Sample Size Calculator

About this tool

The awkward decision before any survey is how many responses to collect. Too few and the estimate wobbles, too many and the budget burns; the answer depends on the confidence you want, the error you can tolerate and the size of the population.

At 95% confidence, ±5% error and an expected proportion of 50%, an infinite population needs 385 responses. With a population of 20,000 the finite correction brings that to 378, seven fewer. Tightening the error to ±3% pushes the requirement past 1,060.

What it does

• Confidence levelsThree confidence levels to choose from Every number shown here maps to a field on the form, so changing one value recomputes the rest. The units are printed next to each input, which saves most of the usual mistakes.
• Conservative defaultUnknown proportion defaults to 50% The main figures sit at the top of the result panel and the breakdown sits below it, so you can read the conclusion first and audit the steps afterwards. Nothing you type leaves the browser.
• Population correctionFinite-population correction included All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
• Share of populationShows sample as a share of population Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
• Before and afterShows the reduction from correction The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
• Rounding ruleAll sample sizes round up Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.

How to use it

1. Start by filling inpick a confidence level The main figures sit at the top of the result panel and the breakdown sits below it, so you can read the conclusion first and audit the steps afterwards. Nothing you type leaves the browser.
2. Next, setenter the margin of error as a percent All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
3. Then pressenter the expected proportion Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
4. Read theenter population size, 0 for infinite The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
5. Finally, usepress Calculate and read the corrected size Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.

Things to keep in mind

• Percentageserror and proportion are percentages All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
• Value rangevalues must sit between 0 and 100 Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
• Zero populationa zero population skips the correction The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
• Sampling designno stratification, clustering or design effect Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.
• Response ratenon-response is not deducted Every number shown here maps to a field on the form, so changing one value recomputes the rest. The units are printed next to each input, which saves most of the usual mistakes.