basic

Sample Size for a Proportion Calculator

n = z² · p̂ · (1 − p̂) / E².

Compute the minimum sample size required to estimate a proportion within a target margin of error E at a chosen confidence level (z critical): n = z² · p̂(1 − p̂) / E². Use p̂ = 0.5 for the most conservative (largest) estimate.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

n = z² · p̂ · (1 − p̂) / E²

In depth

Compute the minimum sample size required to estimate a proportion within a target margin of error E at a chosen confidence level (z critical): n = z² · p̂(1 − p̂) / E². Use p̂ = 0.5 for the most conservative (largest) estimate.