# Fractional Odds Calculator

URL: https://speedycalculator.com/calculators/statistics/fractional-odds/
Last updated: 2026-10-30

> The fractional odds calculator turns a probability, chances for and against, decimal or moneyline odds into traditional fractional odds such as 3/2 or 5/1, and gives the implied chance of winning and losing, the payout on a stake and the chance of consecutive wins or losses.

## Inputs

- I know the odds as
- Chances for (winning outcomes)
- Chances against (losing outcomes)
- Probability of winning (%)
- Fractional odds – first number (profit)
- Fractional odds – second number (stake)
- Decimal odds
- Moneyline odds (minus for favourites) — Type −150 for a favourite or 250 for +250.
- Stake (any currency)
- Times in a row

## Results

- Fractional odds (profit/stake)
- Probability of winning (implied)
- Probability of losing
- Decimal odds
- American moneyline odds
- Odds in favour (win : lose)
- Odds against (lose : win)
- Favourite or underdog
- Total returned if it wins (stake + profit)
- Net profit if it wins
- Probability of winning that many times in a row
- Probability of losing that many times in a row
- Win/lose split

## Formula

```
Fractional odds a/b = (1 − p) ÷ p written as a fraction = chances against ÷ chances for
Probability = b ÷ (a + b) · Profit = stake × a ÷ b
```

## Explanation

Fractional odds are the traditional British and Irish format. They state the profit relative to the stake: at 3/2 a winning stake of 2 earns 3 profit (plus the stake back), and at 5/1 a stake of 1 earns 5. The first number is the "against" side and the second the "for" side, so 3/2 means 3 chances of losing for every 2 of winning – an implied probability of 2 ÷ 5 = 40%.

Odds shorter than evens, such as 1/2 ("two to one on"), belong to favourites: you must stake 2 to win 1, and the implied chance is 2/3 = 66.67%. Evens is 1/1. The calculator converts any probability, pair of chances, decimal or moneyline price into the simplest fraction (approximated with denominators up to 100 when the price is not a neat fraction).

It also shows the equivalent decimal and moneyline odds, a pie chart of win and lose chances, the return and profit for your stake and the probability of a run of identical results. Remember that bookmakers’ fractions include a margin, so the implied probabilities overstate the real chances a little.

### How to use the Fractional Odds Calculator

- **I know the odds as**
- **Chances for (winning outcomes)**
- **Chances against (losing outcomes)**
- **Probability of winning**
- **Fractional odds – first number (profit)**
- **Fractional odds – second number (stake)**
- **Decimal odds**
- **Moneyline odds (minus for favourites)** — Type −150 for a favourite or 250 for +250.
- **Stake (any currency)**
- **Times in a row**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The win probability p is computed from whatever you enter; (1 − p)/p is then expressed as the closest simple fraction, exact when your inputs are whole-number chances or a fraction. Profit = stake × (1 − p)/p.

### Worked example

You estimate a 40% chance of winning. The chance of losing is 60%, so fractional odds are 60/40 = 3/2. The equivalent decimal odds are 2.50 and the moneyline is +150. A 10 stake would win 15 profit and return 25. Two wins in a row have probability 0.4² = 16%.

### Common fractional prices

FractionalImplied probabilityDecimal1/480%1.251/266.67%1.504/555.56%1.801/1 (evens)50%2.006/440%2.505/116.67%6.0010/19.09%11.00

## Worked example

Inputs — I know the odds as: Probability of winning; Probability of winning: 40 %; Stake (any currency): 10; Times in a row: 2.

Results — **Fractional odds (profit/stake) = 3/2**; Probability of winning (implied) = 40 %; Probability of losing = 60 %; Decimal odds = 2.5; American moneyline odds = +150; Odds in favour (win : lose) = 2 : 3.

## Key terms

- **Decimal odds**: The total payout per 1 unit staked, stake included; 1 ÷ decimal odds is the implied probability.
- **Fractional odds**: Profit ÷ stake, written like 5/2 – a winning 2 pays 5 profit.
- **Moneyline odds**: American format: +250 is the profit on a 100 stake, −150 is the stake needed to win 100.
- **Implied probability**: The chance of winning that a price represents, before any bookmaker margin is removed.

## FAQ

**How do fractional odds work?**
a/b means a profit of a for every b staked. At 3/2 a 10 stake wins 15 profit and returns 25.

**How do I convert fractional odds to probability?**
For a/b the probability is b ÷ (a + b): 3/2 → 40%, 5/1 → 16.67%, 1/2 → 66.67%.

**How do I convert a probability to fractional odds?**
Divide the chance of losing by the chance of winning: 40% → 60/40 = 3/2.

**What does "odds-on" mean?**
Odds shorter than evens, such as 4/6 or 1/2, where the favourite is more likely to win than lose.

**What are evens?**
1/1 – stake 1, win 1 profit; implied probability 50%; decimal 2.00; moneyline +100.

**How do fractional odds relate to decimal odds?**
Decimal = fraction + 1, so 3/2 = 1.5 + 1 = 2.50.


## Sources

- [OpenStax – Introductory Statistics 2e, Chapter 3: Probability topics](https://openstax.org/books/introductory-statistics-2e/pages/3-introduction)
- [Khan Academy – Statistics and probability](https://www.khanacademy.org/math/statistics-probability)