Logit Function CalculatorFree online math calculator — instant results, no sign-up
Convert a probability to its log odds.
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About the Logit Function Calculator
The Logit Function Calculator converts a probability into log odds using the natural logarithm. Enter a probability strictly between 0 and 1 to calculate ln(p / (1 − p)). With the default probability of 0.75, the calculator returns 1.0986122887.
- Probability
- The dimensionless probability p of an event, entered as a decimal strictly between 0 and 1; the default is 0.75.
Formula and method
L = logit(p) = ln(p / (1 − p)); for p = 0.75, L = ln(0.75 / (1 − 0.75)) = ln(3) ≈ 1.0986122887.
- pThe probability of the event.
- 1 − pThe probability that the event does not occur.
- LThe dimensionless log odds returned as the result.
- lnThe natural logarithm, using base e.
Subtract the probability from 1 to obtain the complementary probability, then divide the original probability by that complement to obtain the odds. Take the natural logarithm of the odds. For the default input, the complement is 0.25, the odds are 0.75 / 0.25 = 3, and the natural logarithm gives the displayed result of 1.0986122887.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Probability0.75
Results
- Result1.0986122887
How to use the Logit Function Calculator
- 1Enter the event probability in the Probability field, or leave the default value of 0.75.
- 2Check that the value is a decimal strictly between 0 and 1, rather than a percentage entered as a whole number.
- 3Run the calculation to convert the probability to natural-log odds.
- 4Read the Result row: the default input produces 1.0986122887.
- 5Use the sign of the result to determine whether the event is more likely than, less likely than, or equally likely as its complement.
Reading your result
The Result row shows L, the natural logarithm of the event's odds, not the probability or the odds themselves. A positive result means the probability exceeds 0.5, a negative result means it is below 0.5, and zero means it equals 0.5. For p = 0.75, Result = 1.0986122887 corresponds to odds of 3 to 1 in favor of the event.
Limitations
A finite real-valued logit requires 0 < p < 1. As p approaches 0, the logit tends to negative infinity; as p approaches 1, it tends to positive infinity. Endpoint inputs do not have finite logit values, and inputs outside the probability range are invalid. Values very close to either endpoint are sensitive to rounding. The calculator transforms the supplied probability; it does not estimate its accuracy or uncertainty. The displayed example is rounded to ten decimal places.
Common questions
Why does a probability of 0.75 produce 1.0986122887 rather than 3?+
The value 3 is the odds, obtained from 0.75 / 0.25. The logit is the natural logarithm of those odds, so ln(3) ≈ 1.0986122887.
Can I enter a probability of exactly 0 or 1?+
Neither endpoint has a finite real-valued logit. At 0, the formula requires ln(0); at 1, the odds involve division by zero. Use a probability strictly between 0 and 1.
Does this calculator use base-10 logarithms?+
No. It uses the natural logarithm, base e, which is the standard definition of the logit function.
How can I convert the logit result back to a probability?+
Apply the inverse-logit formula p = 1 / (1 + exp(−L)). Using the rounded result L = 1.0986122887 recovers approximately 0.75.
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.