Binary Entropy CalculatorFree online math calculator — instant results, no sign-up
Compute Shannon entropy of a binary outcome probability.
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About the Binary Entropy Calculator
Compute Shannon entropy of a binary outcome probability. Uses the stated mathematical model and consistent units. Display is rounded to six decimal places; preserve precision for chained calculations. Two mutually exclusive exhaustive outcomes are assumed.
- Probability of first outcome
- Enter probability of first outcome. Accepted minimum: 1e-06. Maximum: 0.999999.
Formula and method
Result = -p * log2(p) - (1 - p) * log2(1 - p) [bits]
- pProbability of first outcome
Compute Shannon entropy of a binary outcome probability. Substitute the variables using the units defined above. Uses the stated mathematical model and consistent units. Display is rounded to six decimal places; preserve precision for chained calculations. Two mutually exclusive exhaustive outcomes are assumed.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Probability of first outcome0.5
Results
- Result1 bits
How to use the Binary Entropy Calculator
- 1Enter probability of first outcome.
- 2Check the source quantity against the original measurement.
- 3Read the bits result and compare the stated assumptions with your situation.
Reading your result
Compute Shannon entropy of a binary outcome probability. The displayed quantity is bits. A negative value, when the formula permits one, describes the direction of the difference—not a positive gain.
Limitations
Uses the stated mathematical model and consistent units. Display is rounded to six decimal places; preserve precision for chained calculations. Two mutually exclusive exhaustive outcomes are assumed. Numeric results are rounded for display; the calculation does not establish that your chosen inputs represent a realistic or permitted scenario.
Common questions
Which units does Binary Entropy require?+
Probability of first outcome: dimensionless number. Do not mix incompatible units.
What assumptions matter for Binary Entropy?+
Uses the stated mathematical model and consistent units. Display is rounded to six decimal places; preserve precision for chained calculations. Two mutually exclusive exhaustive outcomes are assumed.
How should I check a Binary Entropy result?+
Use the formula above with the shown starting inputs and compare the worked example generated from the tool. Check the original measurements and terms before using the figure.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.