Mathematics · Statistics
Sample Size Calculator — Surveys and Studies
Find the sample size you need for a survey or study: for a proportion (like the share who say yes) from the margin of error, confidence level and expected percentage, or for a mean from the standard deviation and margin of error. Add the population size to apply the finite-population correction for small populations.
Your inputs
Quick start — try a typical case
50 % gives the largest (safest) sample if you don't know.
Optional — for small populations (e.g. 2,000 employees). 0 = very large.
Your result Live
Sample Size Needed
385
For ±5% at 95% confidence
- Critical Value
- z = 1.96
- If You Expect a 20 % Non-response
- Contact about 482 people
How this is calculated
Proportion: n₀ = z² p(1 − p) ÷ E² · Mean: n₀ = (z σ ÷ E)² · finite population: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
- E
- Margin of error
- N
- Population size
The sample size grows with the square of the confidence z-value and shrinks with the square of the margin of error — halving the margin needs four times the people. For percentages, assuming 50 % gives the most conservative size. When the whole population is small, the finite-population correction reduces the sample you need.
Assumptions & sources
- Simple random sampling; everyone sampled responds.
- 1NIST/SEMATECH e-Handbook of Statistical Methods — US National Institute of Standards and Technology
- 2Sampling Techniques (3rd ed.) — Cochran's sample-size formula — W. G. Cochran, Wiley, 1977
Calculator ID MATH-SAMPLESIZE-001 · version 1.0.0
Common questions
How many people for ±5 % at 95 % confidence?
385 (1.96² × 0.25 ÷ 0.05²), for a large population.
Does population size matter?
Only when it's small. For 2,000 people you'd need 323 instead of 385; for a million it's still 385.
Why 50 %?
p(1 − p) is largest at 50 %, so assuming it guarantees the margin of error whatever the true percentage turns out to be.