Sample Size for Margin of Error
n = (z × σ / E)². Required sample size for given margin E at confidence z.
Result
Required n
865
For 95% CI ± 1 on σ = 15.
- Population SD σ15
- Margin of error E1
- Confidence95%
- Critical z1.96
- Required n865
Step-by-step
- n = (z σ / E)² = (1.96 × 15 / 1)² = 864.36.
- Round up: 865.
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
Standard error scales as 1/√n. Margin = z × SE = z × σ/√n. Solve for n: square.
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