How many responses do you need?
The sample size of a survey decides how trustworthy its results are. Too few responses and the margin of error is wide; too many and you waste time and money. This calculator finds the smallest sample that gives the confidence level and margin of error you want.
You can plan a survey about a percentage (a poll, an approval rating) or about an average (mean height, mean spend). If you know the size of the whole population you can add it for a finite-population correction, which reduces the sample needed for small groups.
How it is calculated
For a percentage: n = z² × p × (1 − p) ÷ e²
For a mean: n = (z × σ ÷ e)²
Finite population: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
Worked example
95% confidence, ±5% margin, unknown percentage (use 50%)
- z-score for 95%
- 1.96
- Sample size needed
- 385
- With a ±3% margin
- 1,068
Choosing the settings
- Confidence level: 95% is standard. Higher confidence needs a larger sample.
- Margin of error: the ± range you can accept. Halving it roughly quadruples the sample.
- Expected percentage: keep 50% if you do not know, because it gives the largest, safest sample.