Sample Size Calculator Formula & How It Works
n = z² × p(1−p) / e² (infinite population) | n_adj = n / (1 + (n−1)/N)
- z = z-score for confidence level (1.96 for 95%)
- p = expected proportion (0.5 = maximum variance, most conservative)
- e = margin of error (e.g. 0.05 for ±5%)
- N = population size (for finite population correction)
The required sample size depends on: desired confidence level (higher = larger sample), acceptable margin of error (smaller margin = larger sample), and expected proportion (0.5 is most conservative). For finite populations, apply the finite population correction to reduce n. Most national surveys use n=1,000–1,500 for ±3% margin at 95% confidence.