Margin of Error Calculator
Find the margin of error for your survey sample. Enter the sample size, population size, confidence level and expected proportion.
How margin of error works
The margin of error is the range within which the true population value is expected to fall, given your sample. If a survey reports 52% with a 4.9% margin of error at 95% confidence, the true value is expected to be between about 47.1% and 56.9%.
It depends on your sample size (larger samples shrink the margin), your confidence level (higher confidence widens it), and the expected proportion (50% gives the widest margin). If you provide the population size, the finite-population correction tightens the margin slightly.
The formula
e = z · √(p(1−p) ÷ n), with FPC: e = z · √(p(1−p) ÷ n) · √((N−n) ÷ (N−1))
z is the z-score for the confidence level, p is the expected proportion, n is the sample size, and N is the population size. The result is the margin of error as a percentage.
Worked example
A sample of 400 at 95% confidence
With an expected proportion of 50% and no finite-population correction: e = 1.96 × √(0.25 ÷ 400) = 1.96 × 0.025 = 0.049, so a 4.9% margin of error.
Frequently asked questions
What does a margin of error of 5% mean?
It means the reported percentage is expected to be within 5 percentage points of the true value, at the chosen confidence level. So 50% could really be between 45% and 55%.
Can I reduce the margin of error?
Yes — the most direct way is to increase your sample size. You can also lower your confidence level, though that makes the result less certain.
When does the population size matter?
Only for small populations relative to the sample. When the population is large or unknown, the finite-population correction has almost no effect, so it can be left blank.
Related research methods
- Survey Sampling
When to use this tool
Use this when you already have (or are planning) a sample and want to know the margin of error — the expected sampling error around an estimate.
Assumptions
- Random sampling from the population of interest.
- A specified confidence level.
Limitations
- The margin of error describes sampling variability only, not non-sampling errors such as non-response or measurement bias.
- It applies to a single estimate, not to differences between two estimates (which have a larger combined error).
How to interpret the result
A 4% margin of error at 95% confidence means the true population value is expected to fall within roughly ±4 percentage points of the sample estimate 95 times out of 100.
How to report the result
Report the margin of error together with the confidence level, sample size, and the observed (or assumed) proportion.
Next steps in your analysis
Related tools
Related guides
- Sample Size and Margin of Error: A Practical GuideHow sample size controls margin of error, the formulas behind both, the finite-population correction, and the practical caveats researchers should not skip.
- Confidence Intervals ExplainedWhat a confidence interval is, how to interpret the 95% level correctly, how to calculate one for a mean or a proportion, and what changes its width.
- Survey Research Statistics: A Practical GuideThe core statistics every survey researcher should understand — response, completion and incidence rates, sample size, margin of error and significance — and how they fit together.
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