First, under "Type of calculation", choose whether to calculate CAC, work back from a budget and target CAC to the customers you need, or work back from LTV and a target LTV:CAC ratio to the max CAC. To calculate CAC, the cost breakdown (ad spend, staff, tools) and new customers are required; LTV, monthly ARPU and gross margin are optional. Depending on what you fill in, it also calculates the paid CAC, LTV:CAC ratio and CAC payback period, and graphs cumulative gross profit against CAC.
Enter amounts as plain numbers in dollars. For % fields, enter just the number (for 40%, enter "40"). Enter costs and new customers for the same period (for example, the same month or the same quarter). If you do not know the cost breakdown, put the total in the ad spend field and it still works.
Result and graph
Choose the type of calculation on the left, enter the values and press "Calculate". The result and a graph of cumulative gross profit against CAC (the payback period) will appear here.
Table of Contents
-
What you can do on this page
-
What is this calculation used for?
-
How to Use
-
Formulas and figures
-
Formula for customer acquisition cost (blended CAC)
-
Formula for the paid CAC (from ad spend and customers from ads)
-
Formula for the LTV:CAC ratio
-
Formula for the CAC payback period
-
Formula for the new customers needed (from a budget and target CAC)
-
Formula for the max CAC (from LTV and a target LTV:CAC ratio)
-
-
Symbols and 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
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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
-
DataChef Features
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Related Features
-
NumberChef Calculators List
What you can do on this page
- Calculates customer acquisition cost (CAC) as "total sales and marketing cost (ad spend + staff + tools, creative and so on) ÷ new customers". It also gives the paid CAC: ad spend alone divided by the customers who came from ads
- Enter the LTV (customer lifetime value) to get the LTV:CAC ratio, how many times CAC the LTV is
- Enter monthly ARPU (monthly revenue per customer) and gross margin to get the number of months to earn back CAC (the CAC payback period), with a graph showing where cumulative gross profit meets CAC
- It also works backward: "the new customers you need from a budget and a target CAC" and "the most you can spend to win one customer (max CAC) from LTV and a target LTV:CAC ratio"
- 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, CAC is the blended CAC, which adds up all sales and marketing costs, not just ad spend, and divides by all new customers won in the same period (from every channel). The paid CAC, ad spend divided by new customers from ads, is calculated in a separate field. The CAC payback period is "CAC ÷ monthly gross profit per customer", a simple definition that ignores customers who cancel before payback. To find the LTV itself, use the customer lifetime value (LTV) calculator page.
What is this calculation used for?
Deciding whether to spend more or less on ads (online advertising and marketing)
With $30,000 in ad spend and 25 new customers from ads, the paid CAC is \(30000 \div 25 = 1200\) dollars. If the gross profit LTV of one customer is $3,000, the LTV:CAC ratio is \(3000 \div 1200 = 2.5\), so each customer you win still adds gross profit. But if your company aims for about 3x, it helps you decide whether to improve ad efficiency or grow LTV first.
Compare with the gross profit LTV, not the revenue LTV. With revenue, the numbers look like they work out before the cost of goods is even paid.
Seeing the efficiency of the whole business, including customers who come for free (management and business planning)
Divide the same month's total cost of $50,000 by all 50 new customers, including those from referrals and search, and the blended CAC is \(50000 \div 50 = 1000\) dollars. It is smaller than the paid CAC of $1,200 because customers from other channels (word of mouth, search, referrals) spread the cost thinner.
Use the blended CAC to see "how much we spend per customer to grow" for the whole business, and the paid CAC to decide how to split the ad budget. If you look only at the blended CAC, it is easy to miss falling ad efficiency, so track both side by side.
Planning cash flow by seeing how many months acquisition spending takes to come back (SaaS and subscriptions)
With a CAC of $1,000, a $250 monthly price and a 40% gross margin, the monthly gross profit per customer is \(250 \times 40 \div 100 = 100\) dollars, and the CAC payback period is \(1000 \div 100 = 10\) months. For those 10 months you are still earning back acquisition money you paid up front, so you need cash to cover that time.
