Sample Size Calculator guide
Sample Size Calculator: How Many Survey Responses Do I Need?
Use our sample size calculator to work out how many survey responses you need for your confidence level and margin of error, with the finite population correction.
By the AllCalculator editorial teamUpdated 15 October 20261 min read
Survey too few people and your results could be well off the mark. Survey too many and you waste time and money. Our Sample Size Calculator tells you how many responses you need.
How to use the calculator (Sample Size Calculator)
- Choose your confidence level. 95% is standard.
- Enter your margin of error, for example ±5%.
- Enter the expected proportion. Use 50% if you don't know, because it gives the largest sample.
- If your population is small, enter its size.
The formula
n = z² × p(1 − p) ÷ e²
where z is the score for your confidence level (1.96 for 95%), p is the expected proportion and e is the margin of error. For smaller populations, the calculator applies the finite population correction: n ÷ (1 + (n − 1) ÷ N).
A worked example
With the calculator's default settings, 95% confidence and ±5% margin:
- n = 1.96² × 0.5 × 0.5 ÷ 0.05² = 385
If you're surveying a group of 2,000 staff, you'd need 323 responses. With a typical 30% response rate, that means inviting about 1,075 people.
Choosing the margin of error
| Margin of error | Sample needed (95%, large population) |
|---|---|
| ±10% | 97 |
| ±5% | 385 |
| ±3% | 1,068 |
| ±2% | 2,401 |
Halving the margin of error roughly quadruples the sample size.
Once you have results, analyse them with our Statistics Calculator.
Frequently asked questions
Why use 50% as the proportion?
It gives the most cautious answer. If you already know roughly what the result will be, you can use that figure.
Does population size matter?
Only for small populations. Above about 100,000, the sample size barely changes.
Is a bigger sample always better?
It reduces random error, but not bias. A large sample of the wrong people is still misleading.
Plan your survey properly with the Sample Size Calculator.
Sources and further reading
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.