Margin of error calculator
Enter how many responses you have to see how far your results may be from the answer of the whole group.
If 50% of the people who answered chose an option, the share in the whole group is likely between 45.1% and 54.9% (95% confidence).
How precise are your survey results?
The margin of error calculator shows how far a share from your survey, such as 62% saying Yes, may be from the share in your whole audience. Enter the number of responses, the share you got and, for a small audience, its size.
It uses the standard formula for a share, with a correction for small audiences, at the confidence level you choose. Everything runs in your browser, and nothing you type is sent anywhere.
- Formula
- z × √(p × (1 − p) ÷ n)
- Input
- Responses, the share you got and the audience size
- Result
- The margin, and the range the true share is likely in
- Your data
- Stays in your browser
How to calculate the margin of error
Multiply the z value for your confidence level by the square root of p × (1 − p) ÷ n, where p is the share you got and n the number of responses. The result is the distance either side of your share.
For a small audience, a correction makes the margin smaller, because a large part of the group answered.
MOE = z × √(p × (1 − p) ÷ n)
z is 1.645 at 90% confidence, 1.96 at 95% and 2.576 at 99%. For an audience of N people, multiply by √((N − n) ÷ (N − 1)).
A margin of error example
Say 400 customers answer and 62% choose Yes. At 95% confidence the margin is 1.96 × √(0.62 × 0.38 ÷ 400), or about 4.8 points.
The share among all your customers is likely between 57.2% and 66.8%. A result of 62% against 58% last quarter sits inside that range, so it isn't a clear change.
- Responses
- 400
- Share that said Yes
- 62%
- Likely range
- 57.2% to 66.8%
- Margin at 95%
- ±4.8 points
Margin of error by number of responses
At 95% confidence and a 50% share, the case with the widest margin, the margin shrinks slowly as answers come in: four times the answers halve it.
| Responses | Margin of error |
|---|---|
| 50 | ±13.9% |
| 100 | ±9.8% |
| 400 | ±4.9% |
| 1,000 | ±3.1% |
| 2,500 | ±2.0% |
What the margin of error doesn't cover
The margin covers chance alone: which customers happened to answer. It says nothing about a leading question, a survey only your happiest customers saw, or people who chose not to answer.
Check who answered as well as how many. A large sample from one corner of your audience is precise about that corner only.
Reading precision in Usertick
Results shows how many responses each survey has, a score on fewer than 30 answers says how many it rests on, and filters by country, device, language, page and answers let you read one group at a time. A group's score on the Audience tab appears once it has 5 answers.
When you compare two versions of a survey, Usertick runs the statistics at 95% confidence and waits for 30 answers on each side before it calls a difference. Variants are on the Business plan.
Questions about this calculator
Within 5 points at 95% confidence is the usual aim for customer surveys. The right margin is one smaller than the difference you need to see.
No. It covers chance only. A leading question, a survey only some customers saw or a group that chose not to answer can move a result more than the margin.
The margin depends on the share: it is widest at 50% and narrower near 0% or 100%. Leave 50% to see the widest margin your number of responses allows.
No. The calculation runs in your browser and nothing you type is sent.
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