MultiConvers

Sample Size Calculator

Enter a confidence level, a margin of error and an expected proportion. The result is the number of observations Cochran’s formula asks for, rounded up.

How it works

This is a sample-size plan for a single proportion, using a normal (z) approximation — not a t-interval for a mean. n = z² p (1−p) / E², then rounded up to the next whole person. p is the expected proportion (0.5 if unknown, which maximises n).

E is the margin as a decimal (5% → 0.05). z comes from the two-sided normal quantile for the confidence level (1.96 at 95%). If you supply a finite population N, the page applies n′ = n / (1 + (n−1)/N).

Formula

n = z² p (1 − p) / E²
n′ = n / (1 + (n − 1) / N)   (optional FPC)
Then round up.

Worked examples

  • A typical opinion poll

    95% confidence, p = 50%, E = 5% → 385

Useful notes

  • This is not a power calculation for a clinical trial or an A/B test.
  • z values are two-sided standard-normal quantiles.

FAQ

Why use 50% for the proportion?

p(1−p) is largest at 0.5, so the sample size is conservative when you do not know the outcome rate.

What does the margin of error mean?

It is the plus-or-minus around the estimated percentage, not a percentage of the population size.

When do I fill in population?

When the group is small enough that sampling without replacement shrinks the needed n. Leave it blank for a large or unknown population.

Related tools

See all Statistics tools.