Odds To Probability CalculatorFree online math calculator — instant results, no sign-up
Convert odds in favor of an event into its probability.
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About the Odds To Probability Calculator
The Odds To Probability Calculator converts odds in favor of an event into its probability by comparing the favorable portion with the total of the favorable and unfavorable portions. With favorable odds of 3 and unfavorable odds of 2, it converts odds of 3:2 into a probability of 0.6.
- Favorable odds
- The favorable portion of the odds ratio, defaulting to 3, is a unitless nonnegative weight representing the event occurring.
- Unfavorable odds
- The unfavorable portion of the odds ratio, defaulting to 2, is a unitless nonnegative weight representing the event not occurring.
Formula and method
p = F / (F + U); with the default inputs, p = 3 / (3 + 2) = 0.6.
- pThe probability of the event occurring, expressed as a unitless decimal from 0 to 1.
- FThe favorable portion of the odds in favor of the event.
- UThe unfavorable portion of the odds in favor of the event.
Add the favorable and unfavorable portions to find the total weight, then divide the favorable portion by that total. For the default inputs, the total is 3 + 2 = 5 and the probability is 3 / 5 = 0.6.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Favorable odds3
- Unfavorable odds2
Results
- Result0.6
How to use the Odds To Probability Calculator
- 1Confirm that your ratio describes odds in favor: favorable outcomes compared with unfavorable outcomes.
- 2Enter the favorable portion in Favorable odds; use 3 for the default example.
- 3Enter the unfavorable portion in Unfavorable odds; use 2 for the default example.
- 4Ensure both values are nonnegative and at least one is greater than zero, then run the calculation.
- 5Read the Result row: the default inputs produce 0.6, equivalent to a 60% probability.
Reading your result
The Result row gives the probability of the event occurring as a decimal, not as an odds ratio. A result of 0.6 means a 60% chance of occurrence and a 40% chance of nonoccurrence. A result of 0 means the event is impossible under the supplied odds, while 1 means it is certain.
Limitations
The inputs must represent odds in favor of the event on the same scale. Negative values are invalid, and two zero inputs leave the probability undefined because the denominator is zero. Decimal weights are mathematically valid; whole-number counts are not required. If the inputs count possible outcomes, those outcomes must be equally likely for the conversion to reflect their probability. The calculator converts supplied odds but does not verify their accuracy or predict individual outcomes. Betting payout formats such as decimal or American odds are not direct inputs for this two-part ratio.
Common questions
Why do odds of 3:2 produce 0.6 rather than 1.5?+
Dividing 3 by 2 gives the ratio of favorable to unfavorable weight, not probability. Probability divides the favorable weight by the total: 3 / (3 + 2) = 0.6.
What if my odds are stated as odds against the event?+
Odds against list the unfavorable portion first. Put that portion in Unfavorable odds and the second portion in Favorable odds before calculating.
Can either portion of the odds be zero?+
Yes. Zero favorable weight with positive unfavorable weight gives probability 0. Zero unfavorable weight with positive favorable weight gives probability 1. Both portions cannot be zero.
Do I need to simplify the odds ratio first?+
No. Multiplying or dividing both portions by the same positive factor leaves F / (F + U) unchanged, so equivalent odds ratios produce the same probability.
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.