Odds to Probability Converter
Odds and probability are two ways of describing the same chance. Odds in favour are written as a ratio, a to b, comparing favourable outcomes to unfavourable ones, while probability expresses the same chance as a single number between 0 and 1. This converter turns odds in favour into a probability, a percentage, decimal odds, and the reverse odds against. The conversion is exact: probability equals a divided by the sum of a and b. Enter the two parts of your odds ratio and read all the equivalent forms at once.
Odds to probability formula
Probability p = a / (a + b)
Percentage = p * 100
Decimal odds = 1 / p = (a + b) / a
Odds against (per 1) = b / a
Here a is the count of favourable outcomes and b the count of unfavourable outcomes. The probability is the favourable share of all outcomes. Decimal odds give the total return per unit staked.
Worked examples
- Odds of 3 to 1 in favour give a probability of 0.75 (75 percent).
- Even odds, 1 to 1, give a probability of 0.50 (50 percent).
- Odds of 1 to 4 give a probability of 0.20 (20 percent) and decimal odds of 5.00.
- Decimal odds equal 1 divided by the probability.
- Odds against is simply the reversed ratio.
Odds to probability: frequently asked questions
How do you convert odds to probability?
If the odds in favour of an event are a to b, the probability is a / (a + b). For example, odds of 3 to 1 give a probability of 3 / (3 + 1) = 0.75, or 75 percent. The two numbers represent favourable to unfavourable outcomes.
What is the difference between odds and probability?
Probability is the chance of an event as a fraction of all outcomes (0 to 1). Odds compare favourable outcomes to unfavourable ones as a ratio. Odds of 3 to 1 mean three favourable for every one unfavourable, equal to a probability of 0.75.
What are decimal odds?
Decimal odds express the total return per unit staked, including the stake. They equal 1 divided by the probability. A probability of 0.25 corresponds to decimal odds of 4.00, meaning a winning unit stake returns four units in total.
How do I read odds against?
Odds against are the reverse ratio: b to a. If the odds in favour are 3 to 1, the odds against are 1 to 3. Odds against are common in betting where most outcomes are unfavourable to the bettor.
Can probability ever exceed 1 with this tool?
No. Because the probability is computed as a / (a + b) with both inputs non-negative and not both zero, the result is always between 0 and 1 inclusive. If both inputs are zero the conversion is undefined and the tool returns n/a.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: Probability definitions.
- MIT OpenCourseWare: Introduction to Probability and Statistics.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.