Confidence Interval For Proportion Calculator

Work out confidence interval for proportion instantly with clear inputs, formula shown and shareable results.

About Confidence Interval For Proportion Calculator

The Wald interval for a proportion is p̂ ± z√(p̂(1 − p̂)/n). It relies on a normal approximation, so it needs both np̂ and n(1 − p̂) to be at least about 10.

Formula

Proportion interval

p̂ ± z(α/2)·√(p̂(1 − p̂)/n)

Worked example

With the default values below, Confidence Interval For Proportion Calculator returns Margin of error of 0.07898436. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of successesminimum 0: 63
Sample sizeminimum 1: 150
Confidence levelaccepts 50–99.99 %: 95 %

Results

Margin of error: 0.07898436
Sample proportion: 0.42000000
Lower bound: 0.34101564
Upper bound: 0.49898436

Step by step

1Values used
2Proportion interval
3Margin of error= 0.07898436
4Sample proportion= 0.42000000
5Lower bound= 0.34101564
6Upper bound= 0.49898436

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 63 successes in 150 at 95%?

p̂ = 0.42, the standard error 0.0403, so the margin is 0.079 and the interval runs 0.341 to 0.499.

What if p̂ is near 0 or 1?

The Wald interval performs badly. Use the Wilson score or Agresti-Coull interval instead.