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Sample Size Calculator

Work out how many responses you need before you run a survey or study.

  • Free
  • No sign-up
  • Nothing is sent or stored
You're estimating a
%
%

Use 50% if you don't know — it gives the safest (largest) sample.

For small populations the required sample is smaller.

Result

Sample size needed
385
Before population correction
385
Critical z
1.96
How it was calculated
  1. n₀ = z² × p(1 − p) ÷ E² = 1.96² × 0.5 × 0.5 ÷ 0.05²
  2. = 384.1459
  3. Round up → 385

The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved.

How to use the Sample Size Calculator

  1. Choose whether you're estimating a percentage or an average.
  2. Set the confidence level and margin of error.
  3. Optionally enter the population size for small populations.

What does this tool do?

To estimate a percentage within ±5% at 95% confidence you need about 385 responses, no matter how big the population — as long as it's large. Halving the margin of error roughly quadruples the sample you need.

If your whole population is small (say 500 employees), the finite population correction reduces the required sample. Using 50% as the expected proportion is the safe choice when you don't know it.

Why use it?

  • Survey and measurement modes.
  • Finite population correction.
  • Shows the calculation step by step.

The formula

Proportion: n₀ = z² p(1 − p) ÷ E²
Mean: n₀ = (z σ ÷ E)²
Finite population: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)

Privacy

The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.

Frequently asked questions

Does a bigger population need a bigger sample?

Barely. Beyond a few tens of thousands, the required sample hardly changes.

Last reviewed by the M2Toolkit team.

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