How it works
This calculator finds the minimum number of completed responses needed so that a survey proportion is within your chosen margin of error at your chosen confidence level. At 95% confidence and ±5%, you need 385 responses from a large population.
The expected proportion is your best guess of the answer (for example, 30% will say yes). If you have no idea, use 50%, which maximizes p(1 − p) and so gives the most conservative sample size.
If your population is small and known, such as 800 employees, the finite population correction reduces the sample needed. For populations above roughly 100,000 the correction makes little difference.
Formula
n₀ = z² × p(1 − p) ÷ e² · With population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
Questions people ask
Why do I only need about 385 people to survey a whole country?
Precision depends mainly on the number of responses, not the share of the population surveyed. Once the population is large, adding more people to it barely changes the sample size needed.
What happens if I halve the margin of error?
The required sample roughly quadruples, because the margin of error shrinks with the square root of the sample size. Going from ±5% to ±2.5% at 95% confidence takes you from 385 to 1,537 responses.
Does this account for people who do not respond?
No. The result is completed responses. Divide by your expected response rate to estimate how many people to invite; the 30% row shows one example.