basic

Sigmoid (Logistic) Function Calculator

σ(x) = 1 / (1 + e^(−x)).

Compute the standard logistic / sigmoid function σ(x) = 1 / (1 + e^(−x)) — the canonical S-shaped activation function and binary-classification probability map. Reports σ(x), the derivative σ′(x) = σ(x)·(1 − σ(x)) (used in back-propagation), and the inverse logit x = ln(σ / (1 − σ)).

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

σ(x) = 1 / (1 + e^(−x)); σ′(x) = σ(x)(1 − σ(x)).

In depth

Compute the standard logistic / sigmoid function σ(x) = 1 / (1 + e^(−x)) — the canonical S-shaped activation function and binary-classification probability map. Reports σ(x), the derivative σ′(x) = σ(x)·(1 − σ(x)) (used in back-propagation), and the inverse logit x = ln(σ / (1 − σ)).