What formula does this use?

It uses Cochran's formula n = z² × p × (1 − p) / e², with an optional finite-population correction n / (1 + (n − 1) / N) when you supply a population size.

Why use 50% for the proportion?

A proportion of 50% maximises p × (1 − p), giving the largest and therefore safest required sample when you have no prior estimate.

Does a smaller population reduce the sample needed?

Yes. For small finite populations the correction lowers the required sample, since you are sampling a larger fraction of the whole.

What z-score goes with each confidence level?

The tool uses 1.282 for 80%, 1.645 for 90%, 1.960 for 95%, 2.326 for 98% and 2.576 for 99% — the two-sided critical values of the standard normal distribution.

How big a sample do I need for a 95% confidence level and 5% margin?

About 385 respondents for a very large population: 1.96² × 0.5 × 0.5 ÷ 0.05² ≈ 384.16, rounded up.

Does a tighter margin of error need a bigger sample?

Yes, and it grows fast. Because the margin is squared in the denominator, halving the margin of error roughly quadruples the required sample.

Sample Size Calculator

Sample size calculator

This tool finds the survey sample size you need for a target margin of error and confidence level. It is built for researchers, marketers and students planning a poll or A/B test who need to know how many responses make the result statistically reliable.

How it works

It uses Cochran’s formula for estimating a proportion:

n₀ = z² · p · (1 − p) ÷ e²

where z is the critical value for your confidence level, p is the expected proportion, and e is the margin of error as a decimal. When you supply a total population N, the finite-population correction is applied:

n = n₀ ÷ ( 1 + (n₀ − 1) ÷ N )

The result is rounded up to a whole number of respondents.

Example

95% confidence (z = 1.96), 5% margin (e = 0.05), proportion 50% (p = 0.5), population unknown:

n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² ≈ 384.16 → 385 respondents

Add a population of 5,000 and the correction trims it to roughly 357. All maths runs in your browser.