CPC, CPM and CPA Calculator (Ad Cost Metrics and Budget from Target CPA)

For "From results", enter the ad spend and whichever of impressions, clicks and conversions you know. For "From targets", enter the target CPA, expected CVR and target conversions (and the expected CTR if you know it) to get the max CPC, clicks needed and budget needed.

Calculation

Ad spend ($)

Impressions

Clicks

Conversions

Target CPA ($)

Expected CVR (%)

Target conversions

Expected CTR (%, optional)

Enter amounts in dollars and rates in % (for 2%, enter "2"). CPM is the cost per 1,000 impressions, and CPA is the cost per conversion. The band widths in the figure only illustrate the flow; they are not to scale.

Result and graph

Enter your ad results (or targets) in the fields on the left and press "Calculate". The costs and rates, and a figure of the flow from impressions to clicks to conversions, 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

From ad spend, impressions, clicks and conversions (just the ones you know), get CPC (cost per click), CPM (cost per 1,000 impressions) and CPA (cost per acquisition), plus CTR (click-through rate) and CVR (conversion rate), all at once
"With a $50 target CPA and a 2% CVR, what is the most I can pay per click? What budget do I need for 20 conversions?" You can also work back from targets (max CPC, clicks needed and budget needed) on this page
The formulas that link the three costs, $\mathrm{CPA} = \mathrm{CPC} \div \mathrm{CVR}$ and $\mathrm{CPC} = \mathrm{CPM} \div 1000 \div \mathrm{CTR}$ (with CVR and CTR as decimals), are explained clearly, including why they work
One figure shows the flow from impressions to clicks to conversions, with the cost at each step
Explanations of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

The definitions on this page are CPC = ad spend ÷ clicks, CPM = ad spend ÷ impressions × 1000 (per 1,000 impressions) and CPA = ad spend ÷ conversions (acquisition = conversion). Whether an "acquisition" is a purchase, a sign-up or a request for information depends on your own definition of a conversion. Enter amounts in dollars.

What is this calculation used for?

Knowing how many customers $2,000 a month in ads brought (small businesses)

If you spend $2,000 a month on ads for an online store or a class, and get 500 clicks and 20 sign-ups, the CPC is $2000 \div 500 = 4$ dollars and the CPA is $2000 \div 20 = 100$ dollars.
If the gross profit left from one sign-up is $160, spending $100 to keep $160 means the ads are worth continuing; if the gross profit is only $80, you lose more the more you advertise. Putting CPA next to gross profit is all it takes to decide.

Setting next month's budget and bids (managing ads)

"Next month we want 30 conversions, at up to $60 each, and our CVR has been 2.5%." Then the budget needed is $60 \times 30 = 1800$ dollars, the max CPC is $60 \times 0.025 = 1.50$ dollars and the clicks needed are $30 \div 0.025 = 1200$.
People who manage ads do this every month to build a budget plan, and set their max CPC bids at $1.50 or less. If the expected CVR turns out wrong, so do the results, so it is normal to check the actual CVR mid-month and adjust the plan.

Comparing social media ads billed by CPM with pay-per-click search ads

Say a social media ad has a CPM of $8, a CTR of 0.8% and a CVR of 2%, and a search ad has a CPC of $2 and a CVR of 4%. The social ad's CPC is $8 \div 1000 \div 0.008 = 1$ dollar and its CPA is $1 \div 0.02 = 50$ dollars. The search ad's CPA is $2 \div 0.04 = 50$ dollars.
Even for ads billed in different ways, converting to CPA with the linking formulas lets you compare what one conversion costs. In this example, the search ad costs twice as much per click, yet the CPA is the same (the rates are assumptions and vary a lot by platform and product).

Measuring the cost-effectiveness of direct mail the same way

If printing and mailing 10,000 postcards costs $4,000 and brings 20 inquiries, the cost per 1,000 pieces is $4000 \div 10000 \times 1000 = 400$ dollars (the same idea as CPM) and the cost per inquiry is $4000 \div 20 = 200$ dollars (the same idea as CPA).
"Cost per 1,000" and "cost per result" work just as well outside the internet: print ads, billboards, trade shows. Put them next to your online CPA to compare where to spend your money.

Finding the cost per applicant for job ads (HR and recruiting)

If you pay a job board $2,000, the job posting is viewed 8,000 times and you get 16 applications, the cost per application is $2000 \div 16 = 125$ dollars and the cost per 1,000 views is $2000 \div 8000 \times 1000 = 250$ dollars.
In recruiting these are called cost per applicant and cost per hire, but the calculation is the same as CPA. Line up the cost per applicant of several job boards to decide where to put your budget.

Looking at sponsored video deals in CPM terms (creators)

If a company pays a creator $6,000 for one sponsored video and the video gets 500,000 views, the company's cost per 1,000 views is $6000 \div 500000 \times 1000 = 12$ dollars.
The company compares this number with the CPM of its own ads to see whether the fee is worth it, and creators can use their view counts to explain a rough basis for their rates. Views are not the same as the number of people who actually watched, so treat the number as a guide.