If you win 100 customers a month, you pay $100,000 up front every month and it comes back over 10 months, so the balance waiting to be earned back grows to around $500,000 at most. The longer the payback period, the bigger this up-front amount. Even with a good LTV:CAC ratio, a business with a long payback period needs more cash on hand.
Setting a customer goal from next month's budget (marketing and sales targets)
If next month's sales and marketing budget is $60,000 and you want to keep CAC within $800, you need \(60000 \div 800 = 75\) new customers. With 74 or fewer, CAC goes above $800. "At least 75 customers if we spend the whole budget" becomes the team's goal.
If instead the goal is set first at "50 customers", the budget you can use is up to \(800 \times 50 = 40000\) dollars. Once you know this multiplication and division, you can start from either the budget or the customer goal and get the other right away.
Setting a ceiling per customer for a new business or channel (new ventures and e-commerce)
If the gross profit LTV is $3,000 and you want an LTV:CAC ratio of at least 3x, the max CAC is \(3000 \div 3 = 1000\) dollars. When you try a new ad platform or a trade show, you can draw the line: "stop if it costs more than $1,000 per customer".
LTV is a forecast, so if the lifetime or churn assumptions are optimistic, the max CAC will be too. Working out the max CAC with somewhat strict assumptions (for example, a shorter lifetime) protects you if actual acquisition costs swing.
Formulas and figures
Formula for customer acquisition cost (blended CAC)
Figure
Standard notation
(the usual math form)
\(\mathrm{CAC}\)
\(=\)
\(E\)
\(\div\)
\(N\)
In words
(symbols replaced with words)
③
\(\mathrm{CAC}\): customer acquisition cost
\(=\)
①
\(E\): total sales and marketing cost
\(\div\)
②
\(N\): new customers
The formula in words
①
Take the
\(E\): total sales and marketing cost
(ad spend + staff + tools, creative and so on),
②
divide it by the
\(N\): new customers
, and you get the
③
\(\mathrm{CAC}\): customer acquisition cost
Quick example
If in one month you spend $30,000 on ads, $15,000 on sales and marketing staff and $5,000 on tools and creative, and win 50 new customers (from all channels), the CAC is
customer acquisition cost \(\mathrm{CAC}\)
\(=\)
total cost ($50,000)
\(\div\)
new customers (50)
\(30000 + 15000 + 5000 = 50000\)
\(50000 \div 50 = 1000\)
Key idea
CAC (customer acquisition cost) is "how much it cost, on average, to win one new customer". The cost on top includes everything spent on winning new customers: not only ad spend but also the cost of sales and marketing staff, software subscriptions, landing page and banner design, agency fees and so on. The bottom is the number of new customers won in the same period, counting everyone, not only those from ads but also those from referrals, search and word of mouth. The value found this way is called the blended CAC, and when this page says just "CAC", it refers to this.
Always use the same period for the top and bottom (a month of costs with a month of new customers). Do not include costs aimed at existing customers (support and retention programs). The difference from CPA (ad spend per conversion), a similar metric, is explained after the paid CAC formula.
