Start with decimal odds
Decimal odds are the simplest common format to use as a bridge. They represent the total potential return for every $1 staked, including the original stake. Once a price is converted to decimal, both implied probability and payout follow directly.
Potential profit = stake × (decimal odds − 1)
Implied probability (%) = 100 ÷ decimal odds
At decimal odds of 2.50, a $20 stake has a total potential return of $50 and potential profit of $30. The price implies a break-even probability of 40%.
American odds to decimal
American odds need two formulas because positive and negative prices communicate different things.
Positive American odds
For positive odds, divide the American number by 100 and add 1.
Example: +150 → (150 ÷ 100) + 1 = 2.50
Positive American odds state the potential profit on a $100 stake. A +150 price therefore represents $150 potential profit and $250 total potential return on $100.
Negative American odds
For negative odds, divide 100 by the absolute value of the American number and add 1.
Example: −200 → (100 ÷ 200) + 1 = 1.50
Negative American odds state the stake required to make $100 potential profit. At −200, a $200 stake produces $100 potential profit and $300 total potential return if successful.
Decimal odds to American
The decimal-to-American formula depends on whether the decimal price is at least 2.00.
Example: 2.50 → (2.50 − 1) × 100 = +150
If decimal < 2.00: American = −100 ÷ (decimal − 1)
Example: 1.50 → −100 ÷ (1.50 − 1) = −200
Converted American odds are normally rounded to a whole number. That rounding can create a very small difference if you convert the displayed number back again.
Fractional and decimal odds
Fractional odds show potential profit relative to the stake. The numerator is the potential profit and the denominator is the stake unit.
Example: 3/2 → (3 ÷ 2) + 1 = 2.50
Decimal to fractional: decimal odds − 1, then express the result as a fraction
Example: 2.50 − 1 = 1.50 = 3/2
Not every decimal price has a neat traditional fractional equivalent. In those cases, converters usually display the nearest sensible fraction.
Convert odds to implied probability
After converting to decimal, divide 1 by the decimal price. Multiply by 100 to express the result as a percentage.
2.50 → 100 ÷ 2.50 = 40%
1.50 → 100 ÷ 1.50 = 66.67%
Common conversion mistakes
- Forgetting the stake in decimal returns. Decimal odds already include the returned stake.
- Treating a negative American number as a negative payout. The minus sign describes the price structure, not a loss.
- Adding parlay odds. Convert legs to decimal and multiply them instead.
- Assuming every fraction is exact. Some fractional displays are rounded approximations.
- Confusing implied probability with prediction. It is a price-derived threshold, not a forecast.