Formulas and figures

Formula for the cost per click (CPC)

Figure

Standard notation (the usual math form)

$\mathrm{CPC}$ $=$ $\mathrm{Cost}$ $\div$ $\mathrm{Clicks}$

In words (symbols replaced with words)

③ $\mathrm{CPC}$: cost per click $=$ ① $\mathrm{Cost}$: ad spend $\div$ ② $\mathrm{Clicks}$: clicks

The formula in words

① Divide the $\mathrm{Cost}$: ad spend

② by the $\mathrm{Clicks}$: clicks

③ and you get the $\mathrm{CPC}$: cost per click (what you paid for each click)

Quick example

If $120 in ad spend brought 40 clicks, the cost per click is

$\mathrm{CPC}$: cost per click $=$ ad spend ($120) $\div$ clicks (40)

$120 \div 40 = 3$

Key idea

CPC stands for cost per click. It is how much you paid on average each time your ad was clicked, the most basic cost measure for search ads and social media ads. The "Avg. CPC" in ad platforms such as Google Ads uses the same definition (cost ÷ clicks). The "max CPC" bid you set is a limit on how much you are willing to pay for one click, which is different from the CPC, the average you actually paid.

Formula for the cost per 1,000 impressions (CPM)

Figure

Standard notation (the usual math form)

$\mathrm{CPM}$ $=$ $\mathrm{Cost}$ $\div$ $\mathrm{Imp}$ $\times$ $1000$

In words (symbols replaced with words)

④ $\mathrm{CPM}$: cost per 1,000 impressions $=$ ① $\mathrm{Cost}$: ad spend $\div$ ② $\mathrm{Imp}$: impressions $\times$ ③ $1000$: per 1,000 impressions

The formula in words

① Divide the $\mathrm{Cost}$: ad spend

② by the $\mathrm{Imp}$: impressions to get the cost per impression,

③ multiply by $1000$: per 1,000 impressions to scale it up to 1,000 impressions,

④ and you get the $\mathrm{CPM}$: cost per 1,000 impressions

Quick example

If $120 in ad spend brought 20,000 impressions, the cost per 1,000 impressions is

$\mathrm{CPM}$: cost per 1,000 impressions $=$ ad spend ($120) $\div$ impressions (20,000) $\times$ per 1,000 (1000)

$120 \div 20000 = 0.006$

$0.006 \times 1000 = 6$

Key idea

CPM stands for cost per mille, and "mille" is Latin for 1,000. Note that it is the cost per 1,000 impressions, not per impression. In the example, one impression costs $0.006, too small to work with, so by convention it is expressed per 1,000 impressions as $6. Display ads and video ads are often billed per 1,000 impressions (CPM bidding), whether or not anyone clicks. Even then, the actual CPM is found with the same formula (cost ÷ impressions × 1000). "vCPM" (viewable CPM), which counts only impressions that could actually be seen on screen, is a different measure whose denominator is viewable impressions.

Formula for the cost per acquisition (CPA)

Figure

Standard notation (the usual math form)

$\mathrm{CPA}$ $=$ $\mathrm{Cost}$ $\div$ $\mathrm{CV}$

In words (symbols replaced with words)

③ $\mathrm{CPA}$: cost per acquisition $=$ ① $\mathrm{Cost}$: ad spend $\div$ ② $\mathrm{CV}$: conversions

The formula in words

① Divide the $\mathrm{Cost}$: ad spend

② by the $\mathrm{CV}$: conversions

③ and you get the $\mathrm{CPA}$: cost per acquisition (what you paid for each conversion)

Quick example

If $120 in ad spend brought 4 conversions (purchases), the cost per acquisition is

$\mathrm{CPA}$: cost per acquisition $=$ ad spend ($120) $\div$ conversions (4)

$120 \div 4 = 30$

Key idea

CPA stands for cost per acquisition, sometimes also called cost per action. Whatever the name, the formula is the same: how much one acquisition, that is, one conversion, cost. What matters is deciding for yourself what counts as one conversion and keeping it fixed: a purchase for an online store, an inquiry for real estate, an account sign-up for an app, and so on. Depending on the kind of conversion, it may also be called CPO (cost per order), CPL (cost per lead) or CPI (cost per install), but the calculation is always this formula.

Formulas for the click-through rate (CTR) and the conversion rate (CVR)

Standard notation (the usual math form)

$\mathrm{CTR}$ $=$ $\mathrm{Clicks}$ $\div$ $\mathrm{Imp}$ $\times$ $100$

$\mathrm{CVR}$ $=$ $\mathrm{CV}$ $\div$ $\mathrm{Clicks}$ $\times$ $100$

In words (symbols replaced with words)

④ $\mathrm{CTR}$: click-through rate (%) $=$ ① $\mathrm{Clicks}$: clicks $\div$ ② $\mathrm{Imp}$: impressions $\times$ ③ $100$: to make a percent

⑧ $\mathrm{CVR}$: conversion rate (%) $=$ ⑤ $\mathrm{CV}$: conversions $\div$ ⑥ $\mathrm{Clicks}$: clicks $\times$ ⑦ $100$: to make a percent

The formula in words

① Divide the $\mathrm{Clicks}$: clicks

② by the $\mathrm{Imp}$: impressions ,

③ multiply by $100$: to make a percent

④ and you get the $\mathrm{CTR}$: click-through rate (%) (what percent of impressions were clicked).

