Margin of Error Calculator
Calculate the margin of error for a survey result given the sample proportion, sample size and confidence level.
Your results
Calculation breakdown
- Margin of error
- E = z × √(p × (1 − p) / n)
Worked example
A poll of 400 voters finds 50% support for a proposal. At 95% confidence, the margin of error is about ±4.9 percentage points, so the true support likely lies between roughly 45.1% and 54.9%.
Assumptions
- Assumes a simple random sample and that the normal approximation to the binomial distribution is valid (reasonable for n × p and n × (1 − p) both above about 5).
- Real-world surveys can have additional error from non-response or sampling bias not captured here.
How this calculator works
Enter the sample proportion, sample size and confidence level from a survey or poll. The calculator returns the margin of error and the resulting confidence interval for the true population proportion.
Frequently asked questions
How does sample size affect margin of error?
Larger sample sizes reduce the margin of error, but the relationship isn't linear — you need roughly four times the sample size to halve the margin of error.
Why does the margin of error use the sample proportion?
The variability of a proportion is largest near 50%, so the sample proportion directly affects how wide the margin of error is.
Does this account for non-response bias?
No, it only covers sampling error from a simple random sample; real surveys can have additional error from non-response or selection bias.