Sample Size Calculator
Deciding How Many Respondents You Actually Need
Before running a survey or an experiment, there's a question that has to come before "what will people say": how many of them do you need to ask? Sample too few and your results are noise; sample far more than necessary and you've wasted budget and time. Cochran's formula answers this directly from three inputs — how confident you want to be, how much error you'll tolerate, and (optionally) how large the total population is.
The Formula
With a known population size N, apply the finite population correction:
n = n₀ ÷ (1 + ((n₀ − 1) ÷ N))
Z is the critical value for your chosen confidence level, p is the expected proportion in the population (50% is the conservative default when it's unknown, since it maximizes the required sample size), and E is your acceptable margin of error.
Sample Sizes at Common Settings
Using the conservative p = 50% assumption, required sample size for an unlimited population looks like this:
| Confidence level | ±3% margin | ±5% margin | ±10% margin |
|---|---|---|---|
| 90% | 752 | 271 | 68 |
| 95% | 1,068 | 385 | 97 |
| 99% | 1,844 | 664 | 166 |
The famous "385 respondents" figure quoted for many national surveys is exactly the 95% confidence, ±5% margin case above.
Where This Matters
- Market research — sizing a customer survey before fielding it.
- Political polling — the standard "margin of error" quoted alongside poll results traces back to this calculation.
- Clinical and scientific studies — determining enrollment targets to detect an effect with adequate precision.
- Quality auditing — sampling a manageable number of units from a production run instead of inspecting every single one.
How to Use This Calculator
- Select a confidence level from the dropdown (95% is the most common default).
- Enter your desired margin of error as a percentage.
- Optionally enter an expected population proportion (defaults to 50%, the most conservative assumption).
- Optionally enter a known population size to apply the finite population correction.
- Select Calculate to get the required sample size, rounded up to a whole respondent.
Related Calculations
Once your survey is complete, use the Confidence Interval Calculator to interpret the results, or check the Standard Error Calculator to see how precision changes with sample size.