Statistics / Surveys
Sample Size Calculator (Surveys)
Find how many survey responses you need for a given margin of error and confidence level, with the finite population correction for small populations.
Sample Size Calculator (Surveys): Cochran's formula gives n₀ = z² × p(1 − p) ÷ e², with z from the confidence level (1.96 for 95%), p the expected proportion, and e the margin of error. With p = 50%, the most cautious choice, and ±5% at 95% confidence, n₀ = 384.16, so 385 responses. For a population of N people, n = n₀ ÷ (1 + (n₀ − 1) ÷ N): for 1,000 people, 278. Runs 100% locally in your browser with zero server file uploads.
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Cochran's formula, n₀ = z² × p(1 − p) ÷ e², gives the responses needed for a survey proportion to be within the margin of error e at the chosen confidence; 50% is the safe guess for p because it needs the most. For a small population N, the finite population correction n = n₀ ÷ (1 + (n₀ − 1) ÷ N) reduces it. It assumes a random sample; low response rates and biased samples are not fixed by size.
Common sizes
At 95% confidence and p = 50%: ±10% needs 97 responses, ±5% needs 385, ±3% needs 1,068, and ±1% needs 9,604. At 99% confidence, ±5% needs 664.
Once results are in, the margin of error you actually achieved depends on the proportion you found: it is largest when the answer is near 50%.
For experiments instead of surveys
Comparing two groups, as in an A/B test or a clinical trial, needs a power analysis based on the effect size you want to detect, which works differently.
A sample is only as good as how it is drawn: a large but self-selected sample can still be badly biased.
How to use it
- Choose the confidence level, usually 95%.
- Enter the margin of error you can accept, and the population size if it is small.
- Read the number of responses needed.
Privacy & limitations
Everything is calculated in your browser.
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Frequently asked questions
Why does a huge population not need a huge sample?
Precision depends on the number of responses, not the share of the population asked: 385 random responses give ±5% whether the population is 100,000 or 100 million.
Why use 50% for the proportion?
p(1 − p) is largest at 50%, so it gives the largest, safest sample; use a different value only if you know roughly what the answer will be.
Does this account for people who do not reply?
No: divide by the response rate you expect. At a 20% response rate, invite 385 ÷ 0.2 = 1,925 people.
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