Margin of error calculator

Calculate a normal-approximation margin of error for a sample proportion: z√(p(1 − p)/n).

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Sample size

Observed proportion (%)

More inputs and assumptions

Normal critical value z

Answer

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Calculate a normal-approximation margin of error for a sample proportion: z√(p(1 − p)/n).

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Precision and calculation record

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Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

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Formula and assumptions

Simple random sample and independent observations. Wald bounds can fall outside 0–100% and become misleading near the extremes or with small samples; they are shown without clipping. A zero margin at 0% or 100% is an approximation failure, not certainty.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Margin of error calculator

Calculate a normal-approximation margin of error for a sample proportion: z√(p(1 − p)/n).

Next: Sample size calculator

Next: T test calculator

A worked example

Example inputs: sample size = 400, observed proportion (%) = 50, normal critical value z = 1.96. Approximate margin (percentage points) = 4.9.

Before you use the result

Example results for sample size

These examples use Observed proportion (%): 50; Normal critical value z: 1.96. They are reference calculations, not recommended settings.

Sample size	Approximate margin (percentage points)
200	6.92964645563
400	4.9
800	3.46482322781

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