Math
Sample Size Calculator
Find the minimum sample size needed for your survey or experiment. Set confidence level, margin of error, and population size.
Required Sample Size
385
At 95% confidence · ±5% margin of error
Sample size by margin of error (at 95% confidence)
±1%
9,604
±2%
2,401
±3%
1,068
±5%
385
±10%
97
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Sample size formula
For an infinite population: n = (Z² × p × (1−p)) / e²
For a finite population: n_adj = n / (1 + (n−1)/N)
- Z = Z-score for confidence level (1.96 for 95%)
- p = Expected proportion (use 0.5 for maximum sample size)
- e = Margin of error as decimal (0.05 for ±5%)
- N = Population size (for finite correction)
Common Z-scores
- 90% confidence → Z = 1.645
- 95% confidence → Z = 1.960
- 99% confidence → Z = 2.576
Why use p = 0.5?
When you don't know the expected proportion, p = 0.5 gives the most conservative (largest) required sample size. This ensures your sample is large enough no matter what the true proportion is.