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Calculation Machine

Sample Size Calculator

How many responses you need for a reliable survey.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
Required sample size
385
Unadjusted (infinite population)
385
Margin of error achieved
5%
Responses needed at 60% response rate
641

Working

  1. 1n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.2

Quick answer

Required sample size is z²·p(1−p) ÷ e², adjusted downward when the population is small.

The formula

n = z²·p(1−p) ÷ e²

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Margin of error5 %
  • Confidence level95%
  • Population size (0 for unlimited)0
  • Expected proportion50 %

Result

  • Required sample size385
  • Unadjusted (infinite population)385
  • Margin of error achieved5%
  • Responses needed at 60% response rate641

How to use the Sample Size Calculator

  1. 1Set the margin of error you can live with.
  2. 2Choose a confidence level.
  3. 3Enter the population size if it is small and known.

Frequently asked questions

Why use 50% as the proportion?

It maximises variance, giving the most conservative (largest) required sample when you have no prior estimate.

Does population size matter?

Only for small populations. Beyond about 20,000 the required sample barely changes.

About this calculator