Sample Size Calculator
Pick a proportion (survey percentage) or a mean, set the margin of error and confidence level, and optionally the population size for a finite-population correction. The result is always rounded up.
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Formula
- Proportion:
n0 = z² × p × (1 - p) / E², with p and E as fractions (a 5-point margin is 0.05) - Mean:
n0 = z² × σ² / E² - Finite population N (optional):
n = n0 / (1 + (n0 - 1) / N) - The answer is rounded up to a whole number, and is never less than 1.
z is the normal quantile for the confidence level: 1.282 (80%), 1.645 (90%), 1.960 (95%), 2.576 (99%), 3.291 (99.9%).
Assumptions
- Simple random sampling and independent responses.
- For a mean, σ is an estimate from a pilot study or earlier data.
- The calculation gives the number of completed responses. Divide by your expected response rate to know how many people to contact.
Worked example
Proportion, 95% confidence, p = 50%, margin 5 points:
- n0 = 1.96² × 0.25 / 0.05² = 384.15, so 385
- With a population of 1,000: 384.15 / (1 + 383.15 / 1000) = 277.73, so 278
Mean, σ = 15, margin 3, 99% confidence: n0 = 2.576² × 15² / 3² = 165.87, so 166.
Frequently asked questions
How do you calculate sample size for a proportion?
Use n = z² × p(1-p) / E². For 95% confidence (z = 1.96), p = 50% and a 5-point margin, n = 1.96² × 0.25 / 0.05² = 384.15, which rounds up to 385.
Why use 50% as the expected proportion?
p(1-p) is largest at 50%, so it gives the biggest, safest sample. If you know the true value is near 10%, you need only 865 respondents for a 2-point margin at 95%, instead of 2,401 at 50%.
When does the population size matter?
Only when your sample is a sizeable share of a small population. The correction is n = n0 / (1 + (n0 - 1) / N). With n0 = 384.15 and N = 1,000 you need 278 people instead of 385. For a population of 100,000 or more it makes almost no difference.
How do I find the sample size for a mean?
Use n = z² × σ² / E², where σ is an estimated standard deviation. For σ = 15, a margin of 3 units and 99% confidence (z = 2.576), n = 165.87, so you need 166 measurements.