Add up all the bars, and you get exactly 100 customers' worth of $A \times L$ (the sum of an infinite geometric series with first term $A$ and common ratio $1 - c \div 100$: $A \div (c \div 100) = A \times 100 \div c$). Writing $\mathrm{LTV} = A \times 100 \div c$ directly, without the average lifetime, is the same formula. To think in terms of gross profit, convert it with the next formula. This formula is an average that assumes the monthly churn rate and monthly price stay the same. In reality, many customers cancel soon after signing up, and plan changes move the monthly price, so use it as a guide.

Formula to convert to LTV on a gross profit basis (from revenue-basis LTV and gross margin)

Standard notation (the usual math form)

$\mathrm{LTV_{g}}$ $=$ $\mathrm{LTV}$ $\times$ $M$ $\div$ $100$

In words (symbols replaced with words)

④ $\mathrm{LTV_{g}}$: LTV (gross profit basis) $=$ ① $\mathrm{LTV}$: LTV (revenue basis) $\times$ ② $M$: gross margin (%) $\div$ ③ $100$: percent base

The formula in words

① Take the $\mathrm{LTV}$: LTV (revenue basis)

② multiply it by the $M$: gross margin (%) ,

③ divide by the $100$: percent base to turn the percentage back into a decimal, and you get the

④ $\mathrm{LTV_{g}}$: LTV (gross profit basis)

Quick example

With an LTV of $600 on a revenue basis and a gross margin of 40%, the LTV on a gross profit basis is

gross profit LTV $\mathrm{LTV_{g}}$ $=$ revenue LTV ($600) $\times$ gross margin (40%) $\div$ $100$

$600 \times 40 \div 100 = 240$

Key idea

With a 40% gross margin, $240 of the $600 in revenue is left after the cost of goods. When you compare LTV with ad spend or customer acquisition cost (CAC), this gross profit LTV is the one to use. If you compare with the revenue LTV instead, you fall into the trap of "looking profitable" by the amount of the cost of goods. Applied to the subscription formula, it becomes $\mathrm{LTV_{g}} = A \times L \times M \div 100 = A \times M \div c$. This is the form widely used in SaaS: "ARPU × gross margin ÷ churn rate". The idea of gross margin (gross profit as a share of revenue) is explained in detail on the profit margin calculator page.

Formula for the lifespan needed for a target LTV (store/e-commerce)

Standard notation (the usual math form)

$T$ $=$ $G$ $\div$ $($ $P$ $\times$ $F$ $)$

In words (symbols replaced with words)

④ $T$: lifespan needed (years) $=$ ③ $G$: target LTV $\div$ $($ ① $P$: average order value $\times$ ② $F$: purchase frequency (per year) $)$

The formula in words

① Take the $P$: average order value ,

② multiply it by the $F$: purchase frequency (per year) to get the spending per year,

③ divide the $G$: target LTV by that spending per year, and you get the

④ $T$: lifespan needed (years)

Quick example

For a customer who spends $50 per order and buys 4 times a year, the lifespan needed to reach an LTV of $600 is

lifespan needed $T$ (years) $=$ target LTV ($600) $\div$ $($ average order value ($50) $\times$ purchase frequency (4 per year) $)$

$50 \times 4 = 200$

$600 \div 200 = 3$

Key idea

This is the first formula, $\mathrm{LTV} = P \times F \times T$, rearranged to solve for the lifespan $T$. Use it to work back from a goal to how long the relationship needs to last, for example: "I spend $200 to win a customer, so I want $600 in sales from them. How many years do they need to stay?" For a target LTV on a gross profit basis, divide by the gross profit per year (spending per year × gross margin); the calculator does this when you enter a gross margin. Multiply the answer by the purchase frequency to get the number of purchases needed (for example, 3 years × 4 per year = 12 purchases).

Formula for the max monthly churn rate for a target LTV (subscription)

Standard notation (the usual math form)

$c$ $=$ $A$ $\times$ $M$ $\div$ $G$

In words (symbols replaced with words)

④ $c$: max monthly churn rate (%) $=$ ① $A$: ARPU (monthly revenue per customer) $\times$ ② $M$: gross margin (%) $\div$ ③ $G$: target LTV

The formula in words

① Take the $A$: ARPU (monthly revenue per customer) ,

② multiply it by the $M$: gross margin (%) (use $M = 100$ for a revenue basis),

③ divide by the $G$: target LTV , and you get the

④ $c$: max monthly churn rate (%)

