Math

Free Margin of Error Calculator

Margin of error for a survey proportion.

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Inputs

%

Result

Margin of error

±4.90%

Estimated range45.1% – 54.9%

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Short answer

Margin of error for a survey proportion.

What is the Margin of Error Calculator?

Margin of error for a survey proportion.

How does the Margin of Error Calculator work?

Enter the inputs above and read the result.

Formula

MOE = z × √(p(1−p) ÷ n)

Variables

  • pSample proportion
  • nSample size

Explanation

A larger sample or a proportion closer to 0% or 100% shrinks the margin of error.

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            Related concepts

            The Margin of Error Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

            distributiondispersionsignificancesamplepopulationexpected value

            Practical use cases and industry applications

            Understanding Margin of Error

            Margin of error for a survey proportion. Within math calculators, margin of error belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.

            Learning how margin of error is calculated

            A larger sample or a proportion closer to 0% or 100% shrinks the margin of error. Working through the variables one at a time — p, n — makes the result reproducible by hand and easier to sanity-check.

            Using margin of error to make a decision

            Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

            How margin of error compares with related measures

            distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

            Frequently asked questions

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