Math
Bayes theorem
Update the probability of A after observing evidence by combining its prior probability with the evidence likelihood under A and under not-A.
Calculators / Math / Binary Shannon entropy
Binary Shannon entropy calculator
Measure uncertainty in a two-outcome probability distribution; equal chances yield one bit, while a certain outcome yields zero bits.
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Entropy1bits
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How to calculate
Measure uncertainty in a two-outcome probability distribution; equal chances yield one bit, while a certain outcome yields zero bits.
Entropy = -(p/100*ln(p/100+1e-300)+(1-p/100)*ln(1-p/100+1e-300))/ln(2) bits
Worked example
Probability of outcome A (%): 50.
Entropy: 1 bits.
Assumptions and limits
Measure uncertainty in a two-outcome probability distribution; equal chances yield one bit, while a certain outcome yields zero bits. Binary Shannon information entropy in bits. Complementary outcomes sum to 100%; deterministic outcomes have zero entropy.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Measure uncertainty in a two-outcome probability distribution; equal chances yield one bit, while a certain outcome yields zero bits.
When this tool is useful
Entropy = -(p/100*ln(p/100+1e-300)+(1-p/100)*ln(1-p/100+1e-300))/ln(2) bits
Understanding your inputs
| Input | What to enter |
|---|---|
| Probability of outcome A (%) | Enter a number of at least 0 and no more than 100. |
Frequently asked questions
What assumptions does this calculation use?
Measure uncertainty in a two-outcome probability distribution; equal chances yield one bit, while a certain outcome yields zero bits. Binary Shannon information entropy in bits. Complementary outcomes sum to 100%; deterministic outcomes have zero entropy.
How is the result calculated?
Entropy = -(p/100*ln(p/100+1e-300)+(1-p/100)*ln(1-p/100+1e-300))/ln(2) bits