Quick example

For a $30/month subscription with a 40% gross margin, the highest monthly churn rate that still gives a gross profit LTV of $240 or more is

max monthly churn rate $c$ (%) $=$ ARPU ($30) $\times$ gross margin (40%) $\div$ target LTV ($240)

$30 \times 40 = 1200$

$1200 \div 240 = 5$

Key idea

This is the fourth formula, $\mathrm{LTV_{g}} = A \times M \div c$, rearranged to solve for the churn rate $c$. The answer, 5%, is the dividing line: "with a monthly churn rate of exactly 5%, you just reach the target", so in practice you need to keep churn below it. For a revenue basis, use $M = 100$: $30 \times 100 \div 600 = 5$ (with the target LTV also on a revenue basis, $600). Divide the target LTV by one month of value ($A \times M \div 100$) and you get the average lifetime needed; its reciprocal ($100 \div$ months) is the max churn rate. People often say "to raise LTV, reduce churn" because the churn rate is in the denominator of this formula. Halve the churn rate and LTV doubles.

LTV is "the total one customer pays you while they stay". For a store or online shop it is "order value × frequency × lifespan"; for a subscription it is "monthly price × average lifetime in months (= 100 ÷ churn rate)". Multiply either by the gross margin to get it on a gross profit basis. Rearrange the formulas, and you can work back from a target LTV to the lifespan needed or the max churn rate.

Symbols and terms

Symbols

$\mathrm{LTV}$	L-T-V	Customer lifetime value (lifetime value). The total value one customer brings while they stay with you. It is also written $\mathrm{CLV}$ or $\mathrm{CLTV}$, short for customer lifetime value.
$\mathrm{LTV_{g}}$	L-T-V sub g	LTV on a gross profit basis. The subscript g is the first letter of "gross margin", added on this page to tell the two apart. Found with $\mathrm{LTV_{g}} = \mathrm{LTV} \times M \div 100$.
$P$	pee	Average order value, from the first letter of "price". The average amount a customer pays per purchase (for example, if the average order is $50, $P = 50$).
$F$	ef	Purchase frequency (per year), from the first letter of "frequency". How many times one customer buys per year: $F = 4$ for 4 times a year, $F = 0.5$ for once every 2 years.
$T$	tee	Customer lifespan (years), from the first letter of "time". The average number of years customers keep buying. In the reverse formula, it is the number of years needed for the target LTV.
$A$	ay	ARPU (monthly revenue per customer). Short for average revenue per user; on this page it is a monthly amount.
$c$	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 that still reaches the target LTV.
$L$	el	Average customer lifetime in months, from the first letter of "lifetime". How many months one customer stays subscribed on average. Found with $L = 100 \div c$.
$M$	em	Gross margin (%), from the first letter of "margin". The share of revenue left after the cost of goods.
$G$	gee	Target LTV, from the first letter of "goal". The total value you want from one customer. In formulas that use the gross margin, it is treated as a gross profit amount.
$100$	one hundred	The base for percentages. Divide a percentage by 100 to get back a decimal ($40\% \div 100 = 0.4$). This conversion is also why the reciprocal of the churn rate, $100 \div c$, is the average lifetime in months.

