The idea behind the result
Odds for an event compare favorable weight a with unfavorable weight b. Probability is a/(a+b).
On this page, the displayed implied probability follows this definition rather than any similarly named measure.
Math calculator
Odds to Probability Calculator
Convert favorable-to-unfavorable ratio odds into probability. The displayed implied probability includes enough working to inspect signs and scale.
Odds to Probability inputs
Numerical setup
Problems this can answer
Odds appear in games, risk communication, forecasts, and betting markets, though prices may include margins.
Follow one set of numbers
Odds 3:2 imply 3/(3+2)=0.6, or 60%.
What matters in Odds to Probability
Keep orientation clear: odds for differ from odds against. Both parts must use the same scale. If the Odds to Probability assumptions do not fit, consider reverse conversion.
When odds to probability looks surprising, restore the sample and vary odds for the event by itself.
Manual method
Add the two odds parts and divide the favorable part by that total.
What changes—and what does not
Write each source value under its matching label before calculating: odds for the event and odds against the event. This preserves the assumptions behind implied probability and makes a later check possible without reopening the original problem.
How the result responds
Increasing only the favorable part raises probability; scaling both parts equally changes nothing. This relationship remains useful even when the final implied probability is rounded.
Probability-to-odds reverses the conversion by comparing p with 1−p. The two results may share inputs while retaining different meanings.
Recording the answer
Before publishing or sharing implied probability, decide on units, significant digits, and whether an exact form is expected. Those choices belong to interpretation rather than the calculator engine.
When reporting the answer, state the implied probability first, then its value and unit. Add odds for the event and odds against the event if someone else must verify the work independently.
Saving a defensible Odds to Probability result
Store Odds for the event, Odds against the event with the Odds to Probability output and identify the event in words. Inputs alone may not reveal whether odds were for or against, whether a row began at zero, or whether a cumulative boundary was inclusive. A short convention note prevents a correct value from being attached to the wrong question.
For Odds to Probability, before saving, check one invariant appropriate to the page: an integer count stays whole, a probability remains bounded, complementary areas total one, or a union does not exceed the summed set sizes.
Questions about Odds to Probability
Must odds total 100?
No.
What is 1:1?
Probability one half.
Are market odds always fair?
No.
Does 3:2 mean 3/2 probability?
No; use 3/5.