Survey sample size and precision
How many responses does your survey need?
Start with the percentage you need to estimate and the precision your decision requires. Check the overall sample, then the groups you need to report.
One percentage. A clearly defined population.
Choose a calculation and describe the estimate. Use the example buttons to see a complete scenario, or enter your own assumptions. Inputs stay in this calculator; the report downloads to your device.
Try an explicitly illustrative example:
Complete the inputs or review the method guidance.
Your inputs
Complete the assumptions to calculate.
- Choose how respondents are selected.
- Population: enter a description of 1–240 characters.
- Response being estimated: enter a description of 1–240 characters.
- Target margin in percentage points: enter a number from 0.01 to 50.
A precise estimate still needs a sound survey.
The calculator addresses random uncertainty under stated assumptions. Recruiting the right people, asking a clear question and understanding missing responses remain part of the research design.
Discuss your survey and reporting groupsWhat does a margin of error tell me?
A planning margin is the approximate distance from a percentage estimate to either limit under the chosen sampling model. An expected 20% with a five-percentage-point margin means 15%–25%. A relative margin of 5% of 20% would be just one percentage point.
The confidence level describes the interval procedure across repeated samples. It does not express a probability that the entire survey is correct. Sampling and precision reference.
Can I use this for an opt-in online panel?
You can explore a hypothetical simple-random-sample benchmark. The result and export identify it as a benchmark; the calculator does not estimate the population error of an opt-in or convenience sample.
Precision claims for a nonprobability sample require an explicitly justified model. Quotas, weights and a large sample alone do not establish that model. AAPOR disclosure requirements.
Why might reporting groups require more people?
In a calculated simple-random-sample scenario at 95% confidence and expected 50%, a base of 500 gives about ±4.38 points. A subgroup base of 100 gives about ±9.80 points. The full study’s sample cannot be used as every group’s denominator.
The planner adds requirements for disjoint quotas and uses expected shares for naturally occurring groups. Overlapping quotas need joint membership information; it reports individual targets without inventing a total. Pooled weighted precision needs a separate design assessment.
When does the population size change the answer?
Use a finite-population correction when you randomly sample without replacement from the specific finite population you want to describe. A list of contacts is not automatically that population.
Observing all units removes sampling error for that population. Sending invitations to everyone does not mean everyone responded, and a complete census can still contain nonsampling errors. Finite-population variance; other survey errors.
Why is an observed interval a separate calculation?
Planning uses an assumed percentage to select a base. An observed Wilson interval uses actual counts and can be asymmetric. For 20 selections out of 100, its 95% limits are about 13.34%–28.88%. For zero out of 100, the upper limit is still about 3.70%.
This mode requires independent, unweighted binomial observations and a negligible sampling fraction. Weighted or substantial finite-population samples need other methods. Wilson interval reference.
Is this enough to detect a change between waves?
Estimating one percentage and detecting a difference are separate objectives. A comparison needs assumptions about both groups, the difference that matters and the probability of detecting it.
Use the detectable-difference calculatorMethods and sources
Read the method alongside the number.
Planning: for a proportion p, absolute margin e and two-sided normal critical value z, the unrounded baseline is n₀ = z²p(1−p)/e². A supplied design effect D multiplies n₀. With an eligible finite population N, this tool instead uses n = ceiling[Nn₀/(N−1+n₀)]. Rounding occurs at the end. Expected-percentage ranges use the value nearest 50%.
Checking a sample: the approximate margin is z√[Dp(1−p)/n]. Eligible finite-population planning uses D = 1 and multiplies the variance by (N−n)/(N−1). The implementation deliberately keeps finite-population and design-effect adjustments separate.
Observed results: two-sided Wilson score limits without continuity correction, based on the number selecting a response and its valid base. The method does not guarantee exact nominal coverage at every sample size and true percentage.
Scope: individual percentages, 80%, 90%, 95% or 99% confidence, and at most 10 million usable observations. Group calculations use their own bases and assumptions. Recruitment conversion, weight-file diagnostics, exact intervals, simultaneous coverage, complex-survey variance estimation and finite-population observed intervals are outside this release. A supplied design effect is planning sensitivity, not a validated analysis of your survey.
Sources were reviewed September 29, 2026. The downloaded report includes active inputs, results and limitations. Numerical checks use independent SciPy and Statsmodels references under matching settings.