Survey Sample Size Calculator
Calculate the minimum survey sample size for a target margin of error and confidence level using Cochran's formula, with an optional finite population correction for known population sizes.
Input
Total people you could survey. Leave empty for unknown or very large populations (no finite population correction is applied).
Acceptable error in your results, e.g. ±5%.
Best guess for the share answering 'yes'. Leave at 50% for the most conservative (largest) estimate.
Output
| Metric | Value |
|---|---|
| No data yet | |
| Margin of error | Sample (Cochran) | Sample (with FPC) |
|---|---|---|
| No data yet | ||
Guides
Work out how many people you actually need to survey to trust your results. This calculator turns a target margin of error and confidence level into the minimum number of respondents, using the standard statistical method that professional researchers rely on — and it corrects for the size of your population when you know it.
How to use it
- Population size — the total number of people you could survey (all your customers, every employee, the whole city). Leave it empty if the population is unknown or very large; the calculator then assumes an effectively infinite population.
- Margin of error (%) — how much sampling error you're willing to accept, expressed as a plus-or-minus percentage. A ±5% margin means a measured result of 60% could plausibly be anywhere from 55% to 65%. Tighter margins need bigger samples.
- Confidence level — how sure you want to be that the true value falls within your margin of error. 95% is the usual default; 99% demands a larger sample.
- Expected proportion (%) — your best guess at the share of people who will answer a certain way. Leave it at 50% when you're unsure: that produces the largest, most conservative sample size, so you can never come up short.
The recommended sample size updates instantly, alongside a full statistical breakdown and a sensitivity table showing how the requirement changes as you tighten or loosen the margin of error.
The math behind it
The core figure comes from Cochran's formula for a proportion:
n = z² × p(1 − p) / e²
where z is the critical value for your confidence level (95% → 1.96, 99% → 2.576), p is the expected proportion, and e is the margin of error. Because p(1 − p) is largest at p = 0.5, the default 50% guess yields the biggest — safest — sample.
When you supply a population size N, the calculator applies the finite population correction:
n_adj = n / (1 + (n − 1) / N)
This can dramatically reduce the required sample. Cochran's formula alone might ask for 384 respondents, but if your entire population is only 5,000 people, the corrected requirement drops to 357 — surveying a large fraction of a small group buys you accuracy that a huge population can't.
Why is the sample size the same for 10,000 people and 10 million?
Sampling error depends on the number of responses, not the share of the population they represent — so once a population is large, the required sample barely moves. The finite population correction only makes a meaningful difference for small, known populations.
What proportion should I use if I have no idea?
Use 50%. It maximizes the required sample, guaranteeing your margin of error is met no matter how the responses actually break down. Lower it only if you have solid prior data (for example, a rare event you expect around 5%).
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