Math tool

Sample Size Calculator

Find how many responses you need for a survey to be statistically representative.

—Recommended sample size

What "50% distribution" means

Using 50% is the safest default — it produces the largest, most conservative sample size, because that's the point of maximum variance in a proportion. If you have a solid prior estimate of the actual response split, using that number instead can lower the required sample size.

About the Sample Size Calculator

The Sample Size Calculator estimates how many people you need to survey to get reliable results. Enter the population size, your confidence level (90, 95 or 99 percent), the margin of error and the expected response distribution.

The calculation uses the standard formula for proportions. A 95 percent confidence level with a 5 percent margin of error means that if you repeated the survey many times, about 95 percent of the intervals would contain the true value within five points. Using 50 percent for the expected distribution is the safest choice because it gives the largest required sample. For large populations, the required sample size levels off at a few hundred to about a thousand.

How to use it

  1. Enter the population size.
  2. Choose the confidence level.
  3. Enter the margin of error.
  4. Read the required sample size.

Tips and good to know

Frequently asked questions

What if my population is unknown?

Use a large number, such as 100,000.

Why 50 percent?

It maximises variance and the sample size.

Is bigger always better?

Returns diminish as the sample grows.