Convert odds between fractional, decimal and American (moneyline) formats and get the implied probability, worked in exact fractions.
A 1-unit stake at these odds returns 3.5 in total (2.5 profit) if it wins. The odds imply a 28.57% chance; a bet only has positive expected value if the true chance is higher than that, and bookmakers' prices include a margin, so implied chances across all outcomes add up to more than 100%.
Worked as exact fractions, so no rounding creeps in between formats.
Decimal odds d are the total return per 1 staked, stake included. Fractional odds a/b give the profit per stake, so d = 1 + a/b. American odds are +100(d − 1) when d is 2 or more and −100/(d − 1) when d is below 2, and the implied probability is 1/d. Every conversion runs through exact fractions, so 10/11 stays 10/11 instead of becoming 0.909…
The default, 5/2, is decimal 3.5 and American +250: a 1-unit stake returns 3.5 if it wins, 2.5 of it profit, and the price implies a 28.57% chance. A −110 line, common on US point spreads, implies 52.38%, the win rate needed to break even.
Implied probability describes the price, not the true chance. Bookmakers build a margin into their prices, so the implied probabilities of all outcomes in a market add up to more than 100%.
Checked against: d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables)
Checked against: d − 1 = 1/2; American −100/0.5 = −200; p = 1/1.5 = 2/3
Checked against: d = 1 + 100/110 = 21/11; p = 11/21 = 52.381% (the standard −110 break-even rate)
Checked against: d = 1/0.25 = 4; 3/1; +300
Divide the first number by the second and add 1: d = a/b + 1. So 5/2 becomes 3.5, 1/2 becomes 1.5 and evens (1/1) becomes 2.0. The 1 is the returned stake: fractional odds quote profit only, while decimal odds quote the total return, so a winning 10-unit bet at 5/2 or 3.5 pays back 35 in both cases.
A plus number is the profit on a 100 stake and a minus number is the stake needed to win 100. At +250, 100 staked wins 250 profit (decimal 3.5); at −150, 150 staked wins 100 (decimal 1.667). +100 and −100 both mean evens, and no American odds exist between −100 and +100.
Divide 1 by the decimal odds: p = 1/d. Decimal 3.5 implies 1/3.5 = 28.57%. For fractional odds a/b the shortcut is b/(a + b), so 5/2 gives 2/7. For American −110 it is 110/(110 + 100) = 52.38%, and for +250 it is 100/(250 + 100) = 28.57%.
The overround is how far the implied probabilities of every outcome in a market add up past 100%. With both sides of a bet priced at −110, the total is 52.38% + 52.38% = 104.76%, an overround of 4.76% and a bookmaker margin (vig) of 1 − 1/1.0476 = 4.55% of stakes. Dividing each implied probability by the total, 52.38/104.76, removes the margin and gives 50%.
Odds-on means the implied probability is above 50%: fractional odds below 1/1, decimal odds below 2.0 and negative American odds. At 1/2 odds-on (1.5, or −200) you stake 2 to win 1, an implied 66.67%. Odds against is the reverse: 5/2 (3.5, or +250) pays more than the stake and implies less than 50%.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “5/2 (defaults)” is checked against d = 1 + 5/2; p = 2/7 = 28.571%; American +100 × 2.5 (standard conversion tables).
Grinstead & Snell, Introduction to Probability (AMS), §1.2 — odds and probability; UK Gambling Commission — how odds work (fractional and decimal).
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
5 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
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