How do I convert betting odds?

Type odds in one format and get the same odds in the other formats, with the win chance they imply. The results are mathematics, not betting advice.

Implied probability: 40%

These odds are +150 American, 2.5 decimal and 3/2 fractional, an implied probability of 40%.

American odds: +150
Decimal odds: 2.5
Fractional odds: 3/2
Chance of losing: 60%

Implied probability: 40%. These odds are +150 American, 2.5 decimal and 3/2 fractional, an implied probability of 40%.

The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use

How to calculate

Converts betting odds between American, decimal and fractional formats and the implied probability, with exact fractions.

Example with the default inputs (Odds format American, Odds +150): These odds are +150 American, 2.5 decimal and 3/2 fractional, an implied probability of 40%.

Method: Decimal odds d: American +A gives d = 1 + A ÷ 100, −A gives d = 1 + 100 ÷ A; fractