Softmax Probability Calculator

Work out softmax probability instantly with clear inputs, formula shown and shareable results.

About Softmax Probability Calculator

Softmax exponentiates each logit and normalises by the sum, turning arbitrary real scores into a probability distribution. Subtracting the maximum logit first is the standard trick that prevents overflow. Temperature divides the logits before exponentiation: below 1 the distribution sharpens toward the argmax, above 1 it flattens toward uniform, which is exactly how sampling temperature controls generation diversity.

Formula

Softmax with temperature

p_i = exp((z_i - max z) / T) / sum_j exp((z_j - max z) / T); entropy = -sum p_i log2(p_i)

Worked example

With the default values below, Softmax Probability Calculator returns Highest class probability of 65.90%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Logits (comma separated): 2.0, 1.0, 0.1
Temperatureaccepts 0.01–10: 1

Results

Highest class probability: 65.90%
Full probability distribution: 0.6590, 0.2424, 0.0986
Distribution entropy: 1.2216 bits
Runner-up probability: 24.24%

Step by step

1Values used
2Softmax with temperature
3Highest class probability= 65.90
4Full probability distribution= 0.6590, 0.2424, 0.0986
5Distribution entropy= 1.2216 bits
6Runner-up probability= 24.24

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does temperature 0 mean?

In the limit it becomes greedy argmax decoding: all probability collapses onto the largest logit. Implementations special-case it rather than dividing by zero.

Why report entropy?

Entropy summarises how uncertain the distribution is in bits. A near-zero entropy means a confident prediction; entropy close to log2(classes) means the model is guessing.