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Shannon entropy calculator

Paste a probability distribution and get its Shannon entropy H = −Σ p·log p in bits — the average information per outcome. It also shows the maximum possible entropy (a uniform distribution) and the redundancy, how far below that maximum you are.

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The Shannon entropy calculator turns Probabilities (sum to 1) into Entropy (bits), Maximum entropy (bits), Redundancy, instantly and for free. For instance, with Probabilities (sum to 1) = 0.25, 0.25, 0.25, 0.25 it returns Entropy (bits) = 2, Maximum entropy (bits) = 2 and Redundancy = 0%.

How to use it

  1. Enter your values: Probabilities (sum to 1).
  2. Read the result instantly: Entropy (bits), Maximum entropy (bits), Redundancy.

Frequently asked questions

How does the Shannon entropy calculator work?

It takes Probabilities (sum to 1) and derives Entropy (bits), Maximum entropy (bits) and Redundancy from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

A single value: Probabilities (sum to 1). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With Probabilities (sum to 1) = 0.25, 0.25, 0.25, 0.25, the calculator returns Entropy (bits) = 2, Maximum entropy (bits) = 2 and Redundancy = 0%. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using Probabilities (sum to 1) = 0.25, 0.26, 0.28, 0.29 instead, Entropy (bits) goes from 2 to 1.998 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Probabilities (sum to 1) = 0.25, 0.25, Entropy (bits) comes out at 1. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

Where do the figures come from, and how current are they?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

All guides →
ExplainerPassword Entropy: What a Strength Meter Cannot KnowEntropy measures the process that produced a password, not the characters in it. H = L x log2(R) is only true when every character was chosen at random — which is exactly why a meter scoring a human-invented password on its character classes is measuring the wrong thing.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.