Why use a proportion of 50%?

The expression p(1−p) is largest at p = 0.5, so using 50% gives the widest, most conservative margin of error. If you know the true proportion is far from half, entering it produces a smaller margin.

How is this different from a confidence interval calculator?

A confidence interval for a mean uses the sample standard deviation, while this tool computes the margin of error for a proportion from the sample size and proportion alone. The margin is the half-width you add and subtract to form the interval.

When should I enter a population value?

Add a population when your sample is a meaningful fraction of a finite group — say surveying 500 of a 1,000-member club. The finite population correction then reduces the margin to reflect that you have measured much of the group.

Which z-scores does the calculator use?

It uses standard normal z-scores: 1.282 for 80%, 1.645 for 90%, 1.96 for 95%, and 2.576 for 99% confidence. Higher confidence means a larger z and therefore a wider margin of error.

Margin of Error Calculator

Sample Size (n)

Sample Proportion50%

Confidence Level

Population (optional)

Margin of Error±3.10%

As a Proportion±0.0310

Z-Score Used1.960

The margin of error tells you how far a survey result for a proportion is likely to sit from the true population value. This calculator uses the proportion formula MOE = z × √(p(1−p)/n), combining your sample size, the sample proportion, and a confidence level into a plus-or-minus percentage. An optional population field applies the finite population correction for small or fully enumerated groups.

Formula

MOE = z × √(p(1 − p) / n)

z: Z-score for the chosen confidence level (e.g. 1.96 for 95%)
p: Sample proportion, between 0 and 1
n: Sample size

How it works

Enter the sample size n and the sample proportion p (use 50% for the most conservative, largest margin), then pick a confidence level.
The calculator looks up the matching z-score and computes z × √(p(1−p)/n), reporting the margin both as a percentage and as a proportion.
If you supply a population, it multiplies by the finite population correction √((N−n)/(N−1)), which shrinks the margin when the sample is a large share of the whole group.

Worked example

A poll of 1,000 voters splits 50/50 at 95% confidence.

Z-score for 95% confidence is 1.96.
Standard error = √(0.5 × 0.5 / 1000) = √0.00025 ≈ 0.015811.
MOE = 1.96 × 0.015811 ≈ 0.030984, or about 3.10%.

The margin of error is about ±3.10 percentage points.

Frequently asked questions

Why use a proportion of 50%?: The expression p(1−p) is largest at p = 0.5, so using 50% gives the widest, most conservative margin of error. If you know the true proportion is far from half, entering it produces a smaller margin.
How is this different from a confidence interval calculator?: A confidence interval for a mean uses the sample standard deviation, while this tool computes the margin of error for a proportion from the sample size and proportion alone. The margin is the half-width you add and subtract to form the interval.
When should I enter a population value?: Add a population when your sample is a meaningful fraction of a finite group — say surveying 500 of a 1,000-member club. The finite population correction then reduces the margin to reflect that you have measured much of the group.
Which z-scores does the calculator use?: It uses standard normal z-scores: 1.282 for 80%, 1.645 for 90%, 1.96 for 95%, and 2.576 for 99% confidence. Higher confidence means a larger z and therefore a wider margin of error.

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Confidence Interval Calculator Sample Size Calculator Percent Error Calculator Average Calculator