Decimal, Fractional and American Odds: A Conversion Guide
Odds are a price, and the same price can be written in three languages. Decimal odds tell you what a winning unit returns. Fractional odds tell you the profit relative to the stake. American odds tell you what a 100 bet pays or what you must risk to win 100. None of them is more accurate than the others, and all of them can be converted in a few seconds.
The confusion is practical rather than mathematical. A bettor who reads only one format will misjudge a price from another country, and a bettor who never converts to probability will struggle to compare a short favourite with a long shot. This guide covers the three formats, the conversion formulas and the table you can keep next to your record.
Decimal odds: total return per unit
Decimal odds include the stake in the return. A price of 2.50 means every unit staked returns 2.50, of which 1.50 is profit. Multiply the stake by the price to get the total return, then subtract the stake to get the profit.
Converting to implied probability is a single division: one divided by the decimal price. A price of 2.00 implies 50 percent, 4.00 implies 25 percent and 1.50 implies 66.7 percent. Add the implied probabilities of every outcome in a market and the total will exceed 100 percent, with the excess being the bookmaker's margin.
Fractional odds: the profit ratio
Fractional odds show profit over stake. A price of 3/2 means you win 3 for every 2 staked, so a 10 bet returns 15 in profit and 25 in total. A price of 1/1, also written evens, doubles your money. A price of 1/4 means a small profit on a large stake.
The format is compact and traditional, and it makes the bookmaker's margin easy to see when the fractions share a denominator. It is less convenient for quick arithmetic, which is why most of the world has moved to decimals.
American odds: the 100 baseline
American odds come in two forms. A positive number tells you the profit on a 100 stake, so +150 returns 150 in profit. A negative number tells you how much you must stake to win 100, so -200 requires 200 to win 100.
The sign is not a quality judgement. Positive prices are underdogs and negative prices are favourites, and the larger the absolute number, the longer or shorter the price. A +1000 shot and a -1000 favourite are both extreme, in opposite directions.
The conversion formulas
To go from fractional to decimal, divide the top by the bottom and add one. To go from decimal to fractional, subtract one and reduce the fraction. For American odds, a positive number becomes decimal by dividing by 100 and adding one, while a negative number becomes decimal by dividing 100 by the absolute number and adding one.
Going the other way is just as simple. A decimal price at or above 2.00 becomes American by multiplying by 100 and subtracting 100. A decimal price below 2.00 becomes American by dividing 100 by the decimal minus one and making the result negative.
- Fractional to decimal: divide the top by the bottom, then add one.
- Decimal to fractional: subtract one, then reduce the fraction to its simplest form.
- Positive American to decimal: divide by 100, then add one.
- Negative American to decimal: divide 100 by the number without its sign, then add one.
Conversion table with returns
The table shows the same prices in all three formats, with the implied probability and the total return on a stake of 10. Every figure can be checked with the formulas above, and the probabilities are rounded to one decimal place.
| Decimal | Fractional | American | Implied | Return on 10 |
|---|---|---|---|---|
| 1.25 | 1/4 | -400 | 80.0% | 12.50 |
| 1.50 | 1/2 | -200 | 66.7% | 15.00 |
| 1.91 | 10/11 | -110 | 52.4% | 19.10 |
| 2.00 | 1/1 | +100 | 50.0% | 20.00 |
| 2.50 | 3/2 | +150 | 40.0% | 25.00 |
| 3.00 | 2/1 | +200 | 33.3% | 30.00 |
| 4.50 | 7/2 | +350 | 22.2% | 45.00 |
The -110 row is the one to memorise. It is the standard price on a spread or total in American football and basketball, and it converts to 1.91 decimal, which is 52.4 percent implied. Two sides at -110 imply 104.8 percent, and the extra 4.8 points are the book's margin on that market.
Why the same bet shows different numbers
Bookmakers display the format their customers expect. A UK site may show fractions, a European site decimals and a US site American odds, all for the same event and the same price. The underlying probability does not change when the display does.
The margin does change between books, though, and comparing across formats is where conversions earn their keep. A fractional 5/2 and an American +250 are the same bet, so a bettor who only reads fractions may not notice that a US book is offering a better price on the same outcome.
Reading across formats also protects against a common sales trick. A price displayed as 1/3 looks small, while the same price shown as -300 looks severe, and a bonus offer quoted in one format can hide how short the underlying odds are. Convert first, then judge the offer.
Using probability rather than price
The most useful habit is to convert every price to implied probability before deciding. A 1.25 favourite implies 80 percent, which leaves very little room for error. A 4.50 shot implies 22.2 percent, which means the bet can lose four times out of five and still be correct if the true probability is higher than the price suggests.
That comparison is the whole point of learning the formats. The numbers are a translation layer, and the decision happens in probability space, where a short price and a long price can be compared on equal terms.
Once the conversions are automatic, the format on the screen stops mattering. If you are placing a first bet, the step by step walkthrough puts the price in context, and line shopping explains why the same outcome can be worth two different prices at two books.
