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Margin of Error Calculator

Compute margin of error from confidence level, sample size, and proportion or standard deviation.

Clear formulas
Educational steps
Detail breakdown

E = z√(p(1−p)/n) or E = zs/√n depending on mode.

Limitation: Educational survey statistics with z critical values.

Jump to calculator · Sources & review

How to Use the Margin of Error Calculator

E = z√(p(1−p)/n) or E = zs/√n depending on mode.

1

Open the Margin of Error calculator and read field labels.

Match the mode

Educational survey statistics with z critical values.

What It Calculates

E = z√(p(1−p)/n) or E = zs/√n depending on mode.

Worked Examples

Poll n=400 p=0.5

Inputs

mode:proportion
confidenceLevel:95
n:400
proportion:0.5

Result

E ≈ 0.049

~±4.9 points.

Mean E

Inputs

mode:mean
confidenceLevel:95
n:30
sd:8

Result

E ≈ 2.86

zs/√n.

Larger n shrinks E

Inputs

mode:proportion
confidenceLevel:95
n:1600
proportion:0.5

Result

E ≈ 0.0245

Quarter the MOE vs n=400.

Check your mode

Educational survey statistics with z critical values.

Frequently Asked Questions

Yes. Results keep the precision shown on the page unless the engine requires integers.

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Formulas

Standard definitions with assumptions noted below.

Formula

E ​=​ z√​(​p​(​1−p​)​​/​n​)​

Scientific Background

Standard statistics definitions with assumptions stated on-page. Educational only—not professional certification.

Sources & review

Margin of Error Calculator documents the references behind its formulas and assumptions. Always treat results as educational estimates, not personalized professional advice.

Last reviewed

July 22, 2026

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