Formula for the paid CAC (from ad spend and customers from ads)
Standard notation
(the usual math form)
\(\mathrm{CAC_{ad}}\)
\(=\)
\(E_{ad}\)
\(\div\)
\(N_{ad}\)
In words
(symbols replaced with words)
③
\(\mathrm{CAC_{ad}}\): paid CAC
\(=\)
①
\(E_{ad}\): ad spend
\(\div\)
②
\(N_{ad}\): new customers from ads
The formula in words
①
Take only the
\(E_{ad}\): ad spend
,
②
divide it by the
\(N_{ad}\): new customers from ads
, and you get the
③
\(\mathrm{CAC_{ad}}\): paid CAC
Quick example
With $30,000 in ad spend, if 25 of the 50 new customers came from ads, the paid CAC is
paid CAC \(\mathrm{CAC_{ad}}\)
\(=\)
ad spend ($30,000)
\(\div\)
new customers from ads (25)
\(30000 \div 25 = 1200\)
Key idea
With the same month's numbers, the blended CAC is $1,000 and the paid CAC is $1,200. The paid CAC looks only at customers who would stop coming if you stopped the ads, and shows the cost per customer from ads. It is used to decide whether to spend more or less on ads. The blended CAC also counts customers who came for free (referrals, search), so it is usually smaller than the paid CAC (but its top also includes staff and tool costs, so if those are large, the blended CAC can be higher). "Our CAC is $1,000" says different things depending on the definition, so match the definitions before comparing.
The "CPA" in an ads dashboard is ad spend divided by the number of conversions (purchases, sign-ups, quote requests and so on). The differences from CAC are that one conversion is not always one customer (some people request a quote but never sign), and that the top is only ad spend. To work with CPA, use the CPC, CPM and CPA calculator or the break-even CPA calculator page.
Formula for the LTV:CAC ratio
Standard notation
(the usual math form)
\(R\)
\(=\)
\(\mathrm{LTV}\)
\(\div\)
\(\mathrm{CAC}\)
In words
(symbols replaced with words)
③
\(R\): LTV:CAC ratio (x)
\(=\)
①
\(\mathrm{LTV}\): customer lifetime value
\(\div\)
②
\(\mathrm{CAC}\): customer acquisition cost
The formula in words
①
Take the
\(\mathrm{LTV}\): customer lifetime value
②
divide it by the
\(\mathrm{CAC}\): customer acquisition cost
, and you get the
③
\(R\): LTV:CAC ratio (x)
Quick example
If the gross profit LTV of one customer is $3,000 and the CAC is $1,000, the LTV:CAC ratio is
LTV:CAC ratio \(R\)
\(=\)
LTV ($3,000)
\(\div\)
CAC ($1,000)
\(3000 \div 1000 = 3\)
Key idea
The LTV:CAC ratio is "how many times the cost of winning a customer is the value that customer brings". At 1x you break even; below 1x, every customer you win loses money. In SaaS and subscriptions, "about 3x" (often written 3:1) is a common benchmark, but it is a rule of thumb, not a rule. The right ratio depends on how high your gross margin is, how much cash you have, and how many years customers stay.
Two cautions when comparing. First, use the LTV on a gross profit basis (after the cost of goods), not on a revenue basis; a revenue LTV makes the ratio look larger than it is. Second, LTV is a forecast while CAC is money already spent, so if the LTV assumptions (lifetime or churn rate) are optimistic, so is the ratio. Even with the same ratio, if the CAC payback period below is long, watch your cash flow during that time.
Formula for the CAC payback period
Figure
Standard notation
(the usual math form)
\(T\)
\(=\)
\(\mathrm{CAC}\)
\(\div\)
\(g\)
In words
(symbols replaced with words)
③
\(T\): CAC payback period (months)
\(=\)
①
\(\mathrm{CAC}\): customer acquisition cost
\(\div\)
②
\(g\): monthly gross profit per customer
The formula in words
①
Take the
\(\mathrm{CAC}\): customer acquisition cost
②
divide it by the
\(g\): monthly gross profit per customer
(= monthly ARPU × gross margin ÷ 100), and you get the
③
\(T\): CAC payback period (months)
Quick example
With a CAC of $1,000, monthly revenue per customer (monthly ARPU) of $250 and a gross margin of 40%, the CAC payback period is
CAC payback period \(T\) (months)
\(=\)
CAC ($1,000)
\(\div\)
monthly gross profit ($250 × 40% = $100)
\(250 \times 40 \div 100 = 100\)
\(1000 \div 100 = 10\)
Key idea
The CAC payback period is "how many months of the gross profit a customer brings each month it takes to earn back what you spent to win them". As the figure shows, it is the month when the line of cumulative gross profit, stacked up month by month, reaches the height of CAC. The standard is to divide by monthly gross profit (monthly ARPU × gross margin). Dividing by revenue without the gross margin makes payback look faster by the amount of the cost of goods (when the gross margin is blank, this calculator shows in the result that it used a revenue basis).
