Sample size calculator
Choose how sure you want to be and how precise, and see how many survey responses you need and how many people to invite.
Responses needed = z² × p × (1 − p) ÷ e², where z comes from the confidence level, p is the expected share and e is the margin of error. A share of 50% gives the largest, safest number.
How many survey responses do you need?
The sample size calculator works out how many answers a survey needs before its percentages are precise enough to act on. Choose a confidence level and a margin of error, add the size of your audience if it is small, and the calculator shows the responses you need. Add an expected response rate to see how many people to invite.
It uses the standard formula for a share, with a correction for small audiences. Everything runs in your browser, and nothing you type is sent anywhere.
- Formula
- z² × p × (1 − p) ÷ e²
- Usual choice
- 95% confidence, a 5% margin of error
- Result
- Responses needed, and people to invite
- Your data
- Stays in your browser
How to calculate sample size
The number of responses you need grows with how sure you want to be (z) and shrinks with the margin of error you accept (e). The expected share (p) is the answer you expect, such as 30% saying Yes; when you don't know, 50% gives the largest and safest number.
For a small audience, such as 600 customers in total, a correction lowers the number, because a large part of the group answers.
n = z² × p × (1 − p) ÷ e²
z is 1.645 at 90% confidence, 1.96 at 95% and 2.576 at 99%. For an audience of N people, divide n by 1 + (n − 1) ÷ N.
A sample size example
Say you want to know the share of customers who would use a new feature, to within 5 points, with 95% confidence. With no guess about the answer, use 50%.
1.96² × 0.5 × 0.5 ÷ 0.05² comes to 384.2, so you need 385 responses. If 20% of the people you email usually answer, invite about 1,925.
- Confidence
- 95%, z = 1.96
- Margin of error
- 5%
- Expected share
- 50%
- At a 20% response rate
- Invite 1,925
- Responses needed
- 385
How the margin of error changes the number
Halving the margin of error needs about four times the responses, so pick the precision the decision needs. A 5 point margin suits most customer surveys; a 10 point margin is enough to spot large differences.
| Margin of error | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| ±10% | 68 | 97 | 166 |
| ±5% | 271 | 385 | 664 |
| ±3% | 752 | 1,068 | 1,843 |
| ±2% | 1,692 | 2,401 | 4,147 |
Sample size for comparing groups
The number applies to each group you want to read on its own. To compare mobile with desktop at a 5 point margin, each needs about 385 responses.
To compare two versions of a survey, use the A/B test calculator once the answers are in: it says whether the difference between the two is clear.
Reaching your sample in Usertick
Results shows how many responses each survey has, and a score on fewer than 30 answers says how many it rests on. The Audience tab shows a group's score once it has 5 answers and flags a group as clearly lower only from 20.
When you test two versions of a survey, Usertick compares them at 95% confidence and names a better or worse variant only once each side has 30 answers. Variants are on the Business plan.
Questions about this calculator
5% at 95% confidence is the usual choice for customer surveys. Use 10% when you only need to spot large differences, and 3% when a small change decides something important.
A share near 50% varies the most from sample to sample, so it needs the most responses to pin down. When you don't know what to expect, 50% keeps you on the safe side.
Enter the share of invited people who usually answer, and the calculator divides the responses you need by it to show how many people to invite.
Only when it is small. For an audience of thousands or more, the number barely changes; for a few hundred people, the correction lowers it noticeably.
No. The calculation runs in your browser and nothing you type is sent.
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