Margin of Error Calculator
Free margin of error calculator for surveys and statistics. Compute margin of error for proportions or means, apply finite population correction, and estimate the sample size needed at a chosen confidence level.
Full original guide (expanded)
Margin of Error Calculator
Quickly compute the margin of error for a survey or experiment. Choose between proportion (percent/yes-no) and mean (numeric values), set your confidence level, and optionally apply the finite population correction (FPC). You can also estimate the sample size needed to achieve a target margin of error.
CL used to find z-score
# of respondents
Use 0.5 for worst case
for FPC
n ≥ 2 recommended
Use sample SD if population σ unknown
Find the minimum sample size needed to achieve a target margin of error for a proportion.
0.5 → largest n
0.03 → 3%
Margin of error
—
in same units; for proportions this is in proportion terms
Lower bound
—
Upper bound
—
Needed n
—
from sample size tab
Margin of error formulas
For a proportion (worst case when p=0.5):
\( ME = z \sqrt{ \frac{p(1-p)}{n} } \)
If population size N is known and not huge, apply finite population correction:
\( ME_{FPC} = ME \times \sqrt{ \frac{N - 1}{N - n} } \)
For a mean: \( ME = z \frac{s}{\sqrt{n}} \)
Common z-scores
| Confidence level | z-score |
|---|---|
| 90% | 1.645 |
| 95% | 1.96 |
| 99% | 2.576 |
What to report
For a survey you'll often write: “With a sample of n=400, at the 95% confidence level, the margin of error is ±4.9 percentage points.”
Formula (LaTeX) + variables + units
','\
For a proportion (worst case when p=0.5): \( ME = z \sqrt{ \frac{p(1-p)}{n} } \) If population size N is known and not huge, apply finite population correction: \( ME_{FPC} = ME \times \sqrt{ \frac{N - 1}{N - n} } \) For a mean: \( ME = z \frac{s}{\sqrt{n}} \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.