Skip to content

Rex, your AI assistant: the busywork, handled. The ideas, yours 👉 Meet Rex

Free tool

Survey sample size calculator

Find out how many survey responses you need for reliable results, or how precise the responses you already have are. Free, no sign-up, and every formula is shown.

What do you want to calculate?

How many people the survey is about, e.g. your customers or subscribers. Leave it empty if the group is very large or you don't know its size.

The share you expect to give a particular answer. If you don't know, keep 50%: it gives the largest, safest sample size.

Example value, not a benchmark. Use the response rate from your own earlier surveys.

Result

Responses needed
–
Invitations to send
–

How it is calculated

  • Sample size for a large population (Cochran's formula): nâ‚€ = z² × p × (1 − p) ÷ e², where z is 1.645, 1.960 or 2.576 for 90%, 95% or 99% confidence, p is the expected proportion and e is the margin of error, both as decimals
  • Finite population correction: n = nâ‚€ ÷ (1 + (nâ‚€ − 1) ÷ N), where N is the population size. The result is rounded up to whole responses.
  • Margin of error for the responses you have: e = z × √(p × (1 − p) ÷ n), multiplied by √((N − n) ÷ (N − 1)) when you give a population size
  • Invitations to send: responses needed ÷ response rate, rounded up
  • Example: 95% confidence, ±5% and p = 50% give 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.15, so 385 responses. With a population of 1,000 it is 384.15 ÷ (1 + 383.15 ÷ 1,000) = 277.7, so 278.

The calculator runs in your browser and nothing you type is sent to us. The formulas assume a random sample: everyone in the population has the same chance of answering. They do not correct for bias, for example when only your most loyal customers reply.

How many survey responses do you need?

A survey asks a sample of people and uses their answers to say something about a larger group, the population. The bigger the sample, the closer the result is likely to be to the true answer. The sample size calculator tells you how many responses you need for the precision you want.

Three numbers decide it:

  1. The margin of error. If 60% of respondents say yes and the margin of error is ±5%, the true share is probably between 55% and 65%. Halving the margin roughly quadruples the sample size.
  2. The confidence level. At 95%, the true value falls inside the margin of error in 95 out of 100 surveys run the same way. 95% is the usual choice; 99% needs a larger sample.
  3. The expected proportion. A question where everyone answers the same needs few responses. A 50/50 split needs the most, so 50% is the safe choice when you don't know.

Why the population size matters less than you think

For a large population, the sample size hardly depends on how big it is. At 95% confidence and ±5%, you need 385 responses whether you survey a city or a whole country. The size only matters when the sample is a noticeable share of the population. That is what the finite population correction does: with 1,000 customers, 278 responses give the same precision. If you don't know the size, leave the field empty and the calculator assumes a large population.

From responses to invitations

The number the calculator gives you is completed responses, not invitations. If 20% of the people you invite usually answer, you need to send five times as many invitations. Use the response rate from your own earlier surveys, not a guess.

Response rates go up when the survey is short, relevant and gives people a reason to take part. An incentive often helps: read our guide to survey incentives for what works and what to avoid. With Scratcher you can build a survey or an online poll as a campaign, add a prize draw, and collect answers and consent in one go. The answers people give you directly are zero-party data, which you can use for segmentation and personalisation.

Check the margin of error afterwards

When the survey closes, switch the calculator to the second mode and enter the number of responses you actually got. It shows the margin of error for that number, so you can report your results honestly, for example "62% (±4.9%)".

The formulas assume a random sample. If some groups are much more likely to answer than others, a larger sample will not fix the bias.

Questions

Questions about survey sample size

Book a meeting

  • Yes. It is free to use as often as you like, and you don't need an account. Nothing you type is sent to us.

  • It depends on the precision you need. At 95% confidence and a margin of error of ±5%, a large population needs 385 responses. For ±3% it is 1,068, and for ±10% it is 97. Smaller populations need fewer.

  • ±5% is common for marketing and customer surveys. Use ±3% or lower when small differences matter, for example when you compare groups. Use ±10% only for a rough first picture.

  • Because 50% gives the largest sample size, so your survey is precise enough whatever the answers turn out to be. If earlier surveys show that around 20% answer yes, you can enter 20 and need fewer responses.

  • No. Leave the field empty if the group is large or unknown. The population size only changes the result noticeably when your sample is more than a few percent of it.