Sample Size Calculator: How Many to Survey for a Mean or a Proportion, and for Comparing Two Groups
Work out how big a sample you need.
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How this calculator works
Choose to estimate a mean, a proportion, or to compare two means or two proportions.
Enter the confidence level and the margin of error, or the power and the difference you want to detect.
The calculator gives the sample size rounded up, with the critical values and the working.
Formulas used
- n = \left(\frac{z\sigma}{E}\right)^2
- n = \frac{z^2p(1 - p)}{E^2}
- n = \frac{2(z_{\alpha/2} + z_\beta)^2\sigma^2}{\Delta^2}
- n = \frac{n_0}{1 + (n_0 - 1)/N}
Worked example
With the default numbers in the calculator above:
- Critical z value for the confidence level (two-sided): 1.96
- Sample size before rounding: 96.0365
- Required sample size (rounded up): 97 (from 96.0365 before rounding up)
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? Estimate a proportion.
- Critical z value for the confidence level (two-sided): 1.96
- Sample size before rounding: 384.146
- Required sample size (rounded up): 385 (from 384.146 before rounding up)
Common questions
How big a sample do I need for a survey?
For a proportion with a margin of error of 5 percent at 95 percent confidence, about 385 people, whatever the size of a large population.
What is statistical power?
The chance that a study finds a difference when there really is one. 80 percent is the usual target.
Why use 50 percent if I do not know the proportion?
It gives the largest possible sample size, so the study will be big enough whatever the true value is.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any statistics text (sample size and power).
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