Logistic Function CalculatorFree online math calculator — instant results, no sign-up
Evaluate the standard logistic sigmoid function.
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About the Logistic Function Calculator
The Logistic Function Calculator evaluates the standard logistic sigmoid for a real-number input. It uses σ(x) = 1 / (1 + e^(−x)) to map the input to a value strictly between 0 and 1. With the default input of 1, the calculator returns 0.7310585786.
- Real number
- The dimensionless real number x is the input to the standard logistic sigmoid, with a default value of 1.
Formula and method
σ(x) = 1 / (1 + e^(−x)); for x = 1, σ(1) = 1 / (1 + e^(−1)) ≈ 0.7310585786.
- xThe dimensionless real-number input.
- σ(x)The dimensionless logistic sigmoid output, displayed as Result.
- eEuler’s number, the base of the natural exponential function.
Negate the input x, evaluate the exponential e^(−x), add 1, and take the reciprocal. For the default input x = 1, this gives 1 / (1 + e^(−1)), displayed as 0.7310585786.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Real number1
Results
- Result0.7310585786
How to use the Logistic Function Calculator
- 1Enter a value in the Real number field, or leave the default value of 1.
- 2Run the calculation to evaluate the standard logistic sigmoid.
- 3Read the Result row; with the default input, it shows 0.7310585786.
- 4Interpret the result as a sigmoid-transformed value between 0 and 1, not automatically as a probability.
Reading your result
The Result row shows σ(x), the sigmoid-transformed input. For x = 1, Result = 0.7310585786. Positive inputs produce outputs above 0.5, negative inputs produce outputs below 0.5, and an input of zero produces 0.5. Larger inputs always produce larger mathematical outputs, although displayed values may coincide because of rounding.
Limitations
This tool evaluates only the standard logistic sigmoid, with no adjustable midpoint, steepness, or upper limit. The input is assumed to be dimensionless, and complex numbers are outside its scope. For finite real inputs, the exact output never equals 0 or 1, but finite-precision arithmetic or display rounding may show these endpoints for extreme inputs. A direct exponential calculation can also encounter numerical overflow for very large negative inputs. The output is not a calibrated probability unless the input comes from an appropriate probabilistic model.
Common questions
Why does the default input of 1 give 0.7310585786 rather than 1?+
The calculator applies a nonlinear transformation rather than returning the input unchanged. Substituting x = 1 into 1 / (1 + e^(−x)) gives approximately 0.7310585786.
Can the logistic sigmoid return exactly 0 or 1?+
Not mathematically for any finite real input. It approaches 0 as x decreases without bound and approaches 1 as x increases without bound; a displayed endpoint can be a numerical or rounding effect.
Can I interpret the result as a probability?+
If x represents log-odds using the natural logarithm, σ(x) is the corresponding probability. For an arbitrary real-number input, the calculator provides only a sigmoid value, not evidence of an event’s likelihood.
Does this calculator support a generalized logistic curve?+
No. It evaluates only σ(x) = 1 / (1 + e^(−x)), centered at x = 0 with output 0.5 there. It does not accept parameters for changing the curve’s midpoint, steepness, or output scale.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.