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Shannon Entropy Calculator

Math Calculators

H=−Σp·log₂p · information content · distribution entropy

Quick Answer

Shannon Entropy Calculator: H=−Σp·log₂p · information content · distribution entropy. Shannon Entropy Calculator uses standard math formulas to compute accurate results instantly.

How it works

  1. 1H=−Σpᵢ·log₂pᵢ in bits
  2. 2Enter a probability distribution (comma/space separated, sums to ~1)
  3. 3Uniform is maximal at log₂n; certainty gives 0
  4. 40·log0 is defined as 0 (contributes nothing)

Probability distribution

Shannon entropy1.500bits
Uniform entropy (same n)：1.585 bits
Sum of probabilities：1.000
Entropy measures average uncertainty: a coin flip is 1 bit, a die ~2.585 bits, a d32 exactly 5 bits. Information gain = parent entropy − weighted child entropy — the decision-tree split criterion. It also bounds lossless compression: any code needs ≥H bits per symbol on average, with Huffman/arithmetic coding approaching it. Sums deviating >5% from 1 are rejected.

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How to Use

  1. Enter values or expressions: type directly into the Shannon Entropy Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Shannon Entropy Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: H=−Σp·log₂p · information content · distribution entropy.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Shannon Entropy Calculator formula

Shannon Entropy Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Shannon Entropy Calculator?
Open the page and fill in the input fields — results update automatically. H=−Σp·log₂p · information content · distribution entropy.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Shannon Entropy Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/shannon-entropy

Results provided by this tool are for reference only and do not constitute professional advice.