Sample Size Calculator

STATISTICS & PROBABILITY

Find the sample size needed to estimate a proportion at a chosen confidence and margin of error. Pick the confidence and enter the margin.

Sample Size
— responses
Needed for the survey.

Usage Tip

Halving the margin of error quadruples the required sample size — precision gets expensive fast.

THE MATH
n = z² × p(1 − p) ÷ E²
z from the confidence level, E the margin of error
This gives the number of responses needed for a survey to hit a target margin of error.
A proportion of 50 percent is the most conservative (largest) sample requirement.
Choose the confidence level and enter the margin of error as a percent.
The expected proportion defaults to 50 percent (worst case).
The result is rounded up to a whole number of responses.
Practical Notes

This calculator finds how many responses are needed to estimate a proportion within a chosen margin of error and confidence level. The standard formula multiplies the squared z value for your confidence level by the expected proportion times one minus that proportion, then divides by the squared margin of error.

If you have no idea what proportion to expect, use 50 percent, which gives the largest and therefore safest sample size. Plan for non-response by dividing the answer by the share of people you expect to reply. For small populations, the required sample can be reduced with a finite population correction.

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The calculators and tools on Formula Factory are provided for general guidance and informational purposes only. Results are estimates based on standard formulas and the values you enter — they do not constitute professional engineering, electrical, or architectural advice. Always verify calculations with a qualified professional before making decisions for any safety-critical, code-compliance, or commercial application. Formula Factory makes no representations or warranties as to the accuracy or completeness of any result, and accepts no liability for errors, omissions, or any outcomes arising from reliance on this information.