How to Convert Betting Odds: American, Decimal and Fractional
Related book: The Sports Investing Blueprint by Ethan Cole · Amazon
The same price can be written three ways. A US book shows -150, a European site shows 1.67, and a UK site shows 4/6. Once you can move between the formats by hand, you can compare any two prices, read the payout on any stake, and turn any number into a break-even win rate. This page gives the formulas, a conversion table, payout examples and the rounding traps that catch people out.
Every price on this page is a made-up example. Displayed figures are rounded to two decimals; the math behind them uses exact fractions.
What each format tells you
- American odds are built around $100. A minus price is what you stake to win $100 profit (-150 means stake $150 to win $100). A plus price is the profit on a $100 stake (+150 means a $100 stake wins $150).
- Decimal odds are the total return on a one-unit stake, stake included. At 2.50, a $1 stake returns $2.50: $1.50 profit plus the $1 back.
- Fractional odds are profit over stake. At 3/2, every $2 staked wins $3 profit, and the stake comes back on top.
Decimal is the easiest hub. Convert anything to decimal first, then to whatever you need.
American to decimal
For a minus price, drop the minus and call the number A:
Decimal = 1 + 100 / A
For a plus price A:
Decimal = 1 + A / 100
- -150: 1 + 100 / 150 = 5 / 3, about 1.67
- -110: 1 + 100 / 110 = 21 / 11, about 1.91
- +150: 1 + 150 / 100 = 2.50
- +100 (even money): 2.00
Decimal to American
Call the decimal D. If D is 2.00 or more, the price is positive:
American = (D − 1) × 100
If D is under 2.00, the price is negative:
American = −100 / (D − 1)
- 2.75: (2.75 − 1) × 100 = +175
- 1.80: −100 / 0.80 = -125
- 1.65: −100 / 0.65 = −153.85, which a US book would usually show as -154 or -155
Fractional odds both ways
Fractional to decimal: add 1. So n/d becomes 1 + n / d.
- 7/4: 1 + 1.75 = 2.75, which is +175
- 4/5: 1 + 0.80 = 1.80, which is -125
- 11/8: 1 + 1.375 = 2.375, which is +137.50
- 1/1 (evens): 2.00, which is +100
Decimal to fractional: subtract 1 and write the rest as a fraction in lowest terms. 2.50 becomes 1.50, which is 3/2. 1.50 becomes 0.50, which is 1/2.
American to fractional directly: a plus price is A/100 (+250 is 250/100, or 5/2). A minus price is 100/A (-200 is 100/200, or 1/2). A fraction with the smaller number on top is an odds-on price, the same as a minus price in American terms.
Conversion table
Implied probability is 1 divided by the decimal: the share of bets a price needs to win to break even. The implied probability and the vig article covers that step in detail.
| American | Decimal | Fractional | Implied probability |
|---|---|---|---|
| -200 | 1.50 | 1/2 | 66.67% |
| -150 | 1.67 | 2/3 | 60.00% |
| -110 | 1.91 | 10/11 | 52.38% |
| +100 | 2.00 | 1/1 | 50.00% |
| +150 | 2.50 | 3/2 | 40.00% |
| +250 | 3.50 | 5/2 | 28.57% |
UK books often show -150 as 4/6 rather than 2/3. The two fractions are equal; 4/6 is simply the traditional way it is printed.
For every American price from -1000 to +1000 with its decimal and break-even rate, use the free American odds implied probability table, which you can also download as a CSV.
Payout on any stake
With decimal odds, total return = stake × D and profit = stake × (D − 1). Here is a $50 stake at four prices:
| Price | Decimal | Profit if it wins | Total return |
|---|---|---|---|
| -110 | 21/11 (about 1.91) | $45.45 | $95.45 |
| +150 | 2.50 | $75.00 | $125.00 |
| 4/5 | 1.80 | $40.00 | $90.00 |
| 2.75 | 2.75 | $87.50 | $137.50 |
A losing bet loses the $50 in every format. The format changes how the price is written, not what the bet pays.
Rounding traps
A displayed decimal is usually rounded. -110 is exactly 21 / 11 = 1.9090…, shown as 1.91. Convert the rounded 1.91 back and you get −100 / 0.91 = −109.89, not -110. The break-even rate drifts too: 52.36% from 1.91 against 52.38% from the exact price. On $100, 1.91 suggests a $91.00 profit; the real figure at -110 is $90.91.
A few cents rarely matters on one bet, but it adds up when you multiply prices together. The parlay odds article shows how chaining rounded decimals moves a payout. Keep the exact fraction until the last step, then round once.
Comparing prices across formats
Say one book offers -105, another 1.95, and a third 19/20. In decimal terms:
- -105: 1 + 100 / 105 = 1.9524…
- 1.95: 1.95
- 19/20: 1 + 0.95 = 1.95
The -105 is the best of the three: $95.24 profit on $100 against $95.00 for the other two. It looks like a tiny gap, but small edges on price are what line shopping is about, and they compound over hundreds of bets. To strip the margin out of a market and find a fair price, see no-vig fair odds.
Put it to work
Pick one format, usually decimal, and convert everything into it before you compare. Record the price you took and the stake in a bet log, and judge each bet against its break-even rate. The free bankroll and line-shopping worksheet puts two books’ prices side by side with the profit and break-even rate at each, and the expected value article shows how to tell whether a price is worth taking at all.
For how pricing, bankroll and record keeping fit together into one system, see the book.