What is a sample size calculator?
A sample-size estimate connects desired precision with confidence and the expected variability of a proportion. It answers how many completed responses a simple random survey may need under stated assumptions.
Use this page for a transparent calculation, then compare the result with the Confidence Interval Calculator when a different view of the same data would be useful.
How does this sample size calculator work?
The calculator uses the normal-approximation formula for one proportion, rounds up, and applies the finite-population correction when a population size is entered.
Before interpreting spread or position, it can help to check the center with the Probability Calculator. Every tool states its assumptions so results can be reproduced.
How to use this calculator
- Enter the requested numbers in the labeled fields.
- Review unit, sample, confidence, or test choices when shown.
- Select Calculate Sample Size.
- Read the main result, supporting facts, and method note.
- Use Copy, Download, or Print when you need to keep the result; select Reset to start over.
If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.
How should you interpret the result?
A smaller margin of error, higher confidence level, or expected proportion near 50% increases the recommended sample. The result counts completed usable responses, not invitations.
For another useful perspective, open the Percentile Calculator; it answers a related question without changing the values you entered here.
Assumptions and limitations
Complex survey designs, clustering, weighting, subgroup targets, nonresponse, and measurement error can require a larger sample. Study planning should consider more than a single formula.
Consider the Chi-Square Calculator for a complementary summary and the Coefficient of Variation Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.
Frequently asked questions
Sources and methodology
The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.