CTR Calculator (Click-Through Rate from Impressions and Clicks, Impressions Needed)

Enter the two values you know out of impressions, clicks and click-through rate (CTR), leave the other blank, and press "Calculate". The blank value is calculated, and a figure shows the clicks per 1,000 impressions.

Impressions

Clicks

Click-through rate, CTR (%)

Fill in exactly two fields (it cannot calculate with all three filled in). Enter the CTR in % (for 2.5%, enter "2.5"). If you enter clicks and CTR and leave impressions blank, you get the impressions needed for that target number of clicks (rounded up to a whole number).

Result and graph

Enter values in two of the fields on the left and press "Calculate". The result and a figure of the clicks per 1,000 impressions 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

Enter the two values you know out of impressions, clicks and click-through rate (CTR), and the third is calculated
"10,000 impressions and 250 clicks - what is the CTR?" "At a 1.5% CTR, how many impressions do I need for 1,000 clicks?" This one page answers click-through rate questions for ads, search results and email
The impressions needed for a target number of clicks are rounded up so that the number of impressions is a whole number
A figure shows the clicks per 1,000 impressions
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, the click-through rate (CTR) is the number of clicks as a percentage of the number of times something was shown. The key point is that it is based on impressions (how many times it was shown). Keep it separate from rates with a different base, such as an email's open rate or "what percent of the people who opened an email clicked". For percentages in general, use the percentage calculator, and for how much CTR improved, use the percentage change calculator.

What is this calculation used for?

Improving the text of search ads (managing online ads)

Say that in a search ad campaign, ad A got 96 clicks from 8,000 impressions (CTR \(96 \div 8000 \times 100 = 1.2\)%), and ad B, with a new headline, got 160 clicks from the same 8,000 impressions (CTR 2%). With the same impressions, B got about 1.67 times as many clicks, and the CTR gap shows in numbers which ad text catches more interest.
People who manage ads repeat this CTR comparison to choose ad text and images. While impressions are still few, though, differences can be due to chance, so it is common to wait until enough impressions build up before deciding.

Rewriting titles in search results (SEO and Search Console)

Say a page on your site appears 20,000 times a month in search results and gets 400 clicks. The CTR is \(400 \div 20000 \times 100 = 2\)%. If a more appealing page title and description raise the CTR to 3%, clicks become \(20000 \times 3 \div 100 = 600\) at the same ranking, 1.5 times as many.
This calculation shows that besides ranking higher, there is another way to improve: getting more clicks from the same impressions. You can check impressions and clicks for free in Google Search Console.

Planning ad delivery from a target number of clicks (marketing work)

Say you want 1,000 clicks (visits) to your site from a campaign. If your ads have had a 1.5% CTR so far, the impressions needed are \(1000 \div 1.5 \times 100 = 66666.6\cdots\), rounded up to 66,667.
Once you know the impressions, you can combine them with the cost per 1,000 impressions (CPM) and past results to estimate the budget and time needed. Actual CTR varies, so it is normal to plan for a bit more.

Checking how readers respond to links in a newsletter (email marketing)

If an email sent to 5,000 people got 150 clicks on the links in it, the click rate based on emails sent is \(150 \div 5000 \times 100 = 3\)%. Compare it with sends that used a different subject line or body text to see which style gets readers to act.
In email, though, a rate based on "what percent of the people who opened it clicked" (called click-to-open, or CTOR) is also used, and a different base gives a different number. When reading a report, always check which base the rate uses.

Testing video thumbnails and titles (video and social media)

On video platforms, the click-through rate is calculated from how many times a video's thumbnail was shown and how many times people clicked to watch, and it appears in the creator dashboard (for example, "impressions click-through rate" in YouTube Studio). If a thumbnail was shown 50,000 times and clicked 2,000 times, the CTR is \(2000 \div 50000 \times 100 = 4\)%.
Watching how this number moves when you change the thumbnail or title shows in numbers what kind of presentation viewers choose. The same idea applies to social media posts and banner ads.

