Odds Calculator
Convert fractional, decimal and moneyline odds into each other and into implied probability, and see the margin built into a two-way market.
Result
Implied probability: 28.5714%
Implied probability is what the price says, not the true chance of the event: the price includes the margin and whatever the price-setter believes.
- Decimal odds
- 3.5
- Fractional odds
- 5/2
- Moneyline odds
- +250
https://calcgallery.com/statistics/odds-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Odds Calculator
- Choose how the odds are written, fractional, decimal, moneyline or as a probability, and enter them.
- Read the same price in the other formats and the probability it implies.
- For a contest with exactly two outcomes, switch on the other side and enter its price to see the margin and the no-vig probabilities.
- Optionally, under More options, enter a stake to see what the price pays.
The conversions
Every format is first turned into decimal odds, the total returned per unit staked when the outcome happens:
fractional a/b decimal = 1 + a ÷ bmoneyline +m decimal = 1 + m ÷ 100moneyline −m decimal = 1 + 100 ÷ mprobability p decimal = 1 ÷ pThen implied probability is 1 ÷ decimal, fractional odds are decimal − 1 written as a fraction, and the moneyline is +100 × (decimal − 1) when the decimal odds are 2 or more, and −100 ÷ (decimal − 1) below that. Fractional odds are reduced to the smallest denominator that gives the value exactly. When no fraction with a denominator up to 1,000 does, the page shows the nearest one with a denominator up to 100, marked ≈.
A two-way market
With both sides entered:
booksum = 1 ÷ decimal₁ + 1 ÷ decimal₂overround = booksum − 1margin = 1 − 1 ÷ booksumno-vig chance = (1 ÷ decimal) ÷ booksumno-vig odds = decimal × booksumThese are the textbook formulas: the overround and the margin as two ways of stating the same gap, and the no-vig figures as each side’s share of the booksum. They only apply when the two sides cover every outcome, so a contest that can end in a draw needs all three prices, which this page does not take.
What this page does not do
It converts numbers. It does not say whether a price is good, compare prices between sellers, or suggest what to stake.
With your numbers
- Decimal odds = 3.5
- Implied probability = 1 ÷ 3.5 = 28.57%
Quick reference
Implied probability is what the price says, not the true chance of the event: the price includes the margin and whatever the price-setter believes.
| Example | Implied probability |
|---|---|
| Fractional 5/2 | 28.5714% |
| Evens, 1/1 | 50% |
| Decimal 1.91 | 52.356% |
| Moneyline −110 | 52.381% |
| Moneyline +150 | 40% |
| A 40% implied probability | 40% |
| Two-way −110 and −110 | 52.381% |
| Two-way −150 and +130 | 60% |
Common questions about the Odds Calculator
- How do I convert fractional odds to decimal odds?
- Divide the first number by the second and add 1. Fractional odds give the profit per unit staked, and decimal odds give the total returned including the stake, so 5/2 is 2.5 plus the stake: 3.5. Going back, subtract 1 from the decimal odds and write the rest as a fraction.
- How do moneyline odds work?
- A plus figure is the profit on a stake of 100, so +250 returns 250 profit on 100. A minus figure is the stake needed to make 100 profit, so −110 means staking 110 to win 100. Evens is +100. A figure between −100 and +100 is not a moneyline, and the page refuses it.
- What is implied probability?
- The chance at which the price would break even in the long run: 1 divided by the decimal odds. Odds of 3.5 imply 1 ÷ 3.5, about 28.6%. It is a way of reading a price, not a forecast. Prices include the margin of whoever sets them and reflect their view and the money placed, so the implied probability is not the true chance of the event.
- Why do the two sides add up to more than 100%?
- Because the prices carry a margin. If both sides of a two-way contest are priced at −110, each implies about 52.4%, and together about 104.8%. The extra 4.8% is the overround. Dividing each side by the total gives no-vig probabilities that add to 100%, here 50% each.
- What is the difference between overround and margin?
- Overround is the total of the implied probabilities minus 100%. Margin, 1 minus 1 divided by that total, is the share of all money staked that the price-setter would keep if stakes were spread in proportion to the prices. For small figures they are close; the page shows both.
- Are no-vig probabilities the real chances?
- Not necessarily. Removing the margin in proportion assumes it is spread evenly across both sides. Studies of sports prices find that longshots usually carry more of it than favourites, which makes the proportional no-vig figure a little low for the favourite and a little high for the longshot.