Sample Size Calculator
Sample size calculator for surveys: respondents needed for a margin of error and confidence level, with finite-population correction.
n = n01 + (n0 − 1)/N · n0 = z² p(1 − p)E²
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
n₀ = z²p(1 − p)/E², corrected for a population of N: n = n₀ / (1 + (n₀ − 1)/N).
With 95 % confidence, ±5 % and p = 50 %, a large population needs about 385 responses.
Formula
n = n01 + (n0 − 1)/N · n0 = z² p(1 − p)E²
| Symbol | Quantity | Units |
|---|---|---|
| z | Z value (1.96 = 95 %) | — |
| p | Expected proportion | %, × |
| E | Margin of error | %, × |
| N | Population size | — |
| n | Required sample size | — |
Worked example
Given: z = 1.96 · p = 30 % · E = 5 % · N = 10 000
n = n01 + (n0 − 1)/N
Result: n = 312.637
Frequently asked questions
Sample for N = 10 000, p = 30 %, ±5 %, 95 %?
About 312.6, so 313 responses.