Survey sample size calculator

This calculator solves the SURVEY problem: estimating one proportion to a target margin of error. It is what you need before firing off a satisfaction survey, a purchase intent study, an NPS round or any questionnaire where the final question is "how many people do I have to hear from?". It is not the A/B test calculator: there the problem is comparing TWO rates and detecting a minimum difference, which needs statistical power and much larger numbers. If your case is page A against page B, use the A/B test sample size calculator. If it is listening to your audience, you are in the right place.

How to use it

1. Pick the mode: how many responses I need (the default) or margin of error of the sample I already have.
2. Set the confidence: 95% is the market standard, 90% is fine for a fast internal call, 99% is for when being wrong is expensive.
3. Enter the margin of error you can live with, in percentage points. Five points is the opinion polling default.
4. Enter the expected proportion. With no history, leave 50%: it is the worst case and the conservative choice.
5. Enter the population (0 if unknown or very large) and your historical response rate, to see how many invites to send.

How it works: the formula

The starting point is the sample size to estimate one proportion with margin of error e, ignoring the size of the population:

Where z is the normal critical value for the chosen confidence (1.96 for 95%), p is the expected proportion, e is the margin of error as a proportion (0.05 for 5 points) and N is the population size. The second line is the finite population correction: it only kicks in when you know N, and it accounts for the fact that in a small population every response carries more information. Run backwards, the margin of error of a sample you already have is e = z · √(p(1−p)/n) · √((N−n)/(N−1)).

Worked example (reproduces the default output)

With the prefilled values: 95% confidence, 5 points of margin, expected proportion of 50%, population of 10,000 and a 25% response rate. First the uncorrected number: n₀ = 1.96² · 0.5 · 0.5 / 0.05² = 3.8415 · 0.25 / 0.0025 = 384.15, so 385 responses rounding up. Now the finite population correction: n = 10,000 · 384.15 / (10,000 + 384.15 − 1) = 3,841,459 / 10,383.15 = 369.97, that is 370 responses. At a 25% response rate, invites are 370 / 0.25 = 1,480 sends. That is exactly what the tool shows when the page loads.

Switching to the second mode, with those same 370 responses, a population of 10,000 and an observed result of 50%: e = 1.96 · √(0.25/370) · √((10,000 − 370)/9,999) = 1.96 · 0.025994 · 0.98137 = 0.0500, that is 5.00 percentage points, a range of 45.00% to 55.00%. The two modes are the same equation read in opposite directions, which is why they close on the same number.

Responses needed by population size

At 95% confidence, 5 points of margin and a proportion of 50%, the table below settles most cases. Notice how the requirement almost stops growing past 10,000: that is the answer to the classic doubt about why a national sample does not have to be bigger than a city one.

How to read it, and where it misleads

The margin of error covers one kind of error only: sampling error, the luck of having drawn these people and not others. It knows nothing about non-response bias (whoever replied differs from whoever ignored you), a badly built list, a leading question or the order of the options. A survey with 2,000 responses from the wrong audience delivers a narrow margin on top of a wrong number. Precision is not validity, and no formula fixes a biased sample.

The second trap is breakdowns. The margin the tool returns applies to the total. If you want to look by region, by plan or by age band, each cut needs its own sample: a segment with 40 responses inside a 400 response survey carries a margin close to 15 points, which supports no conclusion at all. Size the study by the smallest cut you intend to analyse, not by the total.

Finally, resist the urge to tighten the margin. It falls with the square root of the sample: going from 5 to 3 points takes the requirement from 385 to 1,068 responses, nearly triple the work for precision that rarely changes the decision. Pick the margin from the question you are answering, not from perfectionism.

Good practice before you send

• Set the margin by the size of the difference that would change your decision. If 5 points already decide, do not pay for 3.
• Size the sample by the smallest breakdown you will analyse, not just by the total.
• Use your real historical response rate, not the optimistic one. It is what defines how many invites to send.
• With no history for the proportion, stay at 50%: it demands the most and never leaves you short.
• Fight non-response with reminders and different channels. That improves the result more than a bigger sample does.

Frequently asked questions

How many people do I need to survey?

At 95% confidence and 5 percentage points of margin in the most demanding case (expected proportion of 50%), the classic answer is 385 responses when the population is large or unknown. With a small population the number drops: 370 for 10,000 people, 278 for 1,000 and 80 for 100. Note that this is RESPONSES, not invites: at a 25% response rate, 370 responses take about 1,480 invites.

Why do 385 responses work for a city and for a whole country?

Because precision is driven by the size of the sample, not by the share of the population it covers. Population only enters through the finite population correction, and that correction barely moves the number once the population is much larger than the sample. It feels wrong, but 400 responses measure a country of 200 million with almost the same precision as a base of 50,000 customers.

What should I enter as expected proportion if I have no idea?

Leave it at 50%. That value maximises p·(1−p) and therefore demands the largest sample, so it is the conservative choice and you never end up short. If you already have history (say you know about 20% of customers pick a given option), using it cuts the requirement a lot: 20% with 5 points of margin needs 246 responses instead of 385.

Are margin of error and confidence level the same thing?

No. The margin of error is the room around your result (plus or minus 5 percentage points). Confidence is how often that kind of interval is right across many repetitions (90%, 95%, 99%). Raising confidence without touching the margin costs sample: from 90% to 95% the requirement goes from 271 to 385, and at 99% it reaches 664.

Can I use this to size an A/B test?

No, and that is the key distinction on this page. Here the problem is estimating ONE proportion to a target margin (satisfaction survey, purchase intent, NPS). An A/B test compares TWO proportions and needs statistical power to detect a minimum difference, which produces much bigger numbers. For that, use the A/B test sample size calculator.

Does the margin of error cover people who never replied?

No. The formula only covers sampling error, the luck of drawing these people instead of others. It knows nothing about non-response bias, a skewed list, a leading question or the order of the options. A survey with 2,000 responses from the wrong audience has a narrow margin around a wrong number: precision is not validity.

Keep going

Already have the data and want the full uncertainty range? Use the confidence interval calculator. If your problem is comparing two versions of a page instead of surveying people, start with the A/B test sample size calculator and read the guide on CRO for low traffic sites.