About this calculator
Add the population size when your sample is a noticeable share of it, such as surveying 500 of 2,000 employees.
How to use it
- Enter the sample size and result.
- Choose the confidence level.
- Optionally add the population size.
The formula
MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))
- z
- critical value (1.96 at 95%)
- p
- sample proportion
- n
- sample size
- N
- population size
Worked example
1,000 people at 50%, 95% confidence
- MOE = 1.96 × √(0.25 ÷ 1,000) = 3.1%.
What the result means
The margin covers random sampling error only, not biased questions or who chose to respond.
Assumptions
- A random sample.
Limitations
- For very small samples or results near 0% or 100%, use the Wilson interval in the confidence interval calculator.
Frequently asked questions
Why use 50%?
It gives the largest margin, so it is the safe choice before you know the result.
Does a bigger population need a bigger sample?
Hardly, once the population is large. A sample of 1,000 gives about ± 3% for a city or a country.
What margin is acceptable?
± 5% is common for surveys; ± 3% for polls.
Last reviewed on 6 October 2026. Found a mistake? Tell us.