Case 1
- Odds for (a)
- 1
- Odds against (b)
- 4
20.0000%
Open with these valuesOdds to Probability Calculator
20.0000%
Result: 20.0000 %Odds compare the favourable chances with the unfavourable ones; a probability compares them with all of them. Odds of 1 to 4 in favour are one chance out of five, so 20 % — not 25 %, which is the mistake the ratio invites.
Worked examples
Case 2
- Odds for (a)
- 3
- Odds against (b)
- 2
60.0000%
Open with these valuesCase 3
- Odds for (a)
- 9
- Odds against (b)
- 1
90.0000%
Open with these valuesHow it's calculated
P = a ÷ (a + b) × 100 %
- StepEnter the favourable chances — the first number of the odds.
- StepEnter the chances against — the second number.
- ResultRead the probability as a percentage; divide by 100 for the decimal.
What this number means
The first number is the favourable side
This calculator reads a to b as odds in favour. Odds quoted against, as bookmakers usually do, have to be swapped first: 1 to 4 gives 20 %, the same pair reversed gives 80 %.
Odds and probabilities use different denominators
Odds set the favourable chances against the unfavourable ones; a probability sets them against all the chances there are. That is why 1 to 4 in favour is 20 % and not 25 %.
Percentage out, decimal on demand
The result is a percentage. Divide it by 100 for the plain proportion — 20 % is 0.2.
0 % and 100 % are legitimate answers
With no favourable chances the probability is 0 %; with no chances against, every chance is favourable and it is 100 %. Only two zeros leave no total to divide by.
Commonly misread
Odds of 1 to 4 in favour mean a 25 % chance.
1 ÷ 4 is the ratio of the two sides, not the probability. The probability holds 1 against all five chances: 1 ÷ 5 = 20 %.
Odds of 3 to 1 in favour are about 33 %.
That divides 1 by 3 instead of comparing 3 with the four chances in total. 3 ÷ (3 + 1) = 75 %.
Bookmaker odds can be entered exactly as they are quoted.
Bookmakers usually quote the odds against, so the two numbers have to be swapped first. Entered the wrong way round, 1 to 4 reads as 80 % instead of 20 %.
Reference table
| a, b | Odds | Probability |
|---|---|---|
| 1, 4 | 1 to 4 in favour | 20.0000 |
| 1, 1 | even odds | 50.0000 |
| 2, 5 | 2 to 5 in favour | 28.5714 |
| 3, 2 | 3 to 2 in favour | 60.0000 |
| 9, 1 | 9 to 1 in favour | 90.0000 |
Questions
How do I convert odds to a probability?
Divide the favourable chances by the total number of chances: P = a ÷ (a + b). For odds of 1 to 4 in favour that is 1 ÷ 5 = 0.2, or 20 %. Multiply the decimal by 100 to read it as a percentage.
What do odds of a to b actually mean?
Odds of a to b in favour mean a favourable chances for every b chances against. They are a ratio of two outcomes, not a probability. To get the probability you compare the favourable chances with the total, a out of a + b.
Does it matter if my odds are against instead of in favour?
Yes. This calculator treats the first number as the favourable side. If your odds are quoted against, as bookmakers usually do, swap the two numbers before entering them or the probability comes out inverted.
What is 1 to 4 odds as a percentage?
One favourable chance out of five in total, so 1 ÷ (1 + 4) = 0.2, which is 20 %. The event happens once in five tries on average.
Can the probability come out as 0 or 100 %?
Yes. With no favourable chances the probability is 0 %; with no chances against, every chance is favourable and it is 100 %. Only two zeros are undefined, because then there is no total to divide by.
Sources and last check
Information, not professional advice.