Sample Size Calculator
Work out how many survey responses you need for a chosen margin of error and confidence level, with the finite population correction, or to estimate a mean.
Assumes a simple random sample. Clustered or quota samples need more responses (multiply by the design effect), and non-response can bias results no matter how large the sample.
| Margin of error | 90% | 95% | 99% |
|---|---|---|---|
| ±1% | 6,764 | 9,604 | 16,588 |
| ±2% | 1,691 | 2,401 | 4,147 |
| ±3% | 752 | 1,068 | 1,844 |
| ±4% | 423 | 601 | 1,037 |
| ±5% | 271 | 385 | 664 |
| ±6% | 188 | 267 | 461 |
| ±7% | 139 | 196 | 339 |
| ±8% | 106 | 151 | 260 |
| ±9% | 84 | 119 | 205 |
| ±10% | 68 | 97 | 166 |
Before running a survey or experiment you need to know how many responses are enough. This sample size calculator works it out from the margin of error you can accept and the confidence level you want, and it shrinks the number for small populations with the finite population correction. It also handles estimating an average when you know roughly how spread out the values are.
How to use this tool
- Choose whether you are estimating a percentage or an average.
- Pick the confidence level (95% is standard) and the margin of error.
- For a percentage, enter the result you expect; 50% if unsure. For an average, enter the standard deviation.
- Optionally enter the population size, for example the number of employees or customers.
Formula
n₀ = z² × p(1 − p) ÷ E² · mean: n₀ = (z × σ ÷ E)² · finite population: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
z is the critical value for the confidence level (1.645 for 90%, 1.960 for 95%, 2.576 for 99%), p the expected proportion, E the margin of error as a proportion (or in measurement units for a mean), σ the standard deviation and N the population size. The result is always rounded up.
Example
For 95% confidence and a ±5% margin with no prior idea (p = 50%): n₀ = 1.96² × 0.25 ÷ 0.05² = 384.15, so you need 385 responses. If the whole population is only 1,000 people, the correction gives 384.15 ÷ (1 + 383.15 ÷ 1,000) = 278. Halving the margin to ±2.5% roughly quadruples the sample to 1,537.
Frequently asked questions
Why is 50% the safest expected percentage?
p(1 − p) is largest at p = 0.5, so assuming 50% gives the biggest sample size. If you are fairly sure the answer is near 20% or 80%, fewer responses are needed.
Does a bigger population need a much bigger sample?
No. Beyond roughly 20,000 people, the required sample barely changes: about 385 for ±5% at 95%, whether the population is 100,000 or 100 million.
What about A/B tests?
Comparing two groups needs a power calculation with the effect size you want to detect, which gives larger numbers than this single-estimate formula.
Sources
Last updated:
Page address with these inputs: https://kakao.mobile/tools/sample-size-calculator/
Cite or embed this tool
kakaoCalc. (2026, November 8). Sample Size Calculator. https://kakao.mobile/tools/sample-size-calculator/
“Sample Size Calculator.” kakaoCalc, 8 Nov. 2026, kakao.mobile/tools/sample-size-calculator/.
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