About the Odds to Probability Calculator
This odds calculator converts between odds and probability in either direction. Enter odds in favour (for example 2 to 3) or odds against (for example 3 to 1) and it shows the probability of the event happening and not happening as percentages. Or enter a probability and it gives you the equivalent odds for, odds against, "1 in N" chance and decimal odds.
It is useful for statistics and probability homework, for reading odds quoted in games, raffles and sports, and for sense-checking claims such as "the odds are 99 to 1 against". Odds and probability describe the same thing on different scales, and mixing them up is one of the most common probability mistakes.
Odds here are "true" odds with no bookmaker margin. To convert between betting formats such as American (moneyline), fractional and decimal odds including the implied vig, use the odds converter.
With the default inputs, the probability of the event is 25%. Change any value above to recalculate instantly.
How to use the odds to probability calculator
- 1Choose whether you have odds against, odds in favour or a probability.
- 2Enter the two numbers of the odds (e.g. 3 and 1 for 3 to 1), or the percentage.
- 3Read the probability of the event and of it not happening.
- 4Use the odds and "1 in N" outputs to express the same chance another way.
Formula and method
Odds compare the number of favourable outcomes with unfavourable ones, while probability compares favourable outcomes with all outcomes. So odds in favour of A to B mean A favourable chances for every B unfavourable ones, a probability of A/(A + B). Odds against A to B are the reverse: probability B/(A + B).
Going the other way, a probability P becomes odds in favour of P : (1 − P), reduced to lowest whole numbers where possible, and odds against of (1 − P) : P. Fair decimal odds are 1/P — the total return per unit staked with no bookmaker margin.
- A : B
- Odds written "A to B"
- P
- Probability of the event (0 to 1)
Worked examples
Odds of 3 to 1 against
Odds of 3 to 1 against mean three unfavourable outcomes for each favourable one, so the probability is 1 ÷ (3 + 1) = 25%. A fair 1-unit bet would return 4 units in total.
Odds of 2 to 3 in favour
With odds 2 to 3 in favour there are 2 favourable chances out of 2 + 3 = 5, a probability of 40%. The same chance expressed as odds against is 3 to 2.
A 20% chance as odds
A 20% probability means 20 favourable to 80 unfavourable, which reduces to odds of 1 to 4 in favour, or 4 to 1 against. That is a 1 in 5 chance, with fair decimal odds of 5.0.
Frequently asked questions
How do you convert odds to probability?+
For odds in favour of A to B, the probability is A ÷ (A + B). For odds against A to B, it is B ÷ (A + B). For example, 3 to 1 against is 1 ÷ 4 = 25%.
What is the difference between odds and probability?+
Probability is favourable outcomes divided by all outcomes, while odds are favourable divided by unfavourable. A 25% probability is 1 to 3 in favour, or 3 to 1 against — the same chance expressed differently.
What do odds of 10 to 1 mean?+
Quoted odds of 10 to 1 almost always mean 10 to 1 against: the event is expected to fail 10 times for every success, a probability of 1/11 ≈ 9.09%.
How do I convert a percentage to odds?+
Write the probability and its complement as a ratio: P : (100 − P). For 20% that is 20 : 80, which reduces to 1 : 4 in favour, or 4 : 1 against.
Are betting odds the same as true odds?+
No. Bookmaker odds include a margin (vig), so the implied probabilities of all outcomes add up to more than 100%. This calculator shows true, fair odds; use the odds converter for American and fractional betting formats.