Sample Size Calculator

Confidence level

Common choices: 90%, 95% (default), 99%.

Margin of error

As a percentage (e.g., 5 = ±5%).

Estimated proportion

Percent of the population with the attribute. Use 50% if unknown (worst case).

Population size (optional)

Leave blank if effectively infinite or unknown.

Design effect

Use 1.0 for simple random sampling; >1 for clustering/complex designs.

Sample Size – Quick Cheat Sheet (Proportion)

Goal: Find n to estimate a population proportion within ±e at confidence 1−α.
Inputs: Confidence (z), margin of error e (%), estimated proportion p (%), population size N (optional), design effect (DEFF).
Formula (infinite N): n₀ = (z² · p(1−p)) / e², where p and e are fractions (e.g., 0.5 and 0.05).
Finite population: n = n₀ / (1 + (n₀ − 1) / N).
Complex designs: multiply by DEFF. Round up to the next whole number.
Unknown p? Use 50% (worst case, largest n).

Reference z-values