data tool
Sample size calculator for surveys
At 95% confidence and a 5% margin of error, a survey of a large population needs 385 responses; a smaller population needs fewer. Set the confidence, margin, expected share and population, and the calculator gives the responses needed and how many people to invite at your expected response rate.
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- Runs on your device, nothing is uploaded
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- No watermark, no file limit
How it works
- 1
Pick a confidence level
95% is the usual choice. 99% gives more certainty and needs a bigger sample; 90% needs fewer responses.
- 2
Set the margin of error
Five percentage points is common for a general survey; 3 points if the result will drive a large decision.
- 3
Add the population
Leave it blank for a large population, or enter the number of customers, staff or members you are surveying.
- 4
Allow for non response
Enter the response rate you expect and the tool converts responses into invitations.
Where 385 comes from
The usual formula for estimating a percentage multiplies the square of the z value for the confidence level by p times one minus p, then divides by the square of the margin of error. At 95% confidence z is 1.96, and with p at 50%, the most cautious assumption, and a 5% margin, that gives 384.16, which rounds up to 385. Because p times one minus p is largest at 50%, assuming 50% always gives enough responses whatever the true answer turns out to be. That is why 385 appears in so many survey guides.
Small populations need fewer responses
When the population is small, each response is a bigger share of it, so fewer are needed. The finite population correction divides the large population figure by one plus that figure minus one over the population. For 1,000 people, 385 becomes 278; for 200 people it becomes 132. Once a population runs into the tens of thousands, the correction barely changes the answer, which is why a national survey and a survey of one large city need similar sample sizes.
Responses are not invitations
The formula gives completed responses. If a quarter of the people you invite answer, you need to invite four times as many. A staff survey with management support might reach 60% or more; a cold email to customers might get a few percent. The calculator divides the responses needed by your expected rate to give the invitations to send, and warns when that is more than the population holds, in which case the honest plan is to invite everyone and report the wider margin.
Choosing a margin of error
The margin of error is how far the survey result may sit from the true answer at the chosen confidence. Halving the margin roughly quadruples the sample: 5% needs 385 responses, 2.5% needs 1,537. For a quick read on customer satisfaction, 5% or even 10% is often enough. For a figure that will be published or used to justify spending, 3% or tighter is safer. The table shows the trade off across population sizes.
When the sample is not random
The formula assumes everyone in the population had a known chance of being picked. A link posted on social media, or a survey only the most engaged customers answer, does not meet that assumption, so the margin of error does not really apply. Size still helps, but bias matters more: a large self selected sample can be confidently wrong. Invite a random selection where you can, send reminders, and compare who answered with who did not.
Building the survey itself
Once the sample is set, the survey needs to be short enough that people finish it. The form builder makes classic and conversational forms, and its CSV export of responses can be opened in a spreadsheet or the CSV tools on this site for analysis. Keep the key question near the start, so even people who drop out answer it.
Limits
- Assumes a simple random sample. Stratified, cluster and quota designs need their own calculations.
- Gives the sample for one yes or no style percentage. Comparing groups, such as two regions, needs a bigger sample for each group.
- A response rate is a guess until you run the survey; plan for the lower end.
- People who answer can differ from those who do not, and no sample size fixes that bias.
What it does not do
- It does not pick the sample for you.
- It does not weight results.
- It does not store your figures.
Questions people ask
How many responses does my survey need?
For a large population, 385 responses give a 5% margin of error at 95% confidence. For a smaller group, enter its size and the number drops, for example 278 for 1,000 people. If you plan to compare groups, each group needs enough responses on its own.
Why use 50% as the expected share?
The formula needs a guess at the answer, and 50% gives the largest, safest sample. If you know the answer will be near 10% or 90%, a smaller sample gives the same margin. When there is no prior survey to go on, 50% protects against a sample that turns out too small.
What if my population is very small?
Survey everyone if you can. With a population of 50, the formula asks for 45 responses at 95% and 5%, so a census is simpler and removes sampling error altogether. Non response still matters: if only half reply, the result describes those who replied.
Is a bigger sample always better?
Up to a point. Going from 100 to 1,000 responses shrinks the margin of error a lot; going from 1,000 to 10,000 shrinks it much less. Past a thousand or so, effort is better spent on reaching the right people and writing clear questions, because bias and poor wording do more damage than sample size.
Do I need a bigger sample for a 1 to 10 rating question?
The formula here is for a percentage, such as the share who answer yes or score 9 or 10. Averages of rating scales use a different formula based on the spread of answers. In practice, a sample sized for a percentage at a 5% margin is usually adequate for a rating average as well.
Build the survey
Take what you made here into forms.
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Background reading: the question page on this.
Written and checked by the OneCraft team. Last checked .