This is a simple definition that assumes "no one cancels before payback" and "monthly gross profit stays the same". In reality some customers cancel along the way, so if the payback period is longer than the average lifetime in months (100 ÷ monthly churn rate (%); at 5% monthly churn, \(100 \div 5 = 20\) months), the average customer never pays back. The shorter the payback, the sooner the money spent on acquisition comes back to fund the next customers, so for cash flow it is as important as the LTV:CAC ratio. For the payback of investments such as equipment, see the payback period calculator page.
Formula for the new customers needed (from a budget and target CAC)
Standard notation
(the usual math form)
\(N\)
\(=\)
\(B\)
\(\div\)
\(\mathrm{CAC_{t}}\)
In words
(symbols replaced with words)
③
\(N\): new customers needed
\(=\)
①
\(B\): budget
\(\div\)
②
\(\mathrm{CAC_{t}}\): target CAC
The formula in words
①
Take the
\(B\): budget
②
divide it by the
\(\mathrm{CAC_{t}}\): target CAC
, and you get the
③
\(N\): new customers needed
(round up if it does not divide evenly)
Quick example
If next month's sales and marketing budget is $60,000 and you want to keep CAC within $800, the new customers you need are
new customers needed \(N\)
\(=\)
budget ($60,000)
\(\div\)
target CAC ($800)
\(60000 \div 800 = 75\)
Key idea
This is the first formula, \(\mathrm{CAC} = E \div N\), rearranged to solve for the number of customers \(N\). Assuming you spend the whole budget, it is the floor: "if you win fewer customers than this, CAC goes over the target". If it does not divide evenly, round up (for example, \(60000 \div 700 \approx 85.7\) calls for 86 customers; with 85, CAC is \(60000 \div 85 \approx 706\) dollars, over the target).
If instead the customer goal comes first and you want to know how much budget you can use, it is \(B = \mathrm{CAC_{t}} \times N\) (for example, 50 customers × $800 = up to $40,000). The calculator on this page solves for the number of customers, but the multiplication gives the budget right away.
Formula for the max CAC (from LTV and a target LTV:CAC ratio)
Standard notation
(the usual math form)
\(\mathrm{CAC_{max}}\)
\(=\)
\(\mathrm{LTV}\)
\(\div\)
\(R_{t}\)
In words
(symbols replaced with words)
③
\(\mathrm{CAC_{max}}\): max CAC
\(=\)
①
\(\mathrm{LTV}\): customer lifetime value
\(\div\)
②
\(R_{t}\): target LTV:CAC ratio (x)
The formula in words
①
Take the
\(\mathrm{LTV}\): customer lifetime value
②
divide it by the
\(R_{t}\): target LTV:CAC ratio (x)
, and you get the
③
\(\mathrm{CAC_{max}}\): max CAC
Quick example
If the gross profit LTV is $3,000 and you want an LTV:CAC ratio of at least 3x, the max CAC (the most you can spend to win one customer) is
max CAC \(\mathrm{CAC_{max}}\)
\(=\)
LTV ($3,000)
\(\div\)
target LTV:CAC ratio (3x)
\(3000 \div 3 = 1000\)
Key idea
This is the third formula, \(R = \mathrm{LTV} \div \mathrm{CAC}\), rearranged to solve for CAC. It is the ceiling: "you can spend up to one third of LTV to win one customer". The answer, $1,000, is the dividing line: "with a CAC of exactly $1,000, you just reach the 3x target", so in practice keep CAC below it. With a target ratio of 1x, the max CAC equals the LTV itself (acquisition cost and lifetime gross profit break even).
