What this calculator does
Odds and probability describe the same thing on different scales. Probability compares favourable outcomes to all outcomes; odds compare favourable to unfavourable. A 25 per cent probability is odds of 1 to 3 against, and confusing the two conventions is a common source of error.
Three formats are in common use. Decimal odds show the total return per unit staked and dominate in Europe and Australia. Fractional odds show profit relative to stake and persist in the UK. Probability percentages are what most people actually think in. This converter moves between all three.
The formula
Decimal odds are the reciprocal of probability, since staking one unit at those odds returns the reciprocal. Fractional odds express the ratio of unfavourable to favourable outcomes. The break-even win rate is simply the implied probability: the rate at which a bet at these odds would neither gain nor lose over the long run.
| Term | Meaning |
|---|---|
| Decimal odds | Total return per unit staked, including the stake. |
| Fractional odds | Profit relative to stake, as a to 1. |
| Implied probability | 1 ÷ decimal odds. |
| Break-even rate | The win rate at which the bet is neutral. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | The value to convert. |
| Value is | Which format the value is in. Decimal odds of 2.5, a probability of 40 per cent and fractional odds of 1.5 all describe the same thing. |
When to use it
Reading a betting market
Decimal odds convert directly to an implied probability. If your own estimate of an event differs meaningfully from the implied one, that is where a disagreement with the market lies.
Understanding clinical odds ratios
Medical research frequently reports odds rather than probabilities. Converting them makes the findings far easier to interpret, especially when the underlying probability is high.
Comparing across formats
Fractional odds of 5/2 and decimal odds of 3.5 are the same. Converting both to probability is the only way to compare quickly.
Working out a break-even rate
The implied probability is the win rate at which a bet breaks even. Anything below that loses money over the long run, before any margin the bookmaker builds in.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Decimal odds converted to probability
Common decimal odds and what they imply.
| Decimal odds | Probability | Odds against | Fractional odds |
|---|---|---|---|
| 1.1 | 90.9% | 1 to 0.10 | 0.10/1 |
| 1.5 | 66.7% | 1 to 0.50 | 0.50/1 |
| 2 | 50.0% | 1 to 1.00 | 1.00/1 |
| 2.5 | 40.0% | 1 to 1.50 | 1.50/1 |
| 4 | 25.0% | 1 to 3.00 | 3.00/1 |
| 10 | 10.0% | 1 to 9.00 | 9.00/1 |
Probability converted the other way
Percentages converted into the odds formats.
| Probability | Decimal odds | Odds against | Fractional odds |
|---|---|---|---|
| 5% | 20.000 | 1 to 19.00 | 19.00/1 |
| 20% | 5.000 | 1 to 4.00 | 4.00/1 |
| 33.33% | 3.000 | 1 to 2.00 | 2.00/1 |
| 50% | 2.000 | 1 to 1.00 | 1.00/1 |
| 75% | 1.333 | 1 to 0.33 | 0.33/1 |
| 90% | 1.111 | 1 to 0.11 | 0.11/1 |
Questions
What is the difference between odds and probability?
Probability is favourable outcomes divided by all outcomes; odds are favourable divided by unfavourable. A 1 in 4 chance is a probability of 25 per cent but odds of 1 to 3 against.
How do I convert decimal odds to probability?
Divide 1 by the decimal odds. Odds of 4.0 imply a probability of 25 per cent. To go the other way, divide 1 by the probability expressed as a decimal.
What do fractional odds mean?
They show profit relative to stake. Odds of 3/1 return three units of profit plus your stake back, which is the same as decimal odds of 4.0.
Why do bookmaker odds not sum to 100 per cent?
Because a margin is built in. Adding the implied probabilities of all outcomes gives something above 100 per cent, and the excess is the bookmaker’s expected profit: sometimes called the overround.
What are American odds?
A fourth format, using positive numbers for underdogs and negative for favourites. This calculator handles decimal, fractional and probability; American odds of +200 correspond to decimal 3.0.
For combining event probabilities, see the probability calculator. For repeated trials, use binomial probability.