⑤ Divide the $\mathrm{CV}$: conversions

⑥ by the $\mathrm{Clicks}$: clicks ,

⑦ multiply by $100$: to make a percent

⑧ and you get the $\mathrm{CVR}$: conversion rate (%) (what percent of clicks converted)

Quick example

If an ad got 20,000 impressions and 40 clicks, and 4 of those clicks converted, the click-through rate and the conversion rate are

$\mathrm{CTR}$: click-through rate (%) $=$ clicks (40) $\div$ impressions (20,000) $\times$ to make a percent (100)

$\mathrm{CVR}$: conversion rate (%) $=$ conversions (4) $\div$ clicks (40) $\times$ to make a percent (100)

$40 \div 20000 \times 100 = 0.2\ \ (0.2\%)$

$4 \div 40 \times 100 = 10\ \ (10\%)$

Key idea

CTR (click-through rate) and CVR (conversion rate) are the rates at which people move down each step of the flow impression → click → conversion. Keep in mind that the base shifts by one step: the denominator of CTR is impressions, and the denominator of CVR is clicks. With these two rates, the three costs (CPM, CPC and CPA) can be converted into each other with the formulas below. Some people use sessions (site visits) instead of clicks as the denominator of CVR, which changes the value; this page always uses clicks. For more detail on CTR or CVR themselves, see the dedicated calculators.

CPA from CPC and CVR (linking formula 1)

Figure

Standard notation (the usual math form)

$\mathrm{CPA}$ $=$ $\mathrm{CPC}$ $\div$ $\dfrac{\mathrm{CVR}}{100}$

In words (symbols replaced with words)

③ $\mathrm{CPA}$: cost per acquisition $=$ ① $\mathrm{CPC}$: cost per click $\div$ ② $\mathrm{CVR} \div 100$: conversion rate

The formula in words

① Divide the $\mathrm{CPC}$: cost per click

② by the $\mathrm{CVR} \div 100$: conversion rate (the percent written as a decimal)

③ and you get the $\mathrm{CPA}$: cost per acquisition

Quick example

With a cost per click of $3 and a conversion rate of 10%, the cost per acquisition is

$\mathrm{CPA}$: cost per acquisition $=$ cost per click ($3) $\div$ conversion rate ($10 \div 100$)

$10 \div 100 = 0.1$

$3 \div 0.1 = 30$

Key idea

To see why this works, break down the definition of CPA. $\mathrm{CPA} = \dfrac{\mathrm{Cost}}{\mathrm{CV}} = \dfrac{\mathrm{Cost}}{\mathrm{Clicks}} \times \dfrac{\mathrm{Clicks}}{\mathrm{CV}} = \mathrm{CPC} \times \dfrac{1}{\mathrm{CVR}}$ So CPA is "the price of one click" times "the number of clicks needed for one conversion" ($1 \div \mathrm{CVR}$). In the example, a 10% CVR means 1 conversion for every 10 clicks, so you need 10 clicks at $3 each, which is $30. This is the formula used most in practice. It shows at a glance that if CVR falls by half, CPA doubles, and if you can cut CPC by 20%, CPA also falls by 20%.

CPC from CPM and CTR (linking formula 2)

Standard notation (the usual math form)

$\mathrm{CPC}$ $=$ $\mathrm{CPM}$ $\div$ $1000$ $\div$ $\dfrac{\mathrm{CTR}}{100}$

In words (symbols replaced with words)

④ $\mathrm{CPC}$: cost per click $=$ ① $\mathrm{CPM}$: cost per 1,000 impressions $\div$ ② $1000$: per 1,000 impressions $\div$ ③ $\mathrm{CTR} \div 100$: click-through rate

The formula in words

① Divide the $\mathrm{CPM}$: cost per 1,000 impressions

② by $1000$: per 1,000 impressions to get back to the cost per impression,

③ divide by the $\mathrm{CTR} \div 100$: click-through rate (the percent written as a decimal),

④ and you get the $\mathrm{CPC}$: cost per click

Quick example

With a CPM of $6 and a click-through rate of 0.2%, the cost per click is

$\mathrm{CPC}$: cost per click $=$ CPM ($6) $\div$ per 1,000 (1000) $\div$ click-through rate ($0.2 \div 100$)

$6 \div 1000 = 0.006$

$0.2 \div 100 = 0.002$

$0.006 \div 0.002 = 3$

Key idea

The cost per impression is $6 \div 1000 = 0.006$ dollars. A 0.2% click-through rate means 1 click for every 500 impressions ($1 \div 0.002 = 500$), so one click costs $0.006 \times 500 = 3$ dollars. That is the CPC. Combining linking formulas 1 and 2 gives $\mathrm{CPA} = \mathrm{CPM} \div 1000 \div \dfrac{\mathrm{CTR}}{100} \div \dfrac{\mathrm{CVR}}{100}$, so even for ads billed per 1,000 impressions you can estimate what one conversion costs. Thanks to this formula, you can compare social media ads billed by CPM and search ads billed per click with the same yardstick, CPA.