Once the max CAC is set, budget ÷ max CAC tells you "the minimum number of customers to win with that budget" (this calculator does it at the same time if you enter a budget). To set a ceiling on ad spend per conversion (target CPA) from order value and gross margin, use the break-even CPA calculator page.
CAC is "total sales and marketing cost ÷ new customers"; ad spend alone divided by customers from ads is kept separate as the paid CAC. Divide LTV by CAC for the LTV:CAC ratio, and divide CAC by the monthly gross profit per customer for the CAC payback period (in months). Rearrange the formulas, and you can work back from a budget and target CAC to the customers you need, or from LTV and a target ratio to the max CAC.
Symbols and terms
Symbols
| \(\mathrm{CAC}\) | C-A-C (or "cack") | Customer acquisition cost. The average cost of winning one new customer. On this page it is the blended CAC: total cost divided by all new customers. |
| \(E\) | ee | Total sales and marketing cost, from the first letter of "expense". Everything spent on winning new customers added up: ad spend, staff, tools, creative and so on. |
| \(N\) | en | New customers, from the first letter of "number". The customers who signed up or bought for the first time in the same period as the costs, counting everyone, whether from ads or not. In the reverse formula, it is the number of customers needed. |
| \(\mathrm{CAC_{ad}}\) | C-A-C sub ad | Paid CAC. The subscript ad is short for "advertising", added on this page to tell it apart. Ad spend \(E_{ad}\) divided by new customers from ads \(N_{ad}\). |
| \(E_{ad}\) | E sub ad | Ad spend. Only the part of the cost \(E\) that went to running ads. |
| \(N_{ad}\) | N sub ad | New customers from ads. How many of the new customers \(N\) came by clicking an ad. |
| \(\mathrm{LTV}\) | L-T-V | Customer lifetime value. The total value one customer brings while they stay with you. To compare with CAC, the standard is to use the LTV on a gross profit basis (after the cost of goods). |
| \(R\) | ar | LTV:CAC ratio, from the first letter of "ratio". How many times CAC the LTV is. \(R_{t}\), with a subscript, is the target ratio. |
| \(T\) | tee | CAC payback period (months), from the first letter of "time". The number of months of gross profit it takes to earn back the cost of winning a customer. |
| \(g\) | gee | Monthly gross profit per customer, from the first letter of "gross profit". Monthly ARPU times the gross margin, divided by 100. Without a gross margin, it is the monthly ARPU itself (revenue basis). |
| \(B\) | bee | Budget, from the first letter of "budget". The total sales and marketing cost you plan to spend in the period. |
| \(\mathrm{CAC_{t}}\) | C-A-C sub t | Target CAC. The subscript t is the first letter of "target": the most you have decided to spend to win one customer. |
| \(\mathrm{CAC_{max}}\) | C-A-C sub max | Max CAC. The subscript max is short for "maximum": the most you can spend to win one customer, found by dividing LTV by the target ratio. |
Terms
| customer acquisition cost (CAC) | The average cost of winning one new customer. Divide total sales and marketing cost by the new customers in the same period. It is like the price you paid to bring in one customer; comparing it with LTV (the value one customer brings) tells you whether the acquisition cost is worth it. |
| blended CAC | CAC with total cost divided by all new customers (including those from referrals, search and word of mouth). Because some customers come for free, it is usually smaller than the paid CAC. Used to see the efficiency of the whole business. |
| paid CAC | CAC with only ad spend divided by new customers from ads. Because it leaves out customers who come for free, it is usually larger than the blended CAC. Used to decide how much to spend on ads. |
