Before you field
Survey sample size calculator
Calculate a response target from confidence level, margin of error, and population size. Estimate invitations using your expected response rate.
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Completed responses
385
Plan to invite approximately 1,925 people at your expected response rate.
Assumes a simple random sample and a 50% proportion. This estimates precision for one proportion. To size an experiment instead, switch to Compare two groups. A larger opt-in sample does not remove selection bias.
How this tool works
For a large population, the response target is n₀ = z² × p × (1 − p) ÷ e². We use p = 0.5, the conservative choice when the proportion is unknown. The margin e is entered as percentage points and converted to a decimal. The z values are approximately 1.645, 1.960, and 2.576 for 90%, 95%, and 99% confidence.
For a known finite population N sampled without replacement, we use n = n₀ ÷ (1 + (n₀ − 1) ÷ N), then round up. Invitations equal the rounded response target divided by the expected response rate, rounded up again.
Example: at 95% confidence and ±5 percentage points, a large population needs 385 completed responses. At a 20% response rate, that implies about 1,925 invitations. A known population of 1,000 gives a target of 278 completions.
This normal-approximation method assumes simple random sampling. It does not account for clustering, weighting, nonresponse bias, repeated measures, or the power needed to detect a difference between groups. Plan separately for each subgroup you need to estimate.
Method reference: NIST: sample sizes for proportions and finite population correction.
A useful next step
Precision, subgroups, and the assumptions behind the numbers.
Already fielded? Find the precision the sample you got actually gives you.
Keep participant IDs consistent and allow for follow-up attrition.
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Put it into practice in your next survey.
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