Sample Size Calculator
Choose the confidence level and the margin of error you can accept. The page gives the number of responses needed, adjusted for the size of the group if you know it.
Worked examples
A large population
95% confidence, 5% margin, 50%
385 responses
1.96² × 0.25 ÷ 0.05² = 384.15, rounded up.
A group of 1,000
95% confidence, 5% margin, 50%, group 1,000
278 responses
After the finite population correction.
About Sample Size Calculator
Before a survey or experiment, you need to know how many responses will give a result you can trust. The sample size depends on three choices: how confident you want to be, how much error you can accept, and how varied the answers are likely to be. For a percentage, the size is z² × p × (1 - p) divided by the margin of error squared. With 95% confidence, a 5% margin and the cautious guess of 50%, you need 385 people.
If the group you are sampling is small, you need fewer, because each answer covers a larger share of the group. When you enter the size of the group, the page applies the finite population correction: a school of 1,000 pupils needs 278 responses rather than 385. For an average, the size is (z × standard deviation divided by the margin) squared, so you need an estimate of the standard deviation from earlier data or a small pilot. The result is always rounded up to a whole number.
How to use Sample Size Calculator
- Choose whether you are measuring a percentage or an average.
- Choose the confidence level and enter the margin of error you can accept.
- Enter the expected percentage, using 50% if you do not know, or the expected standard deviation.
- Optionally enter the size of the whole group, then read the number of responses needed.
Common uses
- Planning a customer or staff survey
- Choosing how many items to test in quality control
- Dissertation and research proposals
- Deciding how many measurements to take in a lab
Frequently asked questions
Why use 50% if I do not know the percentage?
Because p × (1 - p) is largest at 50%, so it gives the biggest sample size. You will have enough responses whatever the real percentage turns out to be.
How does a smaller margin of error change the size?
The size grows with the square of 1 over the margin. Halving the margin of error needs about four times as many responses.
What does the group size do?
For a small group, a smaller sample gives the same precision. For very large groups it makes almost no difference, so you can leave it empty.
Should I ask for more responses than the number shown?
Yes, if you expect some people not to reply. Divide the number needed by the expected reply rate to see how many to approach.
Which confidence level should I use?
The usual choice is 95%. Use 99% when a wrong answer would be costly, and 90% for a quick estimate.