| CPA (cost per acquisition) | Short for cost per acquisition (or cost per action). Ad spend divided by the number of conversions (purchases, sign-ups, quote requests and so on), shown in ads dashboards. It differs from CAC in two ways - the top is only ad spend, and the bottom is the number of conversions, which is not always the number of customers (some people request a quote but never sign). |
| LTV:CAC ratio | LTV divided by CAC, the best-known measure of profit per customer. Looking at profit per customer (per unit) this way is called unit economics. Below 1x, every customer you win loses money. About 3x is a common SaaS benchmark, but the right value depends on the industry and how much cash you have. |
| CAC payback period | The number of months it takes for the gross profit a customer brings each month to earn back what you spent to win them (CAC). Found with CAC ÷ monthly gross profit per customer. The shorter it is, the sooner the money comes back to fund the next customers. It is a simple definition that ignores cancellations before payback, so if it is longer than the average lifetime, the average customer never pays back. |
| monthly ARPU | Short for average revenue per user. The average revenue from one customer per month, found with "that month's revenue ÷ that month's customers". For the payback period, multiply it by the gross margin to get the monthly gross profit first. |
| gross margin | Gross profit (revenue − cost of goods) as a percentage of revenue. If $250 of revenue has $150 of cost of goods, the gross profit is $100 and the gross margin is 40%. See the profit margin calculator page for details. |
| customer lifetime value (LTV) | The total value one customer brings from their first purchase until they leave. For a store it is "order value × purchase frequency × lifespan"; for a subscription it is "ARPU × gross margin ÷ churn rate". To compare with CAC, use the gross profit basis. See the customer lifetime value (LTV) calculator page for how to find it. |
| rounding up | When a value has a decimal part, moving it up to the next whole number. If the customers needed come out uneven, such as \(85.7\), 85 customers would put CAC over the target, so round up to 86. |
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) |
|
| Unit rates and averages (Grade 6) |
|
| Division and rounding up (Grades 4–5) |
|
| Variables and rearranging equations (Grades 7–8) |
|
| Graphs of proportional relationships (Grade 7) |
|
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 customer acquisition cost (blended CAC)
| Ad spend ($) | 30000 |
| Sales and marketing staff ($) | 15000 |
| Tools, creative and other ($) | 5000 |
| New customers N | 50 |
| Total cost E ($) | =B1+B2+B3 |
| CAC (blended, $) | =B5/B4 |
Table to find the paid CAC
| Ad spend Ead ($) | 30000 |
| New customers from ads Nad | 25 |
| Paid CAC ($) | =B1/B2 |
Table to find the LTV:CAC ratio
| LTV (gross profit basis, $) | 3000 |
| CAC ($) | 1000 |
| LTV:CAC ratio (x) | =B1/B2 |
Table to find the CAC payback period
| CAC ($) | 1000 |
| Monthly ARPU A ($) | 250 |
| Gross margin M (%) | 40 |
| Monthly gross profit per customer g ($) | =B2*B3/100 |
| CAC payback period T (months) | =B1/B4 |
Table to find the new customers needed (from a budget and target CAC)
| Budget B ($) | 60000 |
| Target CAC ($) | 800 |
| New customers needed (exact) | =B1/B2 |
| New customers needed (rounded up) | =ROUNDUP(B1/B2,0) |
Table to find the max CAC (from LTV and a target LTV:CAC ratio)
| LTV (gross profit basis, $) | 3000 |
| Target LTV:CAC ratio Rt (x) | 3 |
| Max CAC ($) | =B1/B2 |
After pasting, the upper rows of column B are your inputs and the lower rows are calculated automatically.
For example, in the first table B5 shows 50000 (total cost) and B6 shows 1000 (CAC $1,000); B3 of the second shows 1200; B3 of the third shows 3 (3x); in the fourth B4 shows 100 and B5 shows 10 (10 months); B3 and B4 of the fifth show 75 (75 customers); and B3 of the sixth shows 1000 (max CAC $1,000).
ROUNDUP in the fifth table is a function that rounds up the decimal part, turning an uneven result such as 85.7 customers into 86. Just replace the inputs with your own numbers.
