What is a margin of error?

The margin of error tells you how far your sample statistic is likely to be from the true population value at a given confidence level.

Does population size affect margin of error?

Yes, if your sample is a large fraction of the population, you can apply the finite population correction to slightly reduce the margin of error.

How can I reduce the margin of error?

Increase the sample size, use a lower confidence level, or use a proportion closer to 0.5 only when necessary; 0.5 is the most conservative.

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.

Confidence level

CL used to find z-score

Sample size (n)

# of respondents

Observed proportion (p)

Use 0.5 for worst case

Population size (N)

for FPC

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.”