Enter a confidence level, margin of error, and proportion to calculate the required survey sample size.
How to Use the Sample Size Calculator
Pick a confidence level from the dropdown, set a margin of error, and estimate the population proportion — 50% is a safe default when that figure is unknown. Population size is optional; leave it blank for a large or unlimited population, or fill it in to see the finite-population correction narrow the result.
n = (Z² × p × (1 − p)) ÷ e²Z comes from the confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the estimated proportion as a decimal, and e is the margin of error as a decimal. The 50% default for p isn't arbitrary — the term p × (1 − p) is mathematically maximized right at p = 0.5, since 0.5 × 0.5 = 0.25 beats any other split. That makes 50% the most conservative assumption available: the largest, safest sample size estimate for a proportion you genuinely don't know yet. A real prior estimate, if you have one, plugs in the same way and produces a smaller — still valid — required sample.
What the Population Size Actually Buys You
Surveying 400 people out of a population of 10,000 tells you proportionally far more than surveying the same 400 out of 10 million, and the finite population correction is what captures that difference.
n adjusted = n ÷ (1 + (n − 1) ÷ population size)Leave population size blank and the calculator skips the correction entirely, which is the right call once a population is large enough that sampling it barely dents the total — the correction's effect only shows up once that's no longer true. This calculator displays both numbers side by side whenever a population size is entered, so the size of the adjustment is visible rather than hidden inside a single final figure.