Working back from targets (max CPC, clicks needed and budget needed)

Figure

Standard notation (the usual math form)

$\mathrm{CPC}_{\max}$ $=$ $\mathrm{CPA}_{\mathrm{target}}$ $\times$ $\dfrac{\mathrm{CVR}}{100}$

$\mathrm{Clicks}_{\mathrm{needed}}$ $=$ $\mathrm{CV}_{\mathrm{target}}$ $\div$ $\dfrac{\mathrm{CVR}}{100}$

$\mathrm{Budget}$ $=$ $\mathrm{CPA}_{\mathrm{target}}$ $\times$ $\mathrm{CV}_{\mathrm{target}}$

In words (symbols replaced with words)

③ $\mathrm{CPC}_{\max}$: max CPC $=$ ① $\mathrm{CPA}_{\mathrm{target}}$: target CPA $\times$ ② $\mathrm{CVR} \div 100$: expected CVR

⑥ $\mathrm{Clicks}_{\mathrm{needed}}$: clicks needed $=$ ④ $\mathrm{CV}_{\mathrm{target}}$: target conversions $\div$ ⑤ $\mathrm{CVR} \div 100$: expected CVR

⑨ $\mathrm{Budget}$: budget needed $=$ ⑦ $\mathrm{CPA}_{\mathrm{target}}$: target CPA $\times$ ⑧ $\mathrm{CV}_{\mathrm{target}}$: target conversions

The formula in words

① Multiply the $\mathrm{CPA}_{\mathrm{target}}$: target CPA

② by the $\mathrm{CVR} \div 100$: expected CVR

③ and you get the $\mathrm{CPC}_{\max}$: max CPC (the most you can pay for one click).

④ Divide the $\mathrm{CV}_{\mathrm{target}}$: target conversions

⑤ by the $\mathrm{CVR} \div 100$: expected CVR

⑥ and you get the $\mathrm{Clicks}_{\mathrm{needed}}$: clicks needed (round up any fraction).

⑦ Multiply the $\mathrm{CPA}_{\mathrm{target}}$: target CPA

⑧ by the $\mathrm{CV}_{\mathrm{target}}$: target conversions

⑨ and you get the $\mathrm{Budget}$: budget needed

Quick example

With a target CPA of $50, an expected CVR of 2% and a goal of 20 conversions, the max CPC, clicks needed and budget needed are

max CPC $=$ target CPA ($50) $\times$ expected CVR ($2 \div 100$)

clicks needed $=$ target conversions (20) $\div$ expected CVR ($2 \div 100$)

budget needed $=$ target CPA ($50) $\times$ target conversions (20)

$50 \times 0.02 = 1$

$20 \div 0.02 = 1000$

$50 \times 20 = 1000$

Key idea

The max CPC formula is just linking formula 1, $\mathrm{CPA} = \mathrm{CPC} \div \mathrm{CVR}$ (with CVR as a decimal), solved for $\mathrm{CPC}$. It means: "If one conversion may cost up to $50, and only 2 in 100 clicks convert, you can pay at most $1 per click." The budget needed is also "max CPC × clicks needed" ($1 \times 1000 = 1{,}000$ dollars). If you also know the expected CTR, the impressions needed are $\mathrm{Clicks}_{\mathrm{needed}} \div \dfrac{\mathrm{CTR}}{100}$ and the max CPM is $\mathrm{CPC}_{\max} \times \dfrac{\mathrm{CTR}}{100} \times 1000$ (the calculator shows them when you enter a CTR). The expected CVR is an assumption based on past results and the like, so if the real CVR is lower, the CPA goes over the target. Use the results as an estimate that holds if the assumption comes true.

CPC, CPM and CPA are all "ad spend ÷ something"; only the divisor differs - clicks, impressions (in units of 1,000) or conversions. The three are linked by CTR and CVR through $\mathrm{CPA} = \mathrm{CPC} \div \mathrm{CVR}$ and $\mathrm{CPC} = \mathrm{CPM} \div 1000 \div \mathrm{CTR}$ (with CVR and CTR as decimals). Once the target CPA is set, the max CPC and the budget needed come from following these formulas backward.

