Estimate the sample size needed for a proportion with a chosen margin of error and z critical value.
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Use this calculator to plan how many independent observations you need for a proportion (a poll, a conversion rate, a prevalence) so the margin of error stays within a target. It solves the usual large-population formula and rounds n up to the next whole number.
The formula is: n = p (1 − p) (z / MoE)², then rounded up. p = 0.5 is the cautious default because it maximises n. A 3% margin (0.03) at 95% (z = 1.96) with p = 0.5 needs about 1068 people.
Finite-population corrections, clustering, and design effects are ignored. MoE is a proportion (0.03 means ±3 percentage points), not a percent written as 3. This is for a proportion, not for a mean.
Proportion (p): Guessed true proportion, 0 to 1. Use 0.5 if unsure.
Margin of error: Desired half-width as a proportion, for example 0.03.
z: Normal critical value. 1.96 is the usual 95% choice.
n: Required sample size, rounded up.
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