Odds Calculator

Odds calculator at a glance#

An odds calculator converts between odds and probability. Odds compare favorable outcomes to unfavorable ones, while probability compares favorable outcomes to the total. Odds in favor are written favorable:unfavorable, so an event with probability 1/6 has 1 favorable and 5 unfavorable outcomes, giving odds of 1:5 in favor, or 5:1 against.

To turn odds back into probability, add the two numbers and divide: odds of 1:5 give a probability of 1 / (1 + 5) = 1/6, which is about 0.167, or 16.7%.

To find odds from a probability, work out the favorable and unfavorable counts: a probability of 1/4 means 1 favorable and 3 unfavorable, so odds in favor are 1:3 and odds against are 3:1. Odds and probability describe the same chance in different ways.

Enter your odds or probability in the calculator above to convert between the two. Betting sites may quote the same odds in American, decimal, or fractional format, so check which one is shown.

Odds and probability are not the same#

Probability compares favorable outcomes to the total number of outcomes, so it runs from 0 to 1, or 0% to 100%. Odds compare favorable outcomes to unfavorable ones, written as a ratio like 1:5. They describe the same chance, but a 1/6 probability is the same event as 1:5 odds in favor, and confusing the two leads to wrong payouts.

To turn odds into a probability, add both sides of the ratio and divide the favorable side by the total. Odds of 1:5 give 1 / (1 + 5) = 1/6, about 16.7%. To go the other way from a probability, the favorable count is the numerator and the unfavorable count is the denominator minus the numerator.

Reading betting odds formats#

Sportsbooks quote the same odds in three formats. American odds use a plus or minus sign: positive odds show the profit on a 100 unit stake, and negative odds show the stake needed to profit 100 units. Decimal odds show the total return per 1 unit staked, including your stake back. Fractional odds, common in the UK, show profit relative to stake as a ratio like 5/2.

A 5/2 fractional bet returns 5 units of profit for every 2 staked, so a 10 unit bet wins 25. Decimal odds of 1.5 on a 100 unit stake return 150 total, which is 100 stake plus 50 profit. The three formats always describe the same payout; only the notation differs.

Implied probability from betting odds#

Implied probability is the chance an outcome happens according to the quoted odds. Each format has its own formula:

• Decimal: divide 1 by the decimal odds, then multiply by 100. Odds of 1.5 imply 1 / 1.5 = 66.7%.
• Fractional: divide the denominator by the sum of numerator and denominator. Odds of 5/2 imply 2 / (5 + 2) = 28.6%.
• American positive: divide 100 by the odds plus 100. Odds of +200 imply 100 / (200 + 100) = 33.3%.
• American negative: divide the odds, without its sign, by that same value plus 100. Odds of -120 imply 120 / (120 + 100) = 54.5%.

Implied probabilities across a single event add up to more than 100% because the sportsbook builds in a margin, sometimes called the overround. That margin is the house edge, so the quoted odds are not a neutral estimate of the true chance.

Calculating a payout#

Multiply your stake by the decimal odds to get the total return, then subtract the stake for the profit. A 100 unit stake at decimal 1.8333 returns about 183.33 total, the same as American odds of -120. For fractional odds, multiply the stake by the fraction to get the profit, then add the stake back.

Frequently asked questions#

What is the difference between odds and probability?#

Probability is favorable outcomes over all outcomes, from 0 to 100%. Odds are favorable outcomes against unfavorable ones, written as a ratio. A probability of 1/4 is the same as odds of 1:3 in favor, or 3:1 against.

How do you convert odds to a probability?#

Add the two parts of the ratio and divide the favorable part by that total. Odds of 3:1 in favor give 3 / (3 + 1) = 3/4, or 75%. Odds against flip which part is favorable.

What does +200 mean in American odds?#

Plus 200 means a 100 unit stake wins 200 units of profit, returning 300 total. It also implies a win probability of 100 / (200 + 100), about 33.3%. Positive American odds always mark the underdog.

How do you read fractional odds like 5/2?#

You win 5 units of profit for every 2 units staked. A 10 unit bet at 5/2 returns 25 in profit plus the 10 stake, for 35 total. The implied probability is 2 / (5 + 2), about 28.6%.

Why do the implied probabilities add up to more than 100%?#

Sportsbooks add a margin, the overround, so their odds pay out less than a fair bet would. Across all outcomes of one event the implied probabilities sum above 100%, and the excess is the house edge.

What is a value bet?#

A value bet is one where your own estimate of an outcome's chance is higher than the implied probability in the odds. If you think a result is 50% likely but the odds imply 40%, the bet has positive expected value over the long run.