Symbols and terms

Symbols

$\mathrm{CPC}$	C P C	Cost per click, found with $\mathrm{CPC} = \mathrm{Cost} \div \mathrm{Clicks}$.
$\mathrm{CPM}$	C P M	Cost per mille (cost per 1,000 impressions); "mille" is Latin for 1,000. Found with $\mathrm{CPM} = \mathrm{Cost} \div \mathrm{Imp} \times 1000$.
$\mathrm{CPA}$	C P A	Cost per acquisition, also called cost per action. Found with $\mathrm{CPA} = \mathrm{Cost} \div \mathrm{CV}$.
$\mathrm{CTR}$	C T R	Click-through rate. "Click-through" means clicking an ad and going through to the next page. Found with $\mathrm{CTR} = \mathrm{Clicks} \div \mathrm{Imp} \times 100$ (%).
$\mathrm{CVR}$	C V R	Conversion rate, found with $\mathrm{CVR} = \mathrm{CV} \div \mathrm{Clicks} \times 100$ (%).
$\mathrm{Cost}$	cost	Ad spend, using the word "cost" itself as the symbol. The unit is dollars.
$\mathrm{Imp}$	imp	Impressions, from the first three letters of "impression" (one showing of an ad).
$\mathrm{Clicks}$	clicks	The number of times the ad was clicked.
$\mathrm{CV}$	C V	Conversions, from "conversion": the number of results such as purchases or sign-ups.
$\mathrm{CPC}_{\max}$	C P C max	Max CPC. The "max" (maximum) below the line means the highest cost per click that still meets the target CPA.
$\mathrm{CPA}_{\mathrm{target}},\ \mathrm{CV}_{\mathrm{target}}$	C P A target, C V target	The target values you enter in the reverse mode. "target" is added below the line to tell them apart from the actual $\mathrm{CPA}$ and $\mathrm{CV}$.
$\mathrm{Budget}$	budget	The budget needed: an estimate of the ad spend needed to get the target number of conversions.

Terms

cost per click (CPC)	The ad cost for each click. It is the most basic cost for pay-per-click ads such as search ads and social media ads, and it has the same definition as "Avg. CPC" in ad platforms (cost ÷ clicks). The max CPC bid you set is a limit, which is different from the actual average CPC.
cost per 1,000 impressions (CPM)	The cost for every 1,000 times an ad is shown. The key point is that it is per 1,000, not per impression. It is common for ads billed just for being shown (CPM billing), such as display and video ads.
cost per acquisition (CPA)	The ad cost for each conversion (result). It shows how much it cost to win one customer, and it is the central measure for judging whether ads pay off. Decide what counts as a conversion (a purchase, a sign-up, a request for information and so on) and keep it fixed.
conversion	One occurrence of the result an ad is for. The word means a viewer "converting" into a customer. It depends on your goal - a purchase for an online store, an inquiry for real estate, a sign-up for an app.
impression	One showing of an ad on screen. If the same person sees it 3 times, that counts as 3 impressions (different from reach, which counts people).
click-through rate (CTR)	The percentage of ad impressions that were clicked. It shows whether the headline and image catch the eye. The denominator is impressions.
conversion rate (CVR)	The percentage of clicks that led to a conversion. It shows whether the page people land on after clicking (the landing page) and the product are appealing. The denominator is clicks (some people use sessions instead; this page always uses clicks).
max CPC	The most you can pay for one click and still meet the target CPA, found as "target CPA × CVR". If you keep your actual bids at or below this, the CPA stays within the target as long as the expected CVR holds.
target CPA	A target set in advance for the most ad spend you will pay for one conversion. The basic way to set it is to work back from the gross profit of the product (the profit left when one sells). With a CPA above the gross profit, looking only at that one sale, the more you advertise the more you lose (for products with repeat purchases, future profit such as customer lifetime value may also be counted).
CPM bidding	A way of paying for ads where you are charged per 1,000 impressions. Whichever way you pay, the actual costs (CPM, CPC, CPA) are calculated with the same formulas and can be converted into each other.
pay per click (PPC)	A way of paying for ads where you are charged for each click (CPC billing). Whichever way you pay, the actual costs (CPM, CPC, CPA) are calculated with the same formulas and can be converted into each other.
view-through conversion	A conversion by someone who saw the ad without clicking it and converted later through another route. The CVR and CPA on this page assume that some of the people who click convert, so view-through conversions are not counted.

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.

Unit rates (Grade 6)	Knowing that "total ÷ count" gives "the amount for one" (CPC and CPA are the cost per click and per conversion) Understanding how to compare in units other than 1, such as "per 1,000" (CPM)
Percents (Grade 6)	Knowing that a percent is found as "part ÷ whole" (CTR and CVR are rates) Being able to switch between percents and decimals ($2\% = 0.02$, $0.2\% = 0.002$) Noticing that the number changes depending on what the rate is based on (CTR is based on impressions, CVR on clicks)
Multiplying and dividing decimals (Grades 5–6)	Being able to divide by a decimal, as in $3 \div 0.1$ or $20 \div 0.02$ (dividing by a decimal less than 1 makes the answer bigger)
Expressions and rearranging equations (Grades 7–8)	Understanding a formula such as $\mathrm{CPA} = \mathrm{CPC} \div \mathrm{CVR}$ and rearranging it to find another value, as in $\mathrm{CPC} = \mathrm{CPA} \times \mathrm{CVR}$ (the formulas of the reverse mode)
Multiplying fractions and canceling (Grades 5–6)	Knowing that when you multiply fractions, a quantity in the middle cancels out, as in $\dfrac{\mathrm{Cost}}{\mathrm{CV}} = \dfrac{\mathrm{Cost}}{\mathrm{Clicks}} \times \dfrac{\mathrm{Clicks}}{\mathrm{CV}}$ (why linking formula 1 works)

