Free sample size calculator
Calculate the required sample size for your survey or study — enter your confidence level, margin of error, and population proportion to see the minimum sample needed, updated live, as you type.
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For proportion surveys. Uses z-score: 1.645 (90%), 1.96 (95%), 2.576 (99%).
Results are estimates. Consult a professional.
How the sample size calculator works
Sample size determines how many observations you need to achieve a desired level of statistical precision. Too few and your results are unreliable; too many and you waste time and resources. This calculator computes the minimum sample size for estimating a proportion or a mean, given a confidence level and margin of error.
Worked example: survey with 95% confidence, ±5% margin
A market researcher wants to estimate the proportion of customers who prefer a new product. She needs 95% confidence with a ±5% margin of error. Since the true proportion is unknown, she uses the conservative p = 0.5.
Required sample sizes by confidence and margin of error
The table below shows minimum sample sizes (n) for estimating a proportion, using p = 0.5 (worst case). Actual requirements are lower if the proportion is far from 0.5.
| Confidence level | ±3% margin | ±5% margin | ±10% margin |
|---|---|---|---|
| 90% | 752 | 271 | 68 |
| 95% | 1,068 | 385 | 97 |
| 99% | 1,849 | 666 | 166 |
Calculated using n = z² × 0.25 ÷ E² with p = 0.5. Round all values up. Finite population correction may reduce these figures for small populations.
Tips for planning your sample size
A well-chosen sample size balances statistical power with practical constraints. These tips help you plan efficiently.
- Use a prior estimate of p if available — if past research suggests p ≈ 0.3, use that instead of 0.5; it will reduce the required sample size significantly.
- Account for non-response — if you expect a 70% response rate, divide your calculated n by 0.70 to determine how many people to contact.
- Apply finite population correction for small populations — if the population N is small relative to n, use n_adj = n ÷ (1 + (n−1) ÷ N) to reduce the required sample.
- Budget for attrition in experiments — in longitudinal studies, some participants drop out; add 10–20% to the sample size to maintain power at the end.
- Set α and power before recruiting — for hypothesis tests, also specify desired power (typically 80% or 90%) in addition to α, and use power-based sample size formulas.
Accuracy and limitations
These formulas assume simple random sampling from a large or infinite population. For stratified, cluster, or systematic sampling designs, the required sample size differs and typically requires specialist software. The proportion formula assumes the normal approximation to the binomial is valid, which holds when both np and n(1−p) are at least 10. For very small populations, apply the finite population correction factor. These calculations give the minimum n for estimation; hypothesis testing (power analysis) may require a larger sample depending on the expected effect size.
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About this calculator
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