Sample Size Calculator

1. Enter the population size, or check "Unknown" if your population is very large (the formula then uses the infinite population version, which gives a slightly larger sample size).
2. Choose the confidence level. 95% is standard for most surveys. 99% needs a larger sample; 90% needs fewer respondents.
3. Set the margin of error. A 5% margin of error means your results could be off by plus or minus 5 percentage points.
4. Enter the expected proportion. If you expect about 40% of respondents to answer yes, enter 40. If unsure, use 50% (gives the largest, most conservative sample size).

For unknown/very large population:
  n = Z² × p(1-p) / e²

For finite population (size N):
  n_adjusted = n / (1 + (n-1)/N)

Where:
  Z = z-score for confidence level (1.96 for 95%)
  p = expected proportion (0.50 for maximum sample size)
  e = margin of error as decimal (0.05 for 5%)
  N = population size

Example: 95% CI, 5% margin, p=50%, N=10000
  n = 1.96² × 0.5 × 0.5 / 0.05²
    = 3.8416 × 0.25 / 0.0025
    = 0.9604 / 0.0025
    = 384.16 → 385

  n_adjusted = 385 / (1 + (385-1)/10000)
             = 385 / (1 + 0.0384)
             = 385 / 1.0384
             = 370.8 → 371