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 CPC, CPM and CPA

Ad spend Cost ($)	120
Impressions Imp	20000
Clicks	40
Conversions CV	4
Cost per click CPC ($)	=B1/B3
Cost per 1,000 impressions CPM ($)	=B1/B2*1000
Cost per acquisition CPA ($)	=B1/B4

Table to find CTR and CVR

Impressions Imp	20000
Clicks	40
Conversions CV	4
Click-through rate CTR (%)	=B2/B1*100
Conversion rate CVR (%)	=B3/B2*100

Table to find CPC and CPA with the linking formulas

CPM ($)	6
Click-through rate CTR (%)	0.2
Conversion rate CVR (%)	10
Cost per click CPC ($)	=B1/1000/(B2/100)
Cost per acquisition CPA ($)	=B4/(B3/100)

Table to work back from targets

Target CPA ($)	50
Expected CVR (%)	2
Target conversions	20
Max CPC ($)	=B1*B2/100
Clicks needed	=ROUNDUP(B3/(B2/100),0)
Budget needed ($)	=B1*B3

After pasting, column A holds the labels and column B holds the inputs and the calculated results.
In the first table, B1 to B4 are inputs, and B5 shows 3 (CPC), B6 shows 6 (CPM) and B7 shows 30 (CPA). The second table shows 0.2 (CTR) in B4 and 10 (CVR) in B5; the third shows 3 (CPC) in B4 and 30 (CPA) in B5; the fourth shows 1 (max CPC) in B4, 1000 (clicks needed) in B5 and 1000 (budget needed) in B6. 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 CPC, CPM and CPA

Ad spend Cost ($)	120
Impressions Imp	20000
Clicks	40
Conversions CV	4
Cost per click CPC ($)	=B1/B3
Cost per 1,000 impressions CPM ($)	=B1/B2*1000
Cost per acquisition CPA ($)	=B1/B4

Table to find CTR and CVR

Impressions Imp	20000
Clicks	40
Conversions CV	4
Click-through rate CTR (%)	=B2/B1*100
Conversion rate CVR (%)	=B3/B2*100

Table to find CPC and CPA with the linking formulas

CPM ($)	6
Click-through rate CTR (%)	0.2
Conversion rate CVR (%)	10
Cost per click CPC ($)	=B1/1000/(B2/100)
Cost per acquisition CPA ($)	=B4/(B3/100)

Table to work back from targets

Target CPA ($)	50
Expected CVR (%)	2
Target conversions	20
Max CPC ($)	=B1*B2/100
Clicks needed	=ROUNDUP(B3/(B2/100),0)
Budget needed ($)	=B1*B3

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

cost = 120           # ad spend ($)
impressions = 20000  # impressions
clicks = 40          # clicks
conversions = 4      # conversions

cpc = cost / clicks                    # cost per click
cpm = cost / impressions * 1000        # cost per 1,000 impressions
cpa = cost / conversions               # cost per acquisition
ctr = clicks / impressions * 100       # click-through rate (%)
cvr = conversions / clicks * 100       # conversion rate (%)

print(f"CPC: ${cpc}  CPM: ${cpm}  CPA: ${cpa}")
print(f"CTR: {ctr}%  CVR: {cvr}%")
print(f"Check the linking formula CPA = CPC / (CVR/100) = ${cpc / (cvr / 100)}")

# Working back: max CPC, clicks needed and budget needed from target CPA, expected CVR and target conversions
target_cpa = 50
assumed_cvr = 2
target_cv = 20
max_cpc = target_cpa * assumed_cvr / 100
clicks_needed = math.ceil(target_cv / (assumed_cvr / 100))
budget = target_cpa * target_cv
print(f"Max CPC: ${max_cpc}  Clicks needed: {clicks_needed}  Budget needed: ${budget}")

Runs with the standard library only. In this example the CPC is $3.0, the CPM $6.0, the CPA $30.0, the CTR 0.2% and the CVR 10.0%, and the linking formula check also gives $30.0. Working back, the max CPC is $1.0, the clicks needed are 1000 and the budget needed is $1000. Change the numbers at the top and run it.

