Sample Size for Margin of Error

n = (z × σ / E)². Required sample size for given margin E at confidence z.

Result

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How to use this calculator

Enter SD + desired margin + confidence.

About this calculator

Required sample size for desired margin of error: n = (z σ / E)². Doubling precision (halving E) quadruples n. Use sample SD if population unknown (slight bias for small n). For proportions: n = (z² × p(1−p)) / E² with p as max-uncertainty 0.5 default. Pre-survey sizing essential for budget planning. Source: NIST Handbook; standard sampling textbooks.

Frequently asked

Why squared?+

Standard error scales as 1/√n. Margin = z × SE = z × σ/√n. Solve for n: square.

Don't know σ?+

Use rough estimate, pilot sample, or worst-case (range/4). Plan to over-sample.

For proportions?+

n = (z²p(1−p))/E². p=0.5 maximum (use for unknown). At ε=±3%, 95% CI: ~1067.

Doubling sample halves margin?+

No — quadrupling n halves margin. Diminishing returns.

Finite population correction?+

For small populations (n > 5% of N): n_adj = n / (1 + (n−1)/N). Reduces required n.

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