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.
Reading the result
- "Sample needed to halve the margin" is literally 4× the entered sample size, following directly from the inverse-square relationship — a fast answer to "what would twice the precision cost."
- Reading the full sensitivity table shows how flat the curve gets beyond a few thousand respondents, not just the single 1,000-to-2,000 comparison in the notes.
Assumptions and limitations
- The default 50% proportion is the most conservative assumption — a more accurate estimate of the true proportion, if known from prior data, would produce a smaller, more precise margin for the same sample size.
Common mistakes
- Reading a "statistically a tie" result as meaning the poll is uninformative — a margin spanning 50% means that specific comparison can't be called with confidence, but the range of plausible true values is still considerably narrowed.
- Treating margin of error as the only source of poll error — it captures sampling error alone, not non-response bias, question wording effects or coverage error.
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.