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

Formula for the cost per click (CPC)

CPC = Cost ÷ Clicks

\mathrm{CPC} = \dfrac{\mathrm{Cost}}{\mathrm{Clicks}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi mathvariant="normal">CPC</mi>
    <mo>=</mo>
    <mfrac><mi mathvariant="normal">Cost</mi><mi mathvariant="normal">Clicks</mi></mfrac>
  </mrow>
</math>

CPC = Cost/Clicks

cost/clicks

CPC := Cost/Clicks;

CPC = Cost/Clicks;

CPC = Cost/Clicks

Formula for the cost per 1,000 impressions (CPM)

CPM = Cost ÷ Imp × 1000

\mathrm{CPM} = \dfrac{\mathrm{Cost}}{\mathrm{Imp}} \times 1000

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi mathvariant="normal">CPM</mi>
    <mo>=</mo>
    <mfrac><mi mathvariant="normal">Cost</mi><mi mathvariant="normal">Imp</mi></mfrac>
    <mo>&#xD7;</mo>
    <mn>1000</mn>
  </mrow>
</math>

CPM = Cost/Imp xx 1000

cost/imp*1000

CPM := Cost/Imp*1000;

CPM = Cost/Imp*1000;

CPM = Cost/Imp × 1000

Formula for the cost per acquisition (CPA)

CPA = Cost ÷ CV

\mathrm{CPA} = \dfrac{\mathrm{Cost}}{\mathrm{CV}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi mathvariant="normal">CPA</mi>
    <mo>=</mo>
    <mfrac><mi mathvariant="normal">Cost</mi><mi mathvariant="normal">CV</mi></mfrac>
  </mrow>
</math>

CPA = Cost/CV

cost/cv

CPA := Cost/CV;

CPA = Cost/CV;

CPA = Cost/CV

Formulas for the click-through rate (CTR) and the conversion rate (CVR)

CTR = Clicks ÷ Imp × 100, CVR = CV ÷ Clicks × 100

\mathrm{CTR} = \dfrac{\mathrm{Clicks}}{\mathrm{Imp}} \times 100,\quad \mathrm{CVR} = \dfrac{\mathrm{CV}}{\mathrm{Clicks}} \times 100

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi mathvariant="normal">CTR</mi>
    <mo>=</mo>
    <mfrac><mi mathvariant="normal">Clicks</mi><mi mathvariant="normal">Imp</mi></mfrac>
    <mo>&#xD7;</mo>
    <mn>100</mn>
    <mo>,</mo>
    <mi mathvariant="normal">CVR</mi>
    <mo>=</mo>
    <mfrac><mi mathvariant="normal">CV</mi><mi mathvariant="normal">Clicks</mi></mfrac>
    <mo>&#xD7;</mo>
    <mn>100</mn>
  </mrow>
</math>

CTR = Clicks/Imp xx 100, CVR = CV/Clicks xx 100

{clicks/imp*100, cv/clicks*100}

CTR := Clicks/Imp*100; CVR := CV/Clicks*100;

CTR = Clicks/Imp*100; CVR = CV/Clicks*100;

CTR = Clicks/Imp × 100, CVR = CV/Clicks × 100

CPA from CPC and CVR (linking formula 1)

CPA = CPC ÷ (CVR/100)

\mathrm{CPA} = \dfrac{\mathrm{CPC}}{\mathrm{CVR}/100}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi mathvariant="normal">CPA</mi>
    <mo>=</mo>
    <mfrac>
      <mi mathvariant="normal">CPC</mi>
      <mrow><mi mathvariant="normal">CVR</mi><mo>/</mo><mn>100</mn></mrow>
    </mfrac>
  </mrow>
</math>

CPA = CPC/(CVR/100)

cpc/(cvr/100)

CPA := CPC/(CVR/100);

CPA = CPC/(CVR/100);

CPA = CPC/(CVR/100)

CPC from CPM and CTR (linking formula 2)

CPC = CPM ÷ 1000 ÷ (CTR/100)

\mathrm{CPC} = \dfrac{\mathrm{CPM}}{1000 \times \mathrm{CTR}/100}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi mathvariant="normal">CPC</mi>
    <mo>=</mo>
    <mfrac>
      <mi mathvariant="normal">CPM</mi>
      <mrow><mn>1000</mn><mo>&#xD7;</mo><mi mathvariant="normal">CTR</mi><mo>/</mo><mn>100</mn></mrow>
    </mfrac>
  </mrow>
</math>

CPC = CPM/(1000 xx CTR/100)

cpm/(1000*ctr/100)

CPC := CPM/(1000*CTR/100);

CPC = CPM/(1000*CTR/100);

CPC = CPM/(1000 × CTR/100)

Working back from targets (max CPC, clicks needed and budget needed)

CPC_max = CPA_target × (CVR/100), Clicks_needed = CV_target ÷ (CVR/100), Budget = CPA_target × CV_target

