Find how many answers a survey needs for a given confidence level and margin of error.
A survey never reaches everyone, so it estimates. The sample size is what decides how good that estimate is, and it depends on three choices: how confident you want to be (the confidence level), how much error you accept around the result (the margin of error) and how divided you expect the answers to be (the expected proportion). Ask 385 people at random and, with 95% confidence, your result will be within ±5 percentage points of what the whole population would have said.
The calculation uses Cochran's formula: n₀ = z² × p × (1 − p) ÷ e². The z value comes from the normal distribution — 1.645 for 90% confidence, 1.96 for 95% and 2.576 for 99%. When you enter a population size, the finite-population correction is applied on top: n = n₀ ÷ (1 + (n₀ − 1) ÷ N). That correction is what makes surveying a small group cheaper: 1,000 people with 95% confidence and ±5% needs 278 answers, not 385.
Two things surprise people. First, the population size matters far less than expected — above roughly 100,000 the required sample barely moves, which is why national polls interview about 2,000 people whether the country has 50 or 200 million inhabitants. Second, cutting the margin of error in half costs four times the sample, because the error appears squared in the denominator. The default proportion of 50% is deliberate: it is the value that maximises the required sample, so it gives you the safest number when you have no prior estimate. The calculation runs entirely in your browser.
n₀ = z² × p × (1 − p) ÷ e², where z = 1.645 (90%), 1.96 (95%) or 2.576 (99%), p is the expected proportion and e the margin of error, both as decimals. For a finite population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N), rounded up.
It means the real value for the whole population is very likely within 5 percentage points of your result. If 60% of your sample says yes with ±5% at 95% confidence, the true figure is probably between 55% and 65%.
Because 50% is the worst case: it maximises p × (1 − p) and therefore the required sample. Using it guarantees the sample is big enough even if you guessed the split wrong.
Yes. Above about 100,000 people the required sample is practically the same as for an infinite population. Precision depends on how many you ask, not on how many exist.
More than the number shown, because not everyone answers. If you expect a 20% response rate, send about five times the calculated sample to end up with enough completed answers.
No. The formula runs in JavaScript on your device and the page makes no network requests with what you type.
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