Sample Size Calculator
Enter your desired confidence level, margin of error, and (optionally) total population size to calculate the minimum sample size needed for a statistically sound survey or study.
How the Sample Size formula works
The base sample size formula, with an optional finite population correction:
n₀ = (Z² × p × (1−p)) / e² n = n₀ / (1 + (n₀−1)/N) [only if population size N is known]
Z is the z-score for your confidence level (1.96 for 95%), p is the expected proportion (0.5 is used by default for maximum required sample size), and e is the margin of error as a decimal.
Step-by-step calculation
- Look up the Z-score for your chosen confidence level.
- Square the Z-score and multiply by p×(1−p) — using 0.5 for p if you don't have a prior estimate, since that maximizes the required sample size.
- Divide by the margin of error squared to get the base sample size.
- If you know your total population size, apply the finite population correction to reduce the required sample size accordingly.
Worked example
For a 95% confidence level (Z=1.96), 5% margin of error, and p=0.5, with no population size given: n₀ = (1.96² × 0.5 × 0.5) / 0.05² = 0.9604 / 0.0025 ≈ 384 respondents.
Frequently asked questions
Why does the calculator default p to 0.5?
p×(1−p) is largest when p=0.5, so using 0.5 without a better estimate gives the most conservative (largest) required sample size — a safe default when you don't already know roughly what proportion to expect.
Do I need the finite population correction?
Only if you're sampling from a relatively small, known population (like all employees at a mid-sized company). For large or effectively unlimited populations (like 'all adults in a country'), the correction makes very little difference and can be skipped.