To convert American odds to decimal odds, use
(odds ÷ 100) + 1for a positive price and(100 ÷ |odds|) + 1for a negative one. So +150 becomes 2.50 and −110 becomes 1.91.
American odds describe profit relative to a 100-unit reference, in two directions. A positive price is the profit on a 100 stake: +150 means 150 profit from 100, so 250 back in total, so decimal 2.50. A negative price is the stake needed to profit 100: −200 means staking 200 to win 100, so 300 back from 200, so decimal 1.50.
Some common conversions:
| American | Decimal | Implied probability |
|---|---|---|
| −400 | 1.25 | 80.00% |
| −200 | 1.50 | 66.67% |
| −110 | 1.91 | 52.38% |
| +100 | 2.00 | 50.00% |
| +150 | 2.50 | 40.00% |
| +250 | 3.50 | 28.57% |
| +1000 | 11.00 | 9.09% |
Going back the other way: (decimal − 1) × 100 when the decimal price is 2.00 or above, and −100 ÷ (decimal − 1) when it is below. Exactly 2.00 is the hinge, conventionally written +100 rather than −100 — the point where the two formulas meet and a price stops being a favourite.
Two practical notes. First, −110 is really 1.909090…, and rounding it to 1.91 introduces a small error; work in full precision and round only for display. Second, a price with an absolute value under 100 (+50, −50) is not a standard quote — the formulas still resolve it unambiguously, and +50 turns out to be the same price as −200, but seeing one usually means a data feed has been mangled somewhere.
For the probability half of the conversion, see decimal odds to implied probability, or how to convert odds to implied probability for worked examples in all three formats.