Sample Size Calculator

This sample size calculator tells you how many responses you need for a survey or study to reach a chosen confidence level and margin of error. It adjusts for smaller populations and can tell you how many people to contact based on your expected response rate.

Sample size formula

n₀ = z² × p × (1 − p) ÷ e²

z is the z-score for your confidence level, p is the expected proportion and e is the margin of error, both as decimals. For a known population N, the finite population correction gives:

n = n₀ ÷ (1 + (n₀ − 1) ÷ N)

Common z-scores

Confidence level z-score
90% 1.645
95% 1.960
99% 2.576

Worked example

For 95% confidence and a ±5% margin of error with p = 50%, n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.2, so you need 385 responses. If the whole population is only 10,000 people, you need 370. If you expect a 25% response rate, invite 1,480 people.

Choosing your inputs

  • Proportion: use 50% if you have no prior estimate; it gives the largest, safest sample size.
  • Margin of error: halving the margin of error roughly quadruples the sample needed.
  • Population: above about 20,000 people, population size barely changes the answer.

Frequently asked questions

What is a good sample size for a survey?

For a large population, about 385 responses give a ±5% margin of error at 95% confidence, and about 1,068 give ±3%.

Why use 50% as the proportion?

p × (1 − p) is largest at 50%, so it gives the biggest sample size and guarantees your margin of error if you do not know the true proportion.

Does population size matter?

Only when the population is small. For large populations, the required sample is almost the same whether there are 100,000 or 100 million people.

What is margin of error?

The range above and below a survey result within which the true value is likely to fall. A result of 60% ±5% means the true figure is likely between 55% and 65%.

Does a bigger sample fix a biased survey?

No. Sample size reduces random error, but not bias from who chooses to respond or how questions are worded.

Related calculators

Last reviewed: October 2026.

Scroll to Top