Formulas and figures

Formula for the click-through rate (CTR)

Figure

Standard notation (the usual math form)

\(\mathrm{CTR}\) \(=\) \(C\) \(\div\) \(I\) \(\times\) \(100\)

In words (symbols replaced with words)

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

The formula in words

① Divide the \(C\): clicks

② by the \(I\): impressions ,

③ multiply by \(100\): to make a percent

④ and you get the \(\mathrm{CTR}\): click-through rate (%)

Quick example

If an ad was shown 10,000 times and clicked 250 times, the click-through rate is

\(\mathrm{CTR}\): click-through rate (%) \(=\) clicks (250) \(\div\) impressions (10,000) \(\times\) \(100\)

\(250 \div 10000 \times 100 = 2.5\ \ (2.5\%)\)

Key idea

The click-through rate tells you what percent of the times something was shown it was clicked. The important point is that the number you divide by (the base) is the number of impressions. In email marketing the same words "click rate" sometimes refer to "what percent of the people who opened the email clicked" (based on opens), and a different base gives a different number. Check what the percent is based on before comparing. The division itself is the same as in the percentage calculator. This page focuses on CTR as a measure for ads and search results, and on working backward from it (the next two formulas).

Formula for expected clicks (from impressions and CTR)

Figure

Standard notation (the usual math form)

\(C\) \(=\) \(I\) \(\times\) \(\mathrm{CTR}\) \(\div\) \(100\)

In words (symbols replaced with words)

④ \(C\): expected clicks \(=\) ① \(I\): impressions \(\times\) ② \(\mathrm{CTR}\): click-through rate (%) \(\div\) ③ \(100\): to turn a percent into a decimal

The formula in words

① Multiply the \(I\): impressions

② by the \(\mathrm{CTR}\): click-through rate (%) ,

③ divide by \(100\): to turn a percent into a decimal

④ and you get the \(C\): expected clicks

Quick example

If an ad with a 2.5% click-through rate is shown 40,000 times, the expected number of clicks is

\(C\): expected clicks \(=\) impressions (40,000) \(\times\) click-through rate (2.5%) \(\div\) \(100\)

\(40000 \times 2.5 \div 100 = 1000\)

Key idea

"Impressions × rate" gives clicks because it is exactly the percent equation, part = percent × whole. The CTR is a percent, so divide it by 100 to turn it into a decimal (\(2.5\% = 0.025\)) before multiplying. This formula only gives an estimate of what happens if the current CTR continues. Showing the ad more often or to a different audience can change the CTR itself. The result can also be a decimal such as \(209.865\) clicks, but actual clicks are whole numbers, so read it as "about 210 clicks".

Formula for the impressions needed (from target clicks and CTR)

Figure

Standard notation (the usual math form)

\(I\) \(=\) \(\lceil\) \(C\) \(\div\) \(\mathrm{CTR}\) \(\times\) \(100\) \(\rceil\)

In words (symbols replaced with words)

⑤ \(I\): impressions needed \(=\) \(\lceil\) ① \(C\): target clicks \(\div\) ② \(\mathrm{CTR}\): click-through rate (%) \(\times\) ③ \(100\): to undo the percent ④ \(\rceil\)

The formula in words

① Divide the \(C\): target clicks

② by the \(\mathrm{CTR}\): click-through rate (%) ,

③ multiply by \(100\): to undo the percent (the same as dividing by the rate written as a decimal),

④ round up to a whole number as the \(\lceil\ \rceil\) symbols say,

⑤ and you get the \(I\): impressions needed

Quick example

For an ad with a 2% click-through rate, the impressions needed to get 50 clicks are

\(I\): impressions needed \(=\) \(\lceil\) target clicks (50) \(\div\) click-through rate (2%) \(\times\) \(100\) \(\rceil\)

\(50 \div 2 \times 100 = 2500\)

Key idea

Dividing the CTR by 100 turns the percent back into a decimal such as \(0.02\). So the formula means "target clicks ÷ rate as a decimal", which is the percent equation solved for the whole: whole = part ÷ percent. When it does not divide evenly, round up. For example, if you need 30 clicks at a 0.7% CTR, \(30 \div 0.7 \times 100 = 4285.71\cdots\). Impressions are whole numbers, and 4,285 impressions give \(4285 \times 0.007 = 29.995\) clicks, which falls short of the target, so the answer is one more: 4,286. The \(\lceil\ \rceil\) symbols (the ceiling function) stand for this "round up to a whole number" step. This result assumes the current CTR continues. CTR changes with the ad text and the ad position, so in practice people plan with some margin.

