Margin of Error Calculator
Margin of error quantifies the precision of an estimate from survey data. This calculator computes the margin of error for a proportion or mean based on sample size, confidence level, and the estimate itself. For proportions, enter your sample size, observed proportion, and confidence level. For means, enter sample size, standard deviation, and confidence level. The calculator shows how much the estimate could vary due to random sampling variation.
Margin of error formulas
For Proportion: MOE = z * sqrt(p(1-p) / n)
For Mean: MOE = z * (s / sqrt(n))
z-values: 90% = 1.645, 95% = 1.96, 99% = 2.576
Understanding margin of error
- What it means: Your estimate is almost certainly within MOE of the true value.
- Example: If a poll shows 52% support with MOE of 3%, the true support is likely between 49% and 55%.
- Larger samples = smaller MOE: More data gives more precision.
- Higher confidence = larger MOE: To be more certain, you accept wider intervals.
- Proportions near 0.5 maximize MOE: For a fixed sample size, MOE is largest when p = 0.5.
Margin of error: frequently asked questions
What is margin of error?
Margin of error (MOE) is the range of uncertainty around a survey estimate. For example, a 95% confidence interval of 50% plus or minus 3% means the true population value is likely between 47% and 53%.
How does sample size affect margin of error?
MOE decreases as sample size increases, following MOE = z * sqrt(p(1-p)/n). Doubling the sample size reduces MOE by about 30%. Margin of error is inversely proportional to the square root of sample size.
What is a good margin of error?
This depends on your application. For political polls, 3-4% is typical. For market research, 5% is common. Smaller margins of error require larger sample sizes and higher costs.
How does confidence level affect margin of error?
Higher confidence level increases margin of error. A 99% confidence level has larger MOE than 95%, which has larger MOE than 90%. You trade narrower intervals for lower confidence.
What is the relationship between MOE and confidence interval?
The confidence interval is estimate ± MOE. For a survey estimate of 50% with MOE of 3%, the 95% CI is 47% to 53%.
Official sources
- NIST/SEMATECH e-Handbook: NIST Handbook.
- U.S. Census Bureau guidance: Census Bureau.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.