Sigmoid Output Calculator

Work out sigmoid output instantly with clear inputs, formula shown and shareable results.

About Sigmoid Output Calculator

The logistic sigmoid maps any real number to (0, 1) via 1 / (1 + e^-z), which is why logistic regression outputs a probability. Its inverse is the logit, so z is literally the log-odds: z = 0 gives 50 percent, z = 2.2 gives about 90 percent. Shifting the decision threshold away from 0.5 trades precision against recall without retraining.

Formula

Logistic sigmoid

p = 1 / (1 + e^-z) where z = logit + bias; odds = p / (1 - p); log-odds = z

Worked example

With the default values below, Sigmoid Output Calculator returns Predicted probability of 81.757%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Raw logit / linear score: 1.2
Bias term: 0.3
Decision thresholdaccepts 0.01–0.99: 0.5

Results

Predicted probability: 81.757%
Odds in favour: 4.4817
Log-odds (z): 1.5000
Class decision: Positive class (p >= threshold)

Step by step

1Values used
2Logistic sigmoid
3Predicted probability= 81.757
4Odds in favour= 4.4817
5Log-odds (z)= 1.5000
6Class decision= Positive class (p >= threshold)

Assumptions and limits

The result is derived only from the 3 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

Why does one unit of logit matter so much?

Each unit of z multiplies the odds by e, about 2.718. That is why coefficients in logistic regression are interpreted as odds ratios.

Should I always threshold at 0.5?

Only if false positives and false negatives cost the same and the classes are balanced. Otherwise pick the threshold from a precision-recall curve on validation data.