Calculators
Sample Size Calculator
Calculate the survey sample size needed for a confidence level and margin of error, with finite population correction and invitations needed at your response rate.
- Runs in your browser
- Nothing uploaded
The tool
Enter your numbers below. Results update as you type, and nothing leaves your browser.
Everything you enter stays on your own machine. Nothing is sent to us or to anyone else, which you can confirm in your browser network tab.
What people use it for
- Customer and employee surveys
- Market research
- Academic studies
- Polling and audits
About this tool
What the Sample Size Calculator does
For estimating a proportion, the sample size is n₀ = z² × p(1 − p) ÷ e², where z is the z-score for the confidence level, p the expected proportion (50% is the cautious choice) and e the margin of error. For small populations, the finite population correction reduces the number needed.
It also works as a survey sample size calculator or a margin of error calculator.
Formula
- n₀ = z² × p × (1 − p) ÷ e²
- n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
- Invitations = n ÷ response rate
Worked example
Using the starting values in the calculator above:
| Input | Value |
|---|---|
| Confidence level | 95% |
| Margin of error | 5% |
| Expected proportion | 50% |
| Population size (0 if very large) | 2,000 |
| Expected response rate | 25% |
| Result | Value |
|---|---|
| Sample size needed | 323 |
| Invitations to send | 1,292 |
| Sample size for an unlimited population | 385 |
| z-score | 1.96 |
| Share of the population | 16.2% |
How to read the result
Use 50% when you do not know the expected proportion; it gives the largest, safest sample.
Sample size does not fix bias: a large sample from the wrong people still gives wrong answers.
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Questions
Questions about this tool
The things clients actually want to know — costs, timelines, ownership and what happens after launch.
About 385 for a 5% margin at 95% confidence in a large population, fewer for small populations.
The range around a survey result that likely contains the true value at the chosen confidence level.
Only when the sample is a sizeable share of the population.
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