Online Tool Store
Margin of Error Calculator
Calculate margin of error from sample size and confidence level, and the sample size needed to reach a target margin.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Margin of error
Find the margin from a sample size, or the sample size needed for a target margin.
Margin of error
Required sample size: 4,262
How the Margin of Error Calculator works
- Enter the sample size and the confidence level you want to report at.
- Read the margin, and apply it to your observed result rather than quoting the result alone.
- To halve the margin, quadruple the sample — the relationship is square-root, not linear.
The method
Margin of error for a proportion depends on the sample size and the proportion itself, and shrinks with the square root of n.
MOE = z × √(p(1−p) ÷ n), with z = 1.96 at 95% confidence
At n = 1,000 and p = 0.5, that is 1.96 × √(0.25/1000) ≈ 0.031, or ±3.1 points — and reaching ±1.5 points needs about 4,000 responses.
FAQ
Why does population size barely matter?
Because for populations much larger than the sample, the margin depends almost entirely on sample size. Polling 1,000 people gives a similar margin whether the population is a million or a hundred million.
What does a 95% confidence level mean?
That if the same survey were repeated many times, about 95% of the intervals produced would contain the true value. It is a statement about the procedure, not a 95% probability about this particular result.
Does margin of error cover all survey error?
No, and this is the important caveat. It covers sampling error only. Non-response bias, question wording, and an unrepresentative sampling frame are usually larger sources of error and appear nowhere in the calculation.
How we compare
| Feature | Online Tool Store | A graphing calculator | A stats package |
|---|---|---|---|
| Sample size solver | ✓ | Manual | ✓ |
| Shows the formula | ✓ | ✗ | ✓ |
| No stats package | ✓ | ✓ | ✗ |
| Covers non-sampling error | ✗ | ✗ | ✗ |
Margin of Error Calculator is explicit that it measures sampling error only — question wording and non-response usually matter more and appear in no formula.