Terms

customer lifetime value (LTV)	How much value (revenue or gross profit) one customer brings in total, from their first purchase until they leave. It is the basis for deciding "how much can we spend to win this customer?" Definitions vary (revenue or gross profit basis, and whether future amounts are discounted), so match the definitions before comparing. Some also call "LTV − CAC" the LTV (subtract the customer acquisition cost from the gross profit LTV on this page and you get that value).
revenue basis	LTV counted as total revenue. If you compare this with ad spend or customer acquisition cost, you overestimate the profit, because the cost of goods has not been subtracted.
gross profit basis	LTV counted as gross profit (revenue minus the cost of goods). Gross profit basis = revenue basis × gross margin. Use this one when you compare with ad spend or customer acquisition cost.
gross margin	Gross profit (revenue − cost of goods) as a percentage of revenue. If $100 of revenue has $60 of cost of goods, the gross profit is $40 and the gross margin is 40%. See the profit margin calculator page for details.
ARPU	Average revenue per user (customer). In subscriptions and apps it is usually per month, found with "total monthly revenue ÷ number of customers". The average over paying customers only is called ARPPU (average revenue per paying user). B2B SaaS often uses ARPA (average revenue per account) instead.
churn rate	The share of customers who cancel in a given period (one month on this page). It is usually found by dividing the customers who canceled during the period by the customers at the start (100 at the start of the month and 5 cancellations = 5%). For an annual rate, working from the share that remains after a year is more accurate than simply multiplying the monthly rate by 12 (at 5% a month, $1 - 0.95^{12} \approx 0.46$, about 46% a year, less than 12 times 5% = 60%).
average customer lifetime	How many months one customer stays subscribed on average. When customers cancel at a steady churn rate each month, the average lifetime is the reciprocal of the churn rate (100 ÷ churn rate). Also called customer lifespan.
expected value of a geometric distribution	The average number of tries until something with the same chance every time happens for the first time. With probability $p$, it is $1 \div p$. If cancellation happens with a chance of 5% each month ($p = 0.05$), customers cancel in month $1 \div 0.05 = 20$ on average. This is the basis for the average lifetime on this page.
discount rate (present value)	The rate used to convert future money into today's value, on the idea that "$100 a year from now is worth less than $100 today". A strict LTV sometimes discounts future revenue with a discount rate, but this page uses a simple undiscounted total.
customer acquisition cost (CAC)	The cost of winning one new customer (ad and sales costs ÷ customers won). The basic use is to put it next to LTV and ask "how many times CAC is LTV?" (the LTV:CAC ratio). A gross profit LTV of about 3 times CAC is often cited as a healthy benchmark.
subscription	A business where customers keep paying monthly or yearly. Video and music streaming services are subscriptions too. Monthly revenue is easy to predict, but every cancellation (churn) directly cuts revenue, so the churn rate and LTV are the most important metrics.
SaaS	Software as a service. A kind of subscription that provides software for a monthly fee. Every cancellation (churn) directly cuts revenue, so the churn rate and LTV are the most important metrics.

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.

Percents (Grades 6–7)	Knowing that a percent is found as "part ÷ whole" Being able to switch between percentages and decimals ($40\% = 0.4$, $0.05 = 5\%$) Being able to find a percentage of an amount by multiplication, as in "40% of revenue" ($600 \times 0.4 = 240$)
Unit rates (Grade 6)	Knowing that an amount "per order", "per year" or "per month" times the number of orders or the length of time gives the total (order value × orders × years)
Inverse variation (Grade 8 and Algebra 1)	Understanding a relation where doubling one quantity halves the other (halve the churn rate and the average lifetime doubles) Being able to calculate a reciprocal ($1 \div 0.05 = 20$)
Variables and rearranging equations (Grades 7–8)	Understanding a formula with letters such as $\mathrm{LTV} = P \times F \times T$, and being able to rearrange it to find another quantity, as in $T = \mathrm{LTV} \div (P \times F)$
Geometric series and expected value (Algebra 2 and statistics; you can skip this and still use the page)	Knowing that adding up numbers that shrink by a fixed ratio every month approaches "first term ÷ (1 − common ratio)" (the basis for LTV = monthly price ÷ churn rate as a decimal) Knowing that "something with the same chance $p$ every time happens on try $1 \div p$ on average" (the expected value of a geometric distribution) gives a deeper understanding of the average lifetime

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 store/e-commerce LTV (revenue basis)

Average order value P ($)	50
Purchase frequency F (per year)	4
Customer lifespan T (years)	3
LTV (revenue basis, $)	=B1B2B3

Table to find the average lifetime in months (from the churn rate)

Monthly churn rate c (%)	5
Average lifetime L (months)	=100/B1

Table to find subscription LTV (revenue basis)

ARPU A (monthly, $)	30
Average lifetime L (months)	20
LTV (revenue basis, $)	=B1*B2

Table to convert to LTV on a gross profit basis

LTV (revenue basis, $)	600
Gross margin M (%)	40
LTV (gross profit basis, $)	=B1*B2/100

Table to find the lifespan needed for a target LTV (store/e-commerce)

Target LTV G ($)	600
Average order value P ($)	50
Purchase frequency F (per year)	4
Lifespan needed T (years)	=B1/(B2*B3)

Table to find the max monthly churn rate for a target LTV (subscription)

ARPU A (monthly, $)	30
Gross margin M (%)	40
Target LTV G (gross profit, $)	240
Max monthly churn rate c (%)	=B1*B2/B3

After pasting, the upper rows of column B are your inputs and the bottom row is calculated automatically.
For example, B4 of the first table shows 600 (LTV $600), B2 of the second shows 20 (20 months on average), B3 of the third shows 600, B3 of the fourth shows 240 (gross profit basis $240), B4 of the fifth shows 3 (3 years), and B4 of the sixth shows 5 (churn rate 5%). 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 store/e-commerce LTV (revenue basis)

