Toolstia / Sample size calculator
Sample size calculator
Before running a survey you need to know how many responses are enough. Choose a confidence level and a margin of error, add the population size if it is small, and see the sample size you need.
Uses n = z² × p(1−p) ÷ e². Using 50% for the proportion gives the largest, safest sample. If you give the population size, the answer is reduced with the finite population correction.
How it works
- Choose the confidence level and margin of error.
- Leave the proportion at 50% unless you have a good estimate.
- Add the population size if you know it, and read the sample size.
The formula
n = z² × p × (1 − p) ÷ e², where z comes from the confidence level, p is the expected proportion and e is the margin of error as a decimal. At 95% confidence and a 5% margin, with p = 50%, you need 385 responses.
Why 50%
The product p × (1 − p) is largest at 50%, so assuming 50% gives the biggest, safest sample size when you do not know the likely answer in advance.
Small populations
If you are sampling from a small group, such as 1,000 customers, the finite population correction reduces the number needed. For large populations it makes almost no difference.
Response rate
The result is the number of completed responses. If only a third of people reply, you must invite roughly three times as many.
Questions
Is bigger always better?
Not past a point. Going from a 5% to a 1% margin needs 25 times more responses.
Does it apply to experiments?
This is for estimating a proportion by survey. Experiments comparing groups use a different calculation.
Is anything uploaded?
No. Your numbers stays in your browser and is never sent anywhere.