Margin of Error Calculator
Find the margin of error of a survey proportion from the sample size, proportion and confidence level, with an optional population size.
Change the values and press Calculate to work out your own figures.
Enter the confidence level, sample size, sample proportion and (optionally) the population size.
Show the working
- MOE = z × √(p(1 − p) ÷ n) = 0.09601823353
How to use it
Enter the confidence level, sample size, sample proportion and (optionally) the population size.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
MOE = z √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))
Only sampling error
The margin of error covers random sampling error only; it doesn't account for biased questions or who chose to answer.
Questions
What is the margin of error for 1,000 responses?
About ±3.1% at 95% confidence.
Why does 50% give the largest margin?
p(1 − p) is largest at p = 0.5.
Formulas
MOE = z √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).