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Arcsine Bounded Interval Probability

Calculate probability between two points under the U-shaped arcsine distribution.

Probability workspace● Runs in your browser
01 Your input
02 Your result
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FormulaProbability = 2*(asin(sqrt(hi))-asin(sqrt(lo)))/PI; Mean = 0.5; Variance = 0.125
Sources and model references

Made for real tasks

  • Calculate probability between two points under the U-shaped arcsine distribution.
Explore step-by-step workflows →

Worked example

Inputs

Interval lower limit
0.25 fraction
Interval upper limit
0.75 fraction

Expected results

Probability
0.3333333333 probability
Mean
0.5 number
Variance
0.125 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter interval lower limit, interval upper limit.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "lo": 0.25,
  "hi": 0.75
}

Accuracy and scope

Standard arcsine distribution on [0,1], not a uniform model or an inverse-sine angle converter.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.