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Shannon Entropy of a 3-Outcome Discrete Distribution Calculator

H = − Σ pᵢ · log₂ pᵢ (bits).

Compute the Shannon entropy H of a 3-outcome discrete distribution: H = −Σ pᵢ · log₂ pᵢ, in bits. Entropy is the average information content. Uniform over 3 outcomes ⇒ H = log₂ 3 ≈ 1.585 bits (maximum). Concentrated on one outcome ⇒ H = 0. Probabilities are automatically normalised to sum to 1.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

H = −Σ pᵢ·log₂ pᵢ.

In depth

Compute the Shannon entropy H of a 3-outcome discrete distribution: H = −Σ pᵢ · log₂ pᵢ, in bits. Entropy is the average information content. Uniform over 3 outcomes ⇒ H = log₂ 3 ≈ 1.585 bits (maximum). Concentrated on one outcome ⇒ H = 0. Probabilities are automatically normalised to sum to 1.