Sample Size Calculator

Plan a survey or study by finding the minimum sample for the precision you want. The default, 95% confidence and ± 5%, gives the well-known 385.

Estimating a
50% is the safe choice if unknown.
Leave blank for a very large population.
Results update as you type.

Sample size needed

385

for a large population

Before rounding up
384.14588
Critical z
1.95996

If you expect only a share of people to respond, divide by the response rate: 385 needed at a 40% response rate means inviting about 963.

About this calculator

If your population is small, such as a school or company, enter its size and the sample needed drops.

How to use it

  1. Choose proportion or mean.
  2. Set the confidence level and margin of error.
  3. Optionally add the population size.

The formula

n₀ = z² × p(1 − p) ÷ E²; n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
z
critical value
p
expected proportion
E
margin of error
N
population size

Worked example

95% confidence, ± 5%, unknown proportion

  1. n₀ = 1.96² × 0.25 ÷ 0.05² = 384.1, rounded up to 385.
  2. For a population of 2,000: 323.

What the result means

This is the number of completed responses. Divide by the expected response rate to know how many to invite.

Assumptions

  • A simple random sample.

Limitations

  • Cluster or stratified designs need adjustments.

Frequently asked questions

Why is 385 so common?

It is the sample for ± 5% at 95% confidence with p = 50% and a large population.

What if I want ± 3%?

About 1,068.

Do I always round up?

Yes, rounding down would miss the target precision.

Last reviewed on 6 October 2026. Found a mistake? Tell us.