Survey Sample Size Calculator

"Responses needed" is the number of completed answers that keeps your result within the margin you chose, at the confidence level you chose. With ±5 percentage points at 95%, a result of 40% means the true share among everyone is likely between 35% and 45%.

The response rate turns that number into invitations. It is a guess, so the invitations are a second line and never the headline: if fewer people answer, keep the survey open or send a reminder until you reach the responses, don't lower the bar.

The "Margin of error" tab reads the other way: you already have the answers, and it shows how far the share you measured could plausibly be from the share among everyone.

CatChow, an online pet-food shop, has 2,000 active subscribers and wants to know what share of them would switch to an evening delivery slot. The team wants ±5 percentage points at 95% confidence and expects about 20% of invited subscribers to answer.

For a large population that would take 385 answers. Because the whole group is only 2,000 people, the finite population correction lowers it to 323 responses. At a 20% response rate that means sending about 1,615 invitations.

Check it in the other tab: 323 answers out of 2,000 at 50% give a margin of 4.994 percentage points (shown rounded as ±5.0), within the promised 5. With 322 answers it would be 5.004: rounding up is what keeps the promise.

The formula only covers one kind of error: chance in who ends up in the sample. These five things matter at least as much.

1. The margin covers luck, not bias. The formula assumes that the people who answer are a random pick from everyone. If 20% answer and 80% don't, the answers may come from your happiest or your angriest customers. A bigger sample doesn't fix that; it only makes a biased number look more precise. What helps: invite a random list rather than whoever is around, send one reminder, compare early and late answers, and report the response rate next to the result. A representative sample is about who answers, not how many. How samples stand for a population
2. A link posted in a community is not a sample. Answers from a newsletter link, a social post or an in-app banner come from people who chose to answer. There is no population they stand for, so no margin of error applies to them. Treat such answers as qualitative input: they tell you what some people think, not how many think it. Who exactly to talk to
3. The margin applies to the whole sample, not to segments. If 323 people answer and 60 of them are on the annual plan, the margin for "annual plan subscribers" is the margin for 60 answers: check it in the second tab. Comparing two segments with each other is a two-group question. Plan a two-group comparison with the A/B test sample size calculator
4. Questions about the future measure politeness. "Would you use evening delivery?" collects optimistic guesses, and a precise estimate of a guess is still a guess. Ask about what people did recently wherever you can. Why answers about the future mislead
5. Many questions, one margin. The 50% default keeps the margin safe for every yes/no question in the survey at once. If you plan with 20% and a key question lands near 50%, its margin will be wider than planned. How the width of a range depends on the share

The calculator uses the normal approximation that survey tools usually use, so you can compare our numbers with theirs. q is the normal quantile for the confidence level (1.645, 1.960 or 2.576), p the expected share and e the margin, both as proportions:

n₀ = q² × p(1 − p) / e²
n  = n₀ / (1 + (n₀ − 1) / N)
responses   = ⌈n⌉
invitations = ⌈responses / r⌉
margin = q × √(p(1 − p) / n) × √((N − n) / (N − 1))

The finite population correction (the second line) lowers the number when the population is small; with 2,000 people it takes 385 down to 323, with 1,000,000 it changes 385 to 384. Responses are rounded up so the promised margin holds, and the invitations are calculated from the rounded responses.

Without a population the first line is the same formula as the "Plan precision" tab of the confidence interval calculator, so the two tools give the same number. The margin-of-error tab uses the conventional survey margin with the same correction. Near 0% or 100%, or with few answers on one side, that margin misbehaves; the confidence interval calculator's Wilson interval stays between 0% and 100%.

Why is 385 the answer so often?

It is the number for the most common settings: 95% confidence, ±5 percentage points, an expected share of 50% and a large population. 1.96² × 0.5 × 0.5 / 0.05² is 384.1, rounded up to 385.

Does population size matter?

Barely, above about 100,000 people: a million people need 384 answers against 385 for an unknown large group. It matters a lot for small groups: 2,000 people need 323 answers and 100 people need 80. The precision comes from the number of answers, not from the share of the population you reach.

Why use 50% if I expect something else?

The margin is widest when the share is 50%, so 50% gives the largest, safest number. A survey has many questions; planning with 50% keeps every yes/no question within the margin. Use your own guess only when one question matters and you are fairly sure of its range.

What's the difference between the confidence level and the margin of error?

The margin is the width: how far the result may be from the truth (±5 points). The confidence level is how often ranges built this way would contain the truth if you repeated the survey (95%). Tightening either one needs more answers.

What response rate should I expect?

We don't give a benchmark, because it depends on your audience, channel, incentive and survey length, and any single number would mislead. Use the rate of your own past surveys. If you have none, plan for a low rate, send one reminder, and keep the survey open until you reach the responses.

Can I use this for a survey I posted on social media?

No. People who chose to answer a public post don't form a random sample of any population, so a margin of error doesn't describe them. Read those answers as qualitative input.

How is this different from the A/B test sample size calculator?

This calculator plans the precision of one share in one group, and a small population lowers the number. The A/B test calculator plans how many people each of two groups needs to detect a difference between them, with statistical power, and usually asks for far more people.

My margin of error is too wide. What now?

Collect more answers for the whole sample: halving the margin takes about four times as many. Split the results into fewer segments, since each segment has its own, wider margin. Or accept a wider margin for secondary questions and plan the sample around the one question that matters most.

• Confidence intervals, in the statistics course
• Read the post: confidence intervals explained
• Bad and good questions, in the customer interviews course
• Read the post: writing questions people answer honestly

To check whether two groups of answers really differ, for example men and women or two plans: statistical significance calculator

• margin of error
• population
• sampling bias
• confidence interval (CI)
• standard error (SE)

• Confidence interval calculator

  Seeing how precise a single conversion rate is.

• A/B test sample size calculator

  Planning for two variants (A/B) before the test starts.

• Cohort retention calculator

  Reading a cohort retention table: heatmap and average curve.