\mathrm{CPC}_{\max} = \mathrm{CPA}_{\mathrm{target}} \times \dfrac{\mathrm{CVR}}{100},\quad \mathrm{Clicks}_{\mathrm{needed}} = \dfrac{\mathrm{CV}_{\mathrm{target}}}{\mathrm{CVR}/100},\quad \mathrm{Budget} = \mathrm{CPA}_{\mathrm{target}} \times \mathrm{CV}_{\mathrm{target}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi mathvariant="normal">CPC</mi><mi>max</mi></msub>
    <mo>=</mo>
    <msub><mi mathvariant="normal">CPA</mi><mi>target</mi></msub>
    <mo>&#xD7;</mo>
    <mfrac><mi mathvariant="normal">CVR</mi><mn>100</mn></mfrac>
    <mo>,</mo>
    <msub><mi mathvariant="normal">Clicks</mi><mi>needed</mi></msub>
    <mo>=</mo>
    <mfrac>
      <msub><mi mathvariant="normal">CV</mi><mi>target</mi></msub>
      <mrow><mi mathvariant="normal">CVR</mi><mo>/</mo><mn>100</mn></mrow>
    </mfrac>
    <mo>,</mo>
    <mi mathvariant="normal">Budget</mi>
    <mo>=</mo>
    <msub><mi mathvariant="normal">CPA</mi><mi>target</mi></msub>
    <mo>&#xD7;</mo>
    <msub><mi mathvariant="normal">CV</mi><mi>target</mi></msub>
  </mrow>
</math>

CPC_max = CPA_target xx (CVR/100), Clicks_needed = CV_target/(CVR/100), Budget = CPA_target xx CV_target

{cpaTarget*cvr/100, cvTarget/(cvr/100), cpaTarget*cvTarget}

CPCmax := CPAtarget*CVR/100; ClicksNeeded := CVtarget/(CVR/100); Budget := CPAtarget*CVtarget;

CPCmax = CPAtarget*CVR/100; ClicksNeeded = CVtarget/(CVR/100); Budget = CPAtarget*CVtarget;

CPC_max = CPA_target × (CVR/100), Clicks_needed = CV_target/(CVR/100), Budget = CPA_target × CV_target

How to have ChatGPT do the calculation

You are a calculation assistant for managing online ads. 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).

Last month's ad results were: ad spend $120, 20,000 impressions, 40 clicks and 4 conversions.
Find each of the following:
1. CPC (ad spend ÷ clicks)
2. CPM (ad spend ÷ impressions × 1000, per 1,000 impressions)
3. CPA (ad spend ÷ conversions)
4. CTR (clicks ÷ impressions × 100, in %) and CVR (conversions ÷ clicks × 100, in %)
5. A check that the linking formula CPA = CPC ÷ (CVR ÷ 100) matches the result of 3
6. For a different plan: with a target CPA of $50, an expected CVR of 2% and 20 target conversions, the max CPC (target CPA × CVR ÷ 100), the clicks needed (target conversions ÷ (CVR ÷ 100), rounded up) and the budget needed (target CPA × target conversions)

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

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

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Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula

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\(\mathrm{CPC}\)	C P C	Cost per click, found with \(\mathrm{CPC} = \mathrm{Cost} \div \mathrm{Clicks}\).
\(\mathrm{CPM}\)	C P M	Cost per mille (cost per 1,000 impressions); "mille" is Latin for 1,000. Found with \(\mathrm{CPM} = \mathrm{Cost} \div \mathrm{Imp} \times 1000\).
\(\mathrm{CPA}\)	C P A	Cost per acquisition, also called cost per action. Found with \(\mathrm{CPA} = \mathrm{Cost} \div \mathrm{CV}\).
\(\mathrm{CTR}\)	C T R	Click-through rate. "Click-through" means clicking an ad and going through to the next page. Found with \(\mathrm{CTR} = \mathrm{Clicks} \div \mathrm{Imp} \times 100\) (%).
\(\mathrm{CVR}\)	C V R	Conversion rate, found with \(\mathrm{CVR} = \mathrm{CV} \div \mathrm{Clicks} \times 100\) (%).
\(\mathrm{Cost}\)	cost	Ad spend, using the word "cost" itself as the symbol. The unit is dollars.
\(\mathrm{Imp}\)	imp	Impressions, from the first three letters of "impression" (one showing of an ad).
\(\mathrm{Clicks}\)	clicks	The number of times the ad was clicked.
\(\mathrm{CV}\)	C V	Conversions, from "conversion": the number of results such as purchases or sign-ups.
\(\mathrm{CPC}_{\max}\)	C P C max	Max CPC. The "max" (maximum) below the line means the highest cost per click that still meets the target CPA.
\(\mathrm{CPA}_{\mathrm{target}},\ \mathrm{CV}_{\mathrm{target}}\)	C P A target, C V target	The target values you enter in the reverse mode. "target" is added below the line to tell them apart from the actual \(\mathrm{CPA}\) and \(\mathrm{CV}\).
\(\mathrm{Budget}\)	budget	The budget needed: an estimate of the ad spend needed to get the target number of conversions.

CPC, CPM and CPA Calculator (Ad Cost Metrics and Budget from Target CPA)

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How to calculate it in Google Sheets

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

How to have ChatGPT do the calculation

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