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Sample Size for Margin of Error of a Proportion Calculator

n = z² · p̂(1 − p̂) / E².

Compute the minimum sample size needed for a desired margin of error E around a proportion p̂ at a given confidence level: n = z² · p̂(1 − p̂) / E². Use p̂ = 0.5 if no prior estimate (most conservative — gives the largest n). For E = 3 % at 95 % CI with p̂ = 0.5: n ≈ 1067.

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 = ceil(z² · p · (1−p) / E²).

In depth

Compute the minimum sample size needed for a desired margin of error E around a proportion p̂ at a given confidence level: n = z² · p̂(1 − p̂) / E². Use p̂ = 0.5 if no prior estimate (most conservative — gives the largest n). For E = 3 % at 95 % CI with p̂ = 0.5: n ≈ 1067.