Statistics & Probability

Margin of Error Calculator (Proportion)

Find the margin of error for a poll or survey result.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Margin of error (± percentage points)
Margin of error (± percentage points)
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Lower bound (%)
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Upper bound (%)
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Margin of Error Calculator (Proportion) by TheCalcTools

How the Margin of Error Calculator (Proportion) works

Enter the percentage observed in your sample, the sample size and a confidence level.

The calculator finds the standard error of a proportion.

Multiplying by the critical z-value gives the margin of error.

The formula

MOE = z × √(p(1 − p) ÷ n)

Worked example

Using the default values shown in the calculator:

Observed proportion (%)50
Sample size (n)1000
Confidence level95%
  1. Standard error = √(0.5 × 0.5 ÷ 1000) = 1.58%.
  2. Margin of error = 1.96 × 1.58% = 3.10 points.
  3. The interval is 46.90% to 53.10%.

Result:

Margin of error (± percentage points)3.10
Lower bound (%)46.90
Upper bound (%)53.10

Frequently asked questions

Why do pollsters use 50%?

A proportion of 50% gives the largest possible margin of error, so it is the safe, conservative case.

Does the population size matter?

Only if the sample is a large share of the population (over about 5%). Otherwise it has almost no effect.

Sources and further reading

Sample Size CalculatorHow many people do you need to survey? Confidence Interval Calculator (Mean)Estimate a range likely to contain the true mean, using the normal (z) approximation Standard Error CalculatorFind the standard error from a standard deviation and sample size

More in Statistics & Probability · All calculators

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