Sample Size Calculator
Calculate the sample size needed for a survey or study, given your confidence level and margin of error.
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Your result
385
Required sample size
AI explanation
Formula
n = Z² × p × (1−p) ÷ E², with a finite-population correction applied when a population size is givenWorked example
95% confidence, 5% margin of error, unknown population
| Field | Value |
|---|---|
| Confidence level | 95 |
| Margin of error (%) | 5 |
| Expected population proportion | 0.5 |
| Population size (0 if unknown or very large) | 0 |
| Required sample size | 385 |
Assumptions
- Uses Cochran's formula for estimating a proportion.
- A population size of 0 means "unknown or very large," which skips the finite-population correction (the sample size no longer shrinks as population grows once it's large relative to the sample).
Frequently asked questions
Why is 385 such a common sample size recommendation?
For a 95% confidence level, 5% margin of error, and the most conservative 50% expected proportion, the formula always gives 385 — a widely cited standard figure in survey research.
What population proportion should I use if I don't know it?
Use 0.5 — it produces the largest (most conservative) required sample size, so it's safe even without prior knowledge of the true proportion.
Does a larger population always need a larger sample?
No — once the population is much larger than the required sample, further population growth barely affects the sample size needed (this is why national surveys with millions of people still only need a few hundred to a few thousand responses).