Sample Size Calculator

This calculator uses the standard survey sample size formula: n = (z² × p × (1 − p)) ÷ e², where z is the critical value for your confidence level, p is the expected proportion (50% is the most conservative, producing the largest sample size), and e is your margin of error. If you enter a population size, a finite population correction is applied to reduce the required sample size for smaller populations.

When the true proportion is unknown, 50% produces the largest possible required sample size, making it the safest, most conservative default. If you have a reasonable estimate of the true proportion from prior data, using it can reduce your required sample size.

For a 95% confidence level (z ≈ 1.96), a 5% margin of error, and the conservative 50% expected proportion, with no population size entered: n = (1.96² × 0.5 × 0.5) ÷ 0.05² = (3.8416 × 0.25) ÷ 0.0025 = 0.9604 ÷ 0.0025 = 384.16, rounded up to 385. So a survey of an unknown or large population would need at least 385 respondents to achieve that confidence level and margin of error.