Free research tool
Sample size calculator
How many survey responses do you need? Pick your confidence level and margin of error — add your population size if you know it — and get the minimum sample from Cochran's formula with the finite population correction.
Required sample size
385
How it works
Cochran's formula for an unlimited population:
n₀ = z² · p(1−p) / e²
where z is the z-score for your confidence level, p the expected proportion, and e the margin of error. With a known population N, the finite population correction shrinks it:
n = n₀ / (1 + (n₀ − 1) / N)
Results are rounded up — a sample can't include a fraction of a person. This gives the sample you need for a proportion estimate (e.g. "% of users who…"); means with known variance need a different formula.
Frequently asked questions
How many responses do I need for a survey?
For a large population at 95% confidence with a 5% margin of error and maximum variability (p = 0.5), Cochran’s formula gives 385 responses. A known, smaller population reduces this via the finite population correction — e.g. 278 for a population of 1,000.
What margin of error should I use?
5% is the common default for surveys; use 3% or lower when decisions are sensitive to small differences. Halving the margin of error roughly quadruples the required sample.
Why is p = 0.5 the default proportion?
p(1−p) is largest at p = 0.5, so it gives the most conservative (largest) sample size when you don’t know the true proportion in advance.