Margin of Error Calculator

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Margin of Error Calculator

The margin of error is the half-width of a confidence interval: the amount by which the sample estimate might reasonably differ from the population value. This calculator handles both common cases: a survey proportion (ME = z√[p̂(1 − p̂)/n]) and a sample mean (ME = z or t × s/√n). Enter the sample size and either the proportion or the standard deviation, then choose the confidence level.

For proportions the default p̂ = 0.5 gives the worst-case margin of error quoted by polling organisations; a poll of 1,000 people has a margin of error of about ±3.1 percentage points at 95% confidence. For means you can choose a t critical value with n − 1 degrees of freedom, which is the right choice when the standard deviation comes from the sample.

The steps show the critical value, the standard error and the multiplication. To turn the question round and ask how big a sample you need for a target margin, use the sample size for a proportion or for a mean calculators.

Frequently asked questions

What is the margin of error for a sample of 1000?

At 95% confidence with p̂ = 0.5 it is 1.96 × √(0.25/1000) ≈ 0.031, or ±3.1 percentage points.

Does the margin of error depend on the population size?

Not in this formula. Unless the sample is a sizeable fraction of the population, only the sample size and confidence level matter.

How do I reduce the margin of error?

Increase the sample size (four times the sample halves the margin) or accept a lower confidence level.

Is the margin of error the same as the standard error?

No. The margin of error is the standard error multiplied by the critical value (1.96 for 95% confidence with z).

Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.