Sample Size Calculator
How many responses a target margin of error actually costs.
Work out Sample Size. How many responses a target margin of error actually costs. Free, with no account and nothing to download.
Leave at 50 unless you have a sound prior estimate — 50 gives the largest, safest sample.
Leave at zero for a very large or unknown population.
This is the statistical minimum, not the number to invite. It assumes everyone responds and that respondents are a random sample. Non-response is the larger threat in practice: a biased sample of 5,000 is worse than a random sample of 400, and no sample size corrects for a skewed frame.
Responses needed
385
for ±5.0 points at 95% confidence
385 responses buy a ±5.0 point margin. Halving that margin to ±2.50 needs 1,537 — roughly four times as many, because precision improves with the square root of the sample. This is why national polls stop around a thousand: the next meaningful gain costs four times the budget.
How the Sample Size Calculator works
The number of responses needed for a target margin of error, at your chosen confidence level. The familiar answer is 385 — that is what a ±5 point margin at 95% confidence costs — and it barely changes whether the population is a city or a country. What changes it is the margin you want, and it changes fast: halving the margin roughly quadruples the sample.
Also known as: survey sample size calculator · how many people do I need to survey · statistically significant sample size · minimum sample size calculator
The calculation itself
n = z² × p(1−p) ÷ e², where e is the margin of error as a proportion and p is the expected result.
p defaults to 0.5 because that value maximises p(1−p), and therefore gives the largest and safest sample. Any other expectation reduces the requirement — legitimately, but only if the estimate is sound.
In practice
The three numbers worth remembering: ±5 points at 95% confidence needs 385 responses, ±3 points needs 1,068, and ±1 point needs 9,604.
That progression is the square root law seen from the cost side. Going from 5 points to 1 point of precision is a five-fold improvement that costs twenty-five times the sample.
It is also why national polls cluster around a thousand responses. That buys roughly ±3 points, and the next meaningful step costs four times the budget for a gain most readers would not notice.
Why the population size barely matters
This is the most counter-intuitive result here. Sampling a city of ten million and a country of three hundred million both need 385 responses for the same precision.
The finite population correction only bites when the sample is a large share of the whole. A population of 1,000 drops the requirement from 385 to 278, because 278 people is a quarter of everyone. A population of ten million leaves it at 385.
The intuition: what determines precision is how much independent information you have gathered, not what fraction of the group you have spoken to. A spoonful tells you about the soup regardless of the pot size, provided it is stirred.
The number this does not give you
This is the statistical minimum of completed responses, and it assumes those responses are a random sample of the population you care about.
Non-response is the larger practical threat. If half the invitations go unanswered, and the half that answer differ systematically from the half that do not, no sample size corrects for it: a biased sample of 5,000 is worse than a random sample of 400, because bias does not shrink as the sample grows.
So invite well above this figure, and spend at least as much attention on who is in the frame as on how many of them respond.
Frequently asked questions
How many people do I need to survey?
For a ±5 point margin at 95% confidence, 385. For ±3 points, 1,068. For ±1 point, 9,604. The precision you ask for is what drives the cost, not the size of the population.
Why does population size barely matter?
Because the finite population correction only bites when you are sampling a large share of a small group. Surveying a town of 10 million and a country of 300 million need the same sample; a group of 1,000 needs 278 rather than 385.
What expected proportion should I use?
Leave it at 50% unless you have a sound prior estimate. It maximises p(1−p) and therefore gives the largest, safest sample — any other value reduces the requirement, but only legitimately if the estimate holds up.
Is 385 a magic number?
It is just the arithmetic of 95% confidence and a 5 point margin, rounded up. It appears everywhere because those two choices are conventional, not because the number itself is special.
Do I need to invite exactly this many people?
No — invite considerably more. This is the number of completed responses required, and response rates are often well under half. Divide by your expected rate to get the invitation list.
Does a bigger sample fix a biased one?
No, and this is the more common failure. A biased sample of 5,000 is worse than a random sample of 400, because the bias does not shrink with size. Sample size only addresses random error.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
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