Average order value P ($)	50
Purchase frequency F (per year)	4
Customer lifespan T (years)	3
LTV (revenue basis, $)	=B1B2B3

Table to find the average lifetime in months (from the churn rate)

Monthly churn rate c (%)	5
Average lifetime L (months)	=100/B1

Table to find subscription LTV (revenue basis)

ARPU A (monthly, $)	30
Average lifetime L (months)	20
LTV (revenue basis, $)	=B1*B2

Table to convert to LTV on a gross profit basis

LTV (revenue basis, $)	600
Gross margin M (%)	40
LTV (gross profit basis, $)	=B1*B2/100

Table to find the lifespan needed for a target LTV (store/e-commerce)

Target LTV G ($)	600
Average order value P ($)	50
Purchase frequency F (per year)	4
Lifespan needed T (years)	=B1/(B2*B3)

Table to find the max monthly churn rate for a target LTV (subscription)

ARPU A (monthly, $)	30
Gross margin M (%)	40
Target LTV G (gross profit, $)	240
Max monthly churn rate c (%)	=B1*B2/B3

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

# Store/e-commerce: order value × frequency × lifespan
unit_price = 50       # average order value ($)
frequency = 4         # purchase frequency (per year)
years = 3             # customer lifespan (years)
gross_margin = 40     # gross margin (%)

ltv_purchase = unit_price * frequency * years          # LTV (revenue basis)
ltv_purchase_gross = ltv_purchase * gross_margin / 100  # LTV (gross profit basis)
print(f"Store LTV (revenue basis): ${ltv_purchase}")
print(f"Store LTV (gross profit basis): ${ltv_purchase_gross}")

# Subscription: ARPU × average lifetime in months (= 100 ÷ churn rate)
arpu = 30             # monthly revenue per customer ($)
churn = 5             # monthly churn rate (%)

avg_months = 100 / churn                         # average lifetime (months)
ltv_subscription = arpu * avg_months             # LTV (revenue basis)
ltv_subscription_gross = arpu * gross_margin / churn   # LTV (gross profit basis) (= ARPU × gross margin ÷ churn rate)
print(f"Average lifetime: {avg_months} months")
print(f"Subscription LTV (revenue basis): ${ltv_subscription}")
print(f"Subscription LTV (gross profit basis): ${ltv_subscription_gross}")

# Work back: lifespan needed for a target LTV (store) and max monthly churn rate (subscription)
target_ltv = 600
required_years = target_ltv / (unit_price * frequency)
print(f"Lifespan needed for a target of ${target_ltv}: {required_years} years")

target_ltv_gross = 240
max_churn = arpu * gross_margin / target_ltv_gross
print(f"Max monthly churn rate for a gross profit target of ${target_ltv_gross}: {max_churn}%")

Runs with the standard library only. In this example, the store LTV is $600 ($240.0 on a gross profit basis), the average lifetime is 20.0 months, the subscription LTV is $600.0 ($240.0 on a gross profit basis), the lifespan needed is 3.0 years, and the max monthly churn rate is 5.0%. Change the order value, frequency and years, or the ARPU and churn rate, at the top and run it.

How to write it in LaTeX and other math languages (copy and paste)

Formula for store/e-commerce LTV (revenue basis)

LTV = P × F × T

\mathrm{LTV} = P \times F \times T

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>LTV</mi>
    <mo>=</mo>
    <mi>P</mi>
    <mo>&#xD7;</mo>
    <mi>F</mi>
    <mo>&#xD7;</mo>
    <mi>T</mi>
  </mrow>
</math>

LTV = P xx F xx T

price*frequency*years

LTV := P*F*T;

LTV = P*F*T;

LTV = P × F × T

Formula for the average customer lifetime of a subscription (from the churn rate)

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/churn

L := 100/c;

L = 100/c;

L = 100/c

Formula for subscription LTV (revenue basis)

LTV = A × L

\mathrm{LTV} = A \times L

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>LTV</mi>
    <mo>=</mo>
    <mi>A</mi>
    <mo>&#xD7;</mo>
    <mi>L</mi>
  </mrow>
</math>

LTV = A xx L

arpu*avgMonths

LTV := A*L;

LTV = A*L;

LTV = A × L

Formula to convert to LTV on a gross profit basis (from revenue-basis LTV and gross margin)

LTVg = LTV × M ÷ 100

\mathrm{LTV_{g}} = \mathrm{LTV} \times \dfrac{M}{100}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>LTV</mi><mi>g</mi></msub>
    <mo>=</mo>
    <mi>LTV</mi>
    <mo>&#xD7;</mo>
    <mfrac><mi>M</mi><mn>100</mn></mfrac>
  </mrow>
</math>

