Sample Size Calculator
Survey responses needed for a confidence level and margin of error, and the reverse.
About this tool
Choose the confidence level and margin of error, optionally enter the population size, expected proportion and response rate. The tool gives the responses needed, invitations to send and share of the population, plus the margin of error for responses you already have and a table for common margins at 90, 95 and 99% confidence.
How sample size is worked out
The standard formula, Cochran's, is n = zยฒ ร p(1 โ p) รท eยฒ, where z is 1.96 for 95% confidence, p the expected proportion and e the margin of error. With p = 50% โ the safe default that gives the largest sample โ 95% confidence and ยฑ5% needs 385 responses from a large population; ยฑ3% needs 1,068 and ยฑ1% needs 9,604, because halving the margin quadruples the sample. When you survey a known group, such as 2,000 customers or 300 staff, the finite-population correction n รท (1 + (n โ 1) รท N) lowers the requirement: 323 for 2,000 at ยฑ5%. The response rate turns responses into the number of invitations to send. Honest notes: every formula here assumes a random sample; a link shared on social media is self-selected, and no sample size fixes a biased one. Each subgroup you want to report separately needs its own sample. The NPS calculator applies the same statistics to a score, the A/B test calculator compares two versions, and Standard deviation explained: what it measures, how it's calculated, and the 68โ95โ99.7 rule covers the underlying spread.
Frequently asked questions
How many survey responses do I need?
For 95% confidence and a ยฑ5% margin of error, about 385 from a large population. Fewer are needed for a small known population: about 323 from 2,000 people.
What confidence level should I use?
95% is the standard for most research. Use 90% for quick internal decisions and 99% when being wrong is costly.
Why use 50% as the expected proportion?
p(1 โ p) is largest at 50%, so it gives the most conservative (largest) sample size when you don't know what to expect.
Is any data stored?
No. The calculation runs in your browser and nothing is saved or sent.