For example, in the first table B5 shows 50000 (total cost) and B6 shows 1000 (CAC $1,000); B3 of the second shows 1200; B3 of the third shows 3 (3x); in the fourth B4 shows 100 and B5 shows 10 (10 months); B3 and B4 of the fifth show 75 (75 customers); and B3 of the sixth shows 1000 (max CAC $1,000).
ROUNDUP in the fifth table is a function that rounds up the decimal part, turning an uneven result such as 85.7 customers into 86. Just replace the inputs with your own numbers.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find customer acquisition cost (blended CAC)
| Ad spend ($) | 30000 |
| Sales and marketing staff ($) | 15000 |
| Tools, creative and other ($) | 5000 |
| New customers N | 50 |
| Total cost E ($) | =B1+B2+B3 |
| CAC (blended, $) | =B5/B4 |
Table to find the paid CAC
| Ad spend Ead ($) | 30000 |
| New customers from ads Nad | 25 |
| Paid CAC ($) | =B1/B2 |
Table to find the LTV:CAC ratio
| LTV (gross profit basis, $) | 3000 |
| CAC ($) | 1000 |
| LTV:CAC ratio (x) | =B1/B2 |
Table to find the CAC payback period
| CAC ($) | 1000 |
| Monthly ARPU A ($) | 250 |
| Gross margin M (%) | 40 |
| Monthly gross profit per customer g ($) | =B2*B3/100 |
| CAC payback period T (months) | =B1/B4 |
Table to find the new customers needed (from a budget and target CAC)
| Budget B ($) | 60000 |
| Target CAC ($) | 800 |
| New customers needed (exact) | =B1/B2 |
| New customers needed (rounded up) | =ROUNDUP(B1/B2,0) |
Table to find the max CAC (from LTV and a target LTV:CAC ratio)
| LTV (gross profit basis, $) | 3000 |
| Target LTV:CAC ratio Rt (x) | 3 |
| Max CAC ($) | =B1/B2 |
The same formulas as in Excel (including ROUNDUP) 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
import math
# CAC (blended CAC): total cost ÷ new customers
ad_cost = 30000 # ad spend ($)
labor_cost = 15000 # sales and marketing staff ($)
tool_cost = 5000 # tools, creative and other ($)
new_customers = 50 # new customers (from all channels)
total_cost = ad_cost + labor_cost + tool_cost
cac = total_cost / new_customers
print(f"Total cost: ${total_cost}")
print(f"CAC (blended CAC): ${cac}")
# Paid CAC: ad spend ÷ new customers from ads
ad_customers = 25
paid_cac = ad_cost / ad_customers
print(f"Paid CAC: ${paid_cac}")
# LTV:CAC ratio: LTV (gross profit basis) ÷ CAC
ltv = 3000
ltv_cac_ratio = ltv / cac
print(f"LTV:CAC ratio: {ltv_cac_ratio}x")
# CAC payback period: CAC ÷ monthly gross profit (= monthly ARPU × gross margin ÷ 100)
arpu = 250 # monthly ARPU ($)
gross_margin = 40 # gross margin (%)
monthly_gross = arpu * gross_margin / 100
payback_months = cac / monthly_gross
print(f"Monthly gross profit per customer: ${monthly_gross}")
print(f"CAC payback period: {payback_months} months")
# Work back: new customers needed from a budget and target CAC (rounded up)
budget = 60000
target_cac = 800
required_customers = math.ceil(budget / target_cac)
print(f"New customers needed: {required_customers}")
# Work back: max CAC from LTV and a target LTV:CAC ratio
target_ratio = 3
max_cac = ltv / target_ratio
print(f"Max CAC: ${max_cac}")
Runs with the standard library only. In this example, the total cost is $50000, the CAC is $1000.0, the paid CAC is $1200.0, the LTV:CAC ratio is 3.0x, the monthly gross profit is $100.0, the CAC payback period is 10.0 months, the new customers needed are 75, and the max CAC is $1000.0. math.ceil is a function that rounds up the decimal part. Change the costs, customers, LTV and so on at the top and run it.
