Odds to Probability Converter

How it works

Probability and odds describe the same chance in different words. A probability is the share of trials in which the event happens: 20% means 1 in 5. Odds compare the ways it happens to the ways it does not: odds for of 1 : 4 means one success for every four failures, and odds against of 4 : 1 is the same thing read the other way.

Bookmakers write odds against in three dialects. Fractional odds (4/1, "four to one") are the profit per unit staked. Decimal odds (5.00) are the total return per unit staked, profit plus stake, so they are always fractional odds plus one. American odds quote the profit on a 100 stake when positive (+400) and the stake needed to win 100 when negative (−150). Each one implies a probability, and the calculator converts whichever you know into all the others.

Quoted betting odds include the bookmaker's margin, so the implied probabilities of all the outcomes of a real market add up to more than 100%. The conversion here is the pure arithmetic; it does not remove that margin.

Formula

odds for a : b        p = a / (a + b)
odds against a : b    p = b / (a + b)
fractional a/b        p = b / (a + b)         (same as odds against)
decimal d             p = 1 / d               d = 1 / p
american +m           p = 100 / (m + 100)     m = 100 (1 − p) / p   when p ≤ 0.5
american −m           p = m / (m + 100)       m = 100 p / (1 − p)   when p > 0.5

Example

Fractional odds of 4/1 mean four ways to lose for every one way to win, so the probability is 1/(4 + 1) = 20%. Odds for are 1 : 4, odds against 4 : 1, decimal odds 1/0.2 = 5.00 and American odds +400.

A moneyline of −150 means staking 150 to win 100, so the implied probability is 150/(150 + 100) = 60%. That is decimal odds of 1.667 and fractional odds of 2/3.

Assumptions and limitations

• Probability must be strictly between 0% and 100%: at the extremes the odds against or for are infinite and no betting format exists.
• American odds of +100 and −100 both mean an even chance (50%); the calculator shows +100 for exactly 50%.
• Fractional and ratio outputs are shown as small whole numbers when a fraction with a denominator of 100 or less reproduces the value exactly; otherwise they are shown as a decimal against 1. American odds are rounded to the nearest whole number.
• Implied probabilities from quoted betting odds include the bookmaker's margin (overround) and are not the true chance of the outcome.

Frequently asked questions