American
-110
Type a price in any format. American, decimal, fractional, and implied probability update live as you type. Free, no account, no data leaves this page.
Every format describes the same thing: the payout on a winning bet, which pins down the implied probability. Here is the exact math this page runs.
positive price A: decimal = 1 + A / 100 negative price A: decimal = 1 + 100 / |A|
So +150 gives 1 + 150/100 = 2.50, and -110 gives 1 + 100/110 = 1.9091.
implied probability p = 1 / decimal decimal = 1 / p
A decimal of 2.00 is an implied probability of 0.5000, or 50%. This is the raw price, before removing the book's margin.
decimal >= 2: American = (decimal - 1) * 100 decimal < 2: American = -100 / (decimal - 1)
A decimal of 2.50 gives +150; a decimal of 1.50 gives -200.
fractional = (decimal - 1), reduced to lowest terms
A decimal of 2.50 means decimal - 1 = 1.5 = 3/2. A decimal of 1.9091 means 0.9091 = 10/11. The page reduces the fraction with a continued-fraction algorithm so you get 3/2, not 15/10.
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For a positive price A, decimal = 1 + A/100, so +150 is 2.50. For a negative price, decimal = 1 + 100/|A|, so -110 is 1.9091 and -200 is 1.50.
The win probability at which a price is exactly break-even: p = 1 / decimal odds. A -110 price (1.9091 decimal) implies 52.38%; +150 (2.50 decimal) implies 40.00%. Implied probabilities include the bookmaker's margin, so a full market's implied probabilities sum to more than 100%; the no-vig calculator removes that margin.
Both +100 and -100 mean exactly even money (2.00 decimal). A magnitude below 100 would be ambiguous between the two conventions, so American boards never use one: prices run upward from +100 and downward from -100. This converter rejects anything in between and tells you why.
Fractional odds state profit per unit staked: decimal minus 1, written as a reduced fraction. Decimal 2.50 is 3/2; decimal 1.9091 is 10/11. This page reduces the fraction with a continued-fraction algorithm so you get 3/2, never 15/10.
These are the exact values the converter produces, and the same cases its built-in self-test checks on every page load. Probabilities are shown to 4 decimal places, decimals to 4, American odds rounded to a whole number.
| Input | American | Decimal | Fractional | Implied prob |
|---|---|---|---|---|
| American +150 | +150 | 2.5000 | 3/2 | 0.4000 |
| American -110 | -110 | 1.9091 | 10/11 | 0.5238 |
| American -200 | -200 | 1.5000 | 1/2 | 0.6667 |
| American +100 | +100 | 2.0000 | 1/1 | 0.5000 |
| Decimal 3.40 | +240 | 3.4000 | 12/5 | 0.2941 |
| Decimal 1.50 | -200 | 1.5000 | 1/2 | 0.6667 |
| Fractional 5/2 | +250 | 3.5000 | 5/2 | 0.2857 |
| Implied 25% | +300 | 4.0000 | 3/1 | 0.2500 |