How to write it in LaTeX and other math languages (copy and paste)
Formula for customer acquisition cost (blended CAC)
CAC = E ÷ N
\mathrm{CAC} = \dfrac{E}{N}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>CAC</mi>
<mo>=</mo>
<mfrac><mi>E</mi><mi>N</mi></mfrac>
</mrow>
</math>
CAC = E/N
expense/newCustomers
CAC := E/N;
CAC = E/N;
CAC = E/N
Formula for the paid CAC (from ad spend and customers from ads)
CACad = Ead ÷ Nad
\mathrm{CAC_{ad}} = \dfrac{E_{ad}}{N_{ad}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>CAC</mi><mi>ad</mi></msub>
<mo>=</mo>
<mfrac>
<msub><mi>E</mi><mi>ad</mi></msub>
<msub><mi>N</mi><mi>ad</mi></msub>
</mfrac>
</mrow>
</math>
CAC_(ad) = E_(ad)/N_(ad)
adCost/adCustomers
CACad := Ead/Nad;
CACad = Ead/Nad;
CAC_ad = E_ad/N_ad
Formula for the LTV:CAC ratio
R = LTV ÷ CAC
R = \dfrac{\mathrm{LTV}}{\mathrm{CAC}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac><mi>LTV</mi><mi>CAC</mi></mfrac>
</mrow>
</math>
R = LTV/CAC
ltv/cac
R := LTV/CAC;
R = LTV/CAC;
R = LTV/CAC
Formula for the CAC payback period
T = CAC ÷ g
T = \dfrac{\mathrm{CAC}}{g}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi>
<mo>=</mo>
<mfrac><mi>CAC</mi><mi>g</mi></mfrac>
</mrow>
</math>
T = CAC/g
cac/monthlyGross
T := CAC/g;
T = CAC/g;
T = CAC/g
Formula for the new customers needed (from a budget and target CAC)
N = B ÷ CACt
N = \dfrac{B}{\mathrm{CAC_{t}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mi>B</mi>
<msub><mi>CAC</mi><mi>t</mi></msub>
</mfrac>
</mrow>
</math>
N = B/CAC_t
budget/targetCac
N := B/CACt;
N = B/CACt;
N = B/CAC_t
Formula for the max CAC (from LTV and a target LTV:CAC ratio)
CACmax = LTV ÷ Rt
\mathrm{CAC_{max}} = \dfrac{\mathrm{LTV}}{R_{t}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>CAC</mi><mi>max</mi></msub>
<mo>=</mo>
<mfrac>
<mi>LTV</mi>
<msub><mi>R</mi><mi>t</mi></msub>
</mfrac>
</mrow>
</math>
CAC_(max) = LTV/R_t
ltv/targetRatio
CACmax := LTV/Rt;
CACmax = LTV/Rt;
CAC_max = LTV/R_t
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). In one month, a company spent $30,000 on ads, $15,000 on sales and marketing staff and $5,000 on tools and creative, and won 50 new customers. 25 of them came from ads. Find each of the following: 1. Blended CAC (total cost ÷ new customers) 2. Paid CAC (ad spend ÷ new customers from ads) 3. The LTV:CAC ratio when the gross profit LTV of one customer is $3,000 (LTV ÷ blended CAC) 4. The CAC payback period with a monthly ARPU of $250 and a 40% gross margin (blended CAC ÷ (monthly ARPU × gross margin ÷ 100)) 5. The new customers needed if next month's budget is $60,000 and CAC must stay within $800 (budget ÷ target CAC, rounded up if it does not divide evenly) 6. The max CAC for an LTV:CAC ratio of at least 3x (LTV ÷ 3) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
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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