Margin of Error Calculator
Calculate the margin of error for a survey result.
What the Margin of Error Calculator does
Margin of error expresses the sampling uncertainty in a survey result. It depends on sample size, the proportion measured and the confidence level — but not on the size of the population, unless the sample is a large share of it.
Formula
MoE = z × √(p(1 − p) ÷ n)With finite population: multiply by √((N − n) ÷ (N − 1))
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Sample size | number | Yes | Accepts 1 or more. |
| Sample proportion | % | Yes | 50% gives the largest, most conservative margin. |
| Confidence level | one of 6 options | Yes | — |
| Population size | number | Optional | Accepts 0 or more. |
How to use it
- Choose Confidence level.
- Enter Sample size and Sample proportion.
- Optionally add Population size.
- Select Calculate.
Worked example
A poll of 1,000 people where 52% support a proposal, at 95% confidence.
- Sample size
- 1000
- Proportion
- 52
- Confidence
- 95%
±3.10 percentage points, so support lies between 48.9% and 55.1% — statistically a tie.
Frequently asked questions
Does population size matter?
Barely, unless your sample is a substantial fraction of it. Polling 1,000 people gives roughly the same margin whether the population is 100,000 or 100 million.
Why do polls use around 1,000 respondents?
It is the point where the margin drops to about ±3 points. Getting to ±1.5 would require 4,000 respondents at four times the cost.