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Confidence interval calculator

Estimate a normal mean interval or a Wilson interval for a proportion.

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  1. Use the example values or enter your own measurements.
  2. Calculate, then copy the result or download the available details.

Example

Input

n = 36, mean 56, standard deviation 8, 99%

Expected result

56 ± 3.434

Try it

Good to know

The calculation runs in your browser. Use consistent units in fields with no explicit unit.

Calculation method

The normal margin is z times the standard error s/√n. Wilson score intervals adjust the center and width for proportions and remain within [0,1].

xˉ±z1−α/2sn\bar{x}\pm z_{1-\alpha/2}\frac{s}{\sqrt n}
p^+z2/(2n)±zp^(1−p^)/n+z2/(4n2)1+z2/n\frac{\widehat{p}+z^2/(2n)\pm z\sqrt{\widehat{p}(1-\widehat{p})/n+z^2/(4n^2)}}{1+z^2/n}

Calculation mode

Normal mean interval
  • Sample size
  • Mean
  • Standard deviation
  • Confidence level · %
Wilson proportion interval
  • Sample size
  • Successes
  • Confidence level · %