Sample Size Calculator
Calculate the sample size needed for surveys and studies given confidence level, margin of error, expected proportion, and population size.
Study design
Updates as you typeConfidence
Confidence level ?
z = 1.96
%
Precision
Margin of error ?
±5%
%
Estimated proportion ?
50% (worst case)
%
Population
Population size ?
Unlimited
people
Formula
n
=
z2 · p · (1 − p)
E2
nadj
=
n
1 + (n − 1) / N
- n
- Required sample size
- z
- Z-critical value for the confidence level (1.96 for 95%)
- p
- Estimated proportion (use 0.5 when unsure — gives the largest n)
- E
- Margin of error as a decimal (e.g. 0.05 for ±5%)
- N
- Population size (for the finite correction)
Worked example — your numbers
- z = —
- p · (1 − p) = —
- E2 = —
- n = z2 · p · (1 − p) / E2 = —
- n (rounded up) = —
- nadj = —
- Required sample size = —
The finite-population correction only meaningfully shrinks n when your population is comparable to the raw sample — say under ~20× the raw n. Above that, the infinite-population formula is accurate enough for most work.