Sample Size Calculator

Find the sample size needed to estimate a proportion to within a margin of error at a chosen confidence level, with a population correction. Calculates in your browser.

Leave the population at 0 for a very large or unknown population.

Required sample size

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Confidence level-
Margin of error-

Show the math

The base sample size for a proportion uses the z value and margin of error:

n = z² × p(1 − p) ÷ e²

The expected proportion is most demanding at 50%, which is the safe default when you have no estimate. A population size applies the finite-population correction, lowering the count. All math runs locally in your browser.

What this does

The sample size calculator finds how many responses a survey needs to estimate a proportion to within a chosen margin of error at a given confidence level. An optional population size applies the finite-population correction.

How to use it

  1. Choose a confidence level (e.g. 95%).
  2. Enter the margin of error you can accept.
  3. Optionally set the expected proportion and population size.
  4. Read the required sample size.

How it works

The base size uses the critical z-value, the expected proportion p, and the margin of error e. A known population size then reduces it via the finite-population correction. With no estimate for p, 50% is used because it needs the largest sample.

n = z² × p × (1 − p) ÷ e²

Understanding your result

The result is the minimum number of valid responses, so plan for non-response by inviting more people than this. Tightening the margin of error raises the sample size sharply — halving the margin roughly quadruples the size — while a larger population barely changes it once you are past a few thousand.

Example

A 95% confidence level with a ±5% margin needs about 385 responses for a large population.

Sources & methodology

Last updated .

Frequently asked questions

Why use 50% for the expected proportion?

A proportion of 50% maximises the required sample size, so using it gives the safest, most conservative estimate when you have no prior data.

Does the population size matter?

Only for small populations. The finite-population correction lowers the sample size noticeably for small groups but barely changes it once the population is in the thousands.

Is this the number of people to invite?

No — it is the number of completed responses you need. Invite more than this to allow for non-response.

Is my data stored?

No. Everything is calculated locally in your browser.