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Find the survey sample size for a target margin of error.
Results update as you type.
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= z²·p(1 − p) / e², where z is the critical value for the confidence level, p the expected proportion and e the target margin of error as a decimal. This sample size calculator finds how many people you need to survey for a chosen margin of error and confidence level — the planning step before you run a poll or study. It uses the standard formula n = z²·p(1 − p) / e², where z is the critical value for the confidence level, p the expected proportion and e the target margin of error as a decimal. This sample size calculator finds how many people you need to survey for a chosen margin of error and confidence level — the planning step before you run a poll or study.Worked example:Worked example:Work
Tambayoyi da ake yi da yawa
Ta yaya ake kimanta girman misali?
The base formula is n = z²·p(1 − p) / e², where z is the confidence critical value, p the expected proportion and e the margin of error as a decimal. The result is rounded up because you cannot survey a fraction of a person.
What is the finite population correction?
When your population is small, you need fewer responses than the base formula suggests. The correction n = n₀ / (1 + (n₀ − 1)/N) shrinks the sample toward the population size N. It matters most when the sample is a large fraction of the whole.
Da yawa mutane ne nake buƙata don 95% na matsakaicin darajar aminci?
It depends on the margin of error you can accept. At 95% confidence with a 5% margin and no prior estimate you need about 385 respondents; a 3% margin needs about 1,068 and a 1% margin about 9,604.
Me ya sa aka kwatanta girman misalin zuwa sama?
You cannot survey part of a person, so any fractional result is rounded up to the next whole number. Rounding up rather than down guarantees the margin of error is no larger than your target.
Should I leave the population size blank?
Leave it at zero (or blank) when the population is very large or unknown, which gives the standard "infinite population" sample size. Enter a real population only when it is small enough that the correction meaningfully reduces the sample.
How can I reduce the required sample size?
Accept a larger margin of error, use a lower confidence level, or supply a proportion further from 50% if you have a reliable estimate. Each of these lowers the number of responses the formula demands.
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[Translation temporarily unavailable. Please try again.] Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. [Translation temporarily unavailable. Please try again.] →
Endpoint
GET https://calculator.free/api/v1/sample-size/curl
curl "https://calculator.free/api/v1/sample-size/?conf=1.96&e=5"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/sample-size/?" + new URLSearchParams({
"conf": "1.96",
"e": "5"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.