Softmax Function Calculator

Enter a numeric vector to compute the softmax probability of each component (summing to 1) and the component with the highest probability.

Input

Enter a numeric vector separated by commas, newlines, or spaces. The softmax probability of each component (summing to 1) is computed.

Input vector z

Example: 2, 1, 0.1 (comma, newline, or space separated)

Highest probability is component 1

65.90%

Components

Sum of probabilities

1.0000

Probability distribution

Per-component details

Component	Input z	Probability	Percent
1	2	0.6590	65.90%
2	1	0.2424	24.24%
3	0.1	0.0986	9.86%

The softmax function turns a real vector z=(z1, …, zn) into a probability vector that sums to 1. Its i-th component is softmax_i = e^(zi) / sum over j of e^(zj).
Every output is greater than 0 and at most 1, and all components add up to exactly 1. This lets you read each value as the probability of belonging to that class in multiclass classification.
This tool uses the numerically stable formulation. To avoid overflow in the exponential, it subtracts the maximum input value from every component before computing e to the power. Subtracting the maximum does not change the mathematical result.
Shifting all inputs by a constant c leaves the output unchanged (shift invariance). Scaling all inputs by a constant changes the sharpness of the peak: larger scaling concentrates more probability on the largest component.
In machine learning, softmax is the activation in the final layer of a neural network that converts logits (scores) into probabilities, typically trained with the cross-entropy loss. For two components it reduces to the sigmoid function.
Enter multiple numbers separated by commas, newlines, or spaces. There is no limit on the number of components, and a table and bar chart show the probability of each one.

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