LTV_g = LTV xx M/100

ltv*margin/100

LTVg := LTV*M/100;

LTVg = LTV*M/100;

LTV_g = LTV × M/100

Formula for the lifespan needed for a target LTV (store/e-commerce)

T = G ÷ (P × F)

T = \dfrac{G}{P \times F}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>T</mi>
    <mo>=</mo>
    <mfrac>
      <mi>G</mi>
      <mrow><mi>P</mi><mo>&#xD7;</mo><mi>F</mi></mrow>
    </mfrac>
  </mrow>
</math>

T = G/(P xx F)

target/(price*frequency)

T := G/(P*F);

T = G/(P*F);

T = G/(P × F)

Formula for the max monthly churn rate for a target LTV (subscription)

c = A × M ÷ G

c = \dfrac{A \times M}{G}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>c</mi>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>A</mi><mo>&#xD7;</mo><mi>M</mi></mrow>
      <mi>G</mi>
    </mfrac>
  </mrow>
</math>

c = (A xx M)/G

arpu*margin/target

c := A*M/G;

c = A*M/G;

c = (A × M)/G

How to have ChatGPT do the calculation

You are a calculation assistant for marketing 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).

Customers of an online store spend $50 per order on average, buy 4 times a year, and keep buying for 3 years on average. The gross margin is 40%.
Find each of the following:
1. LTV on a revenue basis (average order value × purchase frequency × lifespan)
2. LTV on a gross profit basis (revenue LTV × gross margin ÷ 100)
3. For a different subscription service: with $30 of monthly revenue per customer, a 5% monthly churn rate and a 40% gross margin, the average lifetime in months (100 ÷ churn rate) and the LTV on a revenue basis and a gross profit basis (ARPU × average lifetime; ARPU × gross margin ÷ churn rate)
4. For that subscription, the max monthly churn rate if I want a gross profit LTV of $300 or more (ARPU × gross margin ÷ target LTV)

Show the formulas you used and the numbers from the execution result.

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\(\mathrm{LTV}\)	L-T-V	Customer lifetime value (lifetime value). The total value one customer brings while they stay with you. It is also written \(\mathrm{CLV}\) or \(\mathrm{CLTV}\), short for customer lifetime value.
\(\mathrm{LTV_{g}}\)	L-T-V sub g	LTV on a gross profit basis. The subscript g is the first letter of "gross margin", added on this page to tell the two apart. Found with \(\mathrm{LTV_{g}} = \mathrm{LTV} \times M \div 100\).
\(P\)	pee	Average order value, from the first letter of "price". The average amount a customer pays per purchase (for example, if the average order is $50, \(P = 50\)).
\(F\)	ef	Purchase frequency (per year), from the first letter of "frequency". How many times one customer buys per year: \(F = 4\) for 4 times a year, \(F = 0.5\) for once every 2 years.
\(T\)	tee	Customer lifespan (years), from the first letter of "time". The average number of years customers keep buying. In the reverse formula, it is the number of years needed for the target LTV.
\(A\)	ay	ARPU (monthly revenue per customer). Short for average revenue per user; on this page it is a monthly amount.
\(c\)	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 that still reaches the target LTV.
\(L\)	el	Average customer lifetime in months, from the first letter of "lifetime". How many months one customer stays subscribed on average. Found with \(L = 100 \div c\).
\(M\)	em	Gross margin (%), from the first letter of "margin". The share of revenue left after the cost of goods.
\(G\)	gee	Target LTV, from the first letter of "goal". The total value you want from one customer. In formulas that use the gross margin, it is treated as a gross profit amount.
\(100\)	one hundred	The base for percentages. Divide a percentage by 100 to get back a decimal (\(40\% \div 100 = 0.4\)). This conversion is also why the reciprocal of the churn rate, \(100 \div c\), is the average lifetime in months.

Customer Lifetime Value (LTV) Calculator for E-Commerce and Subscriptions

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How to have ChatGPT do the calculation

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Finds break-even CPA from order value and gross margin, target CPA after your profit goal, and max CPC from conversion rate

Customer Acquisition Cost (CAC) Calculator with LTV:CAC Ratio and Payback Period

Calculates CAC from sales and marketing costs and new customers, and compares it with the LTV from this page for the LTV:CAC ratio and CAC payback period

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Calculates the monthly churn rate from starting customers and cancellations, with average customer lifetime and annual churn. Find the monthly churn rate for subscription LTV here

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