# How do I convert betting odds?

Converts betting odds between American, decimal and fractional formats and the implied probability, with exact fractions.

- Page: https://www.acalculator.org/game/odds-calculator
- JSON spec: https://www.acalculator.org/game/odds-calculator.json
- Version: 29b4333b0b2a

## Default answer

Example with the default inputs (Odds format American, Odds +150): These odds are +150 American, 2.5 decimal and 3/2 fractional, an implied probability of 40%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| format | Odds format | The format of the odds you type: American, decimal, fractional, or an implied probability. |
| odds | Odds | The odds in the chosen format, for example +150, 2.5, 3/2, or 40%. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| probability | Implied probability | The win chance the odds imply: 1 ÷ decimal odds, in percent. |
| american | American odds | Profit on a 100 stake (+) or the stake needed to win 100 (−), rounded to 2 decimals, halves away from 0. |
| decimal | Decimal odds | The total return per 1 staked, stake included. |
| fractional | Fractional odds | The exact profit per 1 staked (decimal odds − 1), as a fraction in lowest terms. |
| against | Chance of losing | The chance the odds imply that the bet loses: 100% − implied probability. |

## Method

Decimal odds d: American +A gives d = 1 + A ÷ 100, −A gives d = 1 + 100 ÷ A; fractional a/b gives d = 1 + a ÷ b; probability p% gives d = 100 ÷ p. Implied probability = 100 ÷ d percent.

## Assumptions

- Implied probability is 1 ÷ decimal odds. It includes the bookmaker’s margin, so the implied probabilities of all outcomes of one event add up to more than 100%.
- Conversions are exact fractions. Only American odds and the displayed decimals are rounded.
- Decimal odds must be above 1 and at most 1,000,001 (American +100,000,000).
- Results are mathematics, not betting advice.

## Worked examples

1. format = american, odds = +150 gives american = +150, decimal = 2.5, fractional = 3/2, probability = 40%, against = 60%. Source: hand calculation in content.mdx: 1 + 150 ÷ 100 = 2.5; 1 ÷ 2.5 = 40%.
2. format = american, odds = -110 gives american = -110, decimal = 1.909091, fractional = 10/11, probability = 52.380952%. Source: hand calculation in content.mdx: 1 + 100 ÷ 110 = 21/11; 11/21 = 52.380952…%.
3. format = fractional, odds = 5/2 gives american = +250, decimal = 3.5, fractional = 5/2, probability = 28.571429%. Source: hand calculation in content.mdx: 1 + 5/2 = 7/2; 2/7 = 28.571428…%.
4. format = decimal, odds = 1.8 gives american = -125, fractional = 4/5, probability = 55.555556%. Source: hand calculation in content.mdx: 100 ÷ 0.8 = 125; 0.8 = 4/5; 1 ÷ 1.8 = 55.5…%.
5. format = probability, odds = 75% gives american = -300, decimal = 1.333333, fractional = 1/3, probability = 75%. Source: hand calculation in content.mdx: 100 ÷ 75 = 4/3; 4/3 − 1 = 1/3; −100 ÷ (1/3) = −300.
6. format = decimal, odds = 1.91 gives american = -109.89, fractional = 91/100. Source: hand calculation in content.mdx: 100 ÷ 0.91 = 109.890…, rounded to 109.89.

## FAQ

### How do I convert American odds to decimal odds?

For positive American odds, divide by 100 and add 1: +150 is 1 + 150 ÷ 100 = 2.5. For negative American odds, divide 100 by the number without its sign and add 1: −110 is 1 + 100 ÷ 110 = 1.9091.

### How do I convert decimal odds to fractional odds?

Subtract 1 and write the result as a fraction in lowest terms. Decimal 2.5 gives 1.5 = 3/2, and decimal 1.8 gives 0.8 = 4/5. The fraction is the profit for each 1 you stake.

### What is implied probability?

It is the win chance that the odds stand for: 1 ÷ decimal odds. Decimal 2.5 implies 1 ÷ 2.5 = 40%. It includes the bookmaker’s margin, so it is usually a little higher than the true chance.

### What do plus and minus mean in American odds?

A plus number is the profit on a 100 stake: +150 wins 150 for 100 staked. A minus number is the stake you need to win 100: −110 means you stake 110 to win 100. Plus odds are for the less likely side, minus odds for the favourite.

### Why do +100 and −100 give the same odds?

Both mean an even-money bet: you win as much as you stake. Both are decimal 2.0, fractional 1/1, and a 50% implied probability. The calculator writes even money as +100.

### Why is the fractional answer sometimes a large fraction?

The calculator keeps the exact value. Decimal 1.91 is exactly 91/100 in fractional odds, and a 52.38% probability is exactly 2381/2619. Bookmakers round such odds to a nearby simple fraction such as 10/11.

## Sources

- Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 1.2, odds and probabilities (page 28): https://math.dartmouth.edu/~prob/prob/prob.pdf
- Wikipedia, Fixed-odds betting (fractional, decimal and moneyline odds): https://en.wikipedia.org/wiki/Fixed-odds_betting
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/