The click-through rate (CTR) is "clicks ÷ impressions × 100", a percentage based on impressions. Rearrange this one formula to solve for clicks or for impressions, and you can estimate expected clicks and work out the impressions needed (rounded up).

Symbols and terms

Symbols

\(\mathrm{CTR}\)	C T R	Click-through rate. Clicks as a percentage of impressions, found with \(\mathrm{CTR} = C \div I \times 100\).
\(C\)	C	Clicks, from the first letter of "clicks". In the working-backward formula it is the target number of clicks. (Example - 250 clicks means \(C = 250\))
\(I\)	I	Impressions, from the first letter of "impressions". The number of times an ad, a search result or a link was shown on screen; it is the number you divide by (the base) in the CTR formula.
\(100\)	one hundred	The base of a percent. Multiply a decimal rate by 100 to get a percent, and divide a percent by 100 to get back the decimal (\(0.025 \times 100 = 2.5\%\), \(2.5\% \div 100 = 0.025\)).
\(\lceil\ \rceil\)	ceiling	The symbol for rounding the number inside up to a whole number (the ceiling function). Whole numbers stay the same: \(\lceil 4285.71 \rceil = 4286\), \(\lceil 2500 \rceil = 2500\). "Ceiling" means the nearest whole number at or above the number.

Terms

click-through rate (CTR)	Clicks as a percentage of the times something was shown. It is the basic measure of how well anything that is "shown and clicked" performs - ads, search results, social media posts, email links. It changes a lot with the headline, the image and the ad position.
impression	One showing of an ad, a search result or a post on screen. If the same person sees it 3 times, that counts as 3 impressions (it counts times, not people). It is sometimes shortened to "impr." in ad reports.
clicks	The number of times what was shown was actually clicked (or tapped). For an ad, it is the number of times people went to the ad's landing page; for a search result, the number of times the page was opened.
search ads	Ads shown above or below search results, matched to the words people search for (such as Google Ads and Microsoft Advertising search campaigns). Impressions, clicks and CTR can be checked every day in the account, so this is the field where CTR is calculated and improved most often. Also called paid search or pay-per-click (PPC) ads.
organic search	The part of search results that is not ads. How many times your site appeared (impressions) and was clicked can be checked with free tools such as Google Search Console, and improving that CTR is one of the basic tasks of SEO.
conversion rate (CVR)	The percentage of people who clicked and then took the action you want, such as a purchase or a sign-up (a conversion). If CTR is the rate from "saw it" to "clicked", CVR is the rate from "clicked" to "bought", the next step after CTR.
rounding up	Rounding to the next whole number up (4285.71 → 4286). When you want a number that is enough, like the impressions needed, rounding down or to the nearest whole number may fall short of the target, so you round up.
percent equation	part = percent × whole, and its rearranged forms percent = part ÷ whole and whole = part ÷ percent. The three formulas on this page are exactly these, with clicks as the part and impressions as the whole.

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 (Grade 6)	Knowing that a percent is found as "part ÷ whole" Being able to switch between percents and decimals (\(2.5\% = 0.025\), \(0.02 = 2\%\)) Noticing that the number changes depending on what the percent is based on (the whole)
The percent equation (Grades 6–7)	Being able to choose between "part = percent × whole" and "whole = part ÷ percent" depending on what you want to find (this is why expected clicks use multiplication and impressions needed use division)
Multiplying and dividing decimals (Grades 5–6)	Being able to divide by a decimal, as in \(50 \div 0.6\)
Rounding (Grades 3–4)	Knowing the difference between rounding up, rounding down and rounding to the nearest, and choosing to round up when you need "enough"
Expressions and rearranging equations (Grades 7–8)	Understanding a formula such as \(\mathrm{CTR} = C \div I \times 100\) and rearranging it to solve for another value, as in \(C = I \times \mathrm{CTR} \div 100\)

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 the click-through rate (CTR)

Clicks C	250
Impressions I	10000
Click-through rate CTR (%)	=B1/B2*100

Table to find the expected clicks

Impressions I	40000
Click-through rate CTR (%)	2.5
Expected clicks C	=B1*B2/100

Table to work out the impressions needed (rounded up)

Target clicks C	50
Click-through rate CTR (%)	2
Impressions needed I	=ROUNDUP(B1/B2*100,0)

After pasting, B1 and B2 are your inputs and B3 is calculated automatically.
For example, the first table shows 2.5 in B3 (a 2.5% CTR), the second shows 1000 (1,000 expected clicks) and the third shows 2500 (2,500 impressions needed). The ROUNDUP function in the third table rounds up to a whole number, so when it does not divide evenly (for example, 30 ÷ 0.7 × 100 = 4285.71…) it returns one more, such as 4286. Just replace B1 and B2 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 the click-through rate (CTR)

Clicks C	250
Impressions I	10000
Click-through rate CTR (%)	=B1/B2*100

Table to find the expected clicks

Impressions I	40000
Click-through rate CTR (%)	2.5
Expected clicks C	=B1*B2/100

Table to work out the impressions needed (rounded up)

Target clicks C	50
Click-through rate CTR (%)	2
Impressions needed I	=ROUNDUP(B1/B2*100,0)

The same formulas as in Excel (including the ROUNDUP function) work as is. Copy the whole table, paste it into cell A1, and replace B1 and B2 with your own numbers.

How to calculate it in Python

import math

clicks = 250          # clicks
impressions = 10000   # impressions

ctr = clicks / impressions * 100   # click-through rate CTR (%)
print(f"Click-through rate: {ctr}%")

# Expected clicks: from impressions and CTR
impressions2 = 40000
ctr2 = 2.5
expected_clicks = impressions2 * ctr2 / 100
print(f"Expected clicks: {expected_clicks}")

# Impressions needed: from target clicks and CTR (rounded up)
target_clicks = 50
ctr3 = 2
# round(..., 6) guards against floating-point error (such as 1000.0000000001) making the result one too high
required_impressions = math.ceil(round(target_clicks / ctr3 * 100, 6))
print(f"Impressions needed: {required_impressions}")

Runs with the standard library only. In this example the click-through rate is 2.5%, the expected clicks are 1000.0 and the impressions needed are 2500. math.ceil does the rounding up. Change the clicks, impressions and other values at the top and run it.

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

Formula for the click-through rate (CTR)

CTR = C ÷ I × 100

\mathrm{CTR} = \dfrac{C}{I} \times 100

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

CTR = C/I xx 100

clicks/impressions*100

CTR := clicks/impressions*100;

CTR = clicks/impressions*100;

CTR = C/I × 100

Formula for expected clicks (from impressions and CTR)

C = I × CTR ÷ 100

C = I \times \dfrac{\mathrm{CTR}}{100}

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

C = I xx CTR/100

impressions*ctr/100

clicks := impressions*ctr/100;

clicks = impressions*ctr/100;

C = I × CTR/100

Formula for the impressions needed (from target clicks and CTR)

I = ⌈C ÷ CTR × 100⌉

I = \left\lceil \dfrac{C}{\mathrm{CTR}} \times 100 \right\rceil

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>I</mi>
    <mo>=</mo>
    <mo>&#x2308;</mo>
    <mfrac><mi>C</mi><mi>CTR</mi></mfrac>
    <mo>&#xD7;</mo>
    <mn>100</mn>
    <mo>&#x2309;</mo>
  </mrow>
</math>

I = |~ C/CTR xx 100 ~|

Ceiling[clicks/ctr*100]

impressions := ceil(clicks/ctr*100);

impressions = ceil(clicks/ctr*100);

I = ⌈C/CTR × 100⌉

How to have ChatGPT do the calculation

You are an assistant for online advertising 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).

An ad was shown 10,000 times and clicked 250 times.
Find each of the following:
1. The click-through rate CTR (clicks ÷ impressions × 100, in %)
2. The expected clicks if it is shown 40,000 times at the same CTR (impressions × CTR ÷ 100)
3. For a different ad: with a CTR of 0.7%, the impressions needed to get 30 clicks (clicks ÷ CTR × 100, rounded up to a whole number)

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

Calculate

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