Sample Size Calculator
Work out how many survey responses you need for a chosen margin of error and confidence level, with an optional correction for small populations.
Last updated: October 2026
Required Sample Size
370
Formula below · 3 sources (itl.nist.gov, edis.ifas.ufl.edu, measuringu.com) · Updated Oct 2026
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About this calculator
This calculator uses Cochran's formula for estimating a proportion, the method behind most survey and poll planning.
Step 1, large population: n₀ = z² × p × (1 − p) ÷ e²
z is the critical value for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), e is the margin of error as a decimal (5% = 0.05) and p is the proportion you expect to see (as a decimal). If you do not know p, leave it at 50%: p × (1 − p) is largest at 0.5, so 50% gives the safest, largest sample.
Step 2, finite population correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
N is the population size. The correction matters only when the sample would be a noticeable share of the population. Leave the population blank for a very large or unknown population, and the result is n₀. The answer is rounded up, because you cannot survey part of a person.
The result is the number of completed responses you need. If you expect only 40% of the people you contact to respond, divide by 0.4 to find how many to invite. The formula assumes a simple random sample; cluster or quota samples usually need more responses for the same precision.
| Margin of error | Population 500 | Population 1,000 | Population 10,000 | Very large population |
|---|---|---|---|---|
| ±10% | 81 | 88 | 96 | 97 |
| ±5% | 218 | 278 | 370 | 385 |
| ±3% | 341 | 517 | 965 | 1,068 |
| ±2% | 414 | 707 | 1,937 | 2,401 |
| ±1% | 476 | 906 | 4,900 | 9,604 |
How to use
Choose the confidence level, enter the margin of error and, if you know it, the population size. The default (95% confidence, ±5%, population 10,000, expected proportion 50%) works out as n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16, then 384.16 ÷ (1 + 383.16 ÷ 10,000) = 369.98, which rounds up to 370 responses. Clear the population field and the result is 385, the familiar figure for a large population. Tighten the margin to ±2% with the population of 10,000 and you need 1,937. For a population of 500 at ±5%, the correction brings the requirement down to 218.
Frequently asked questions
Why does the required sample barely change for large populations?
Precision depends mainly on the number of responses, not on the share of the population you reach. At 95% confidence and ±5%, a population of 10,000 needs 370 responses, 100,000 needs 383 and an unlimited population needs 385. The population size only matters when the sample would be a sizable share of it.
Why does halving the margin of error need about four times the sample?
The margin of error shrinks with the square root of the sample size. Going from ±5% to ±2.5% at 95% confidence takes a large-population sample from 385 to 1,537, roughly four times as many responses.
What expected proportion should I enter?
Use 50% unless you have good evidence of the likely answer. It gives the largest, most cautious sample. If earlier data suggest about 10% of people will say yes, entering 10 reduces the sample, but if the true figure turns out near 50% your margin of error will be wider than planned.
Is this the right tool for an A/B test or an experiment?
No. This formula sizes a survey to estimate a single proportion within a margin of error. Detecting a difference between two groups is a power-analysis question, which also needs the smallest effect you care about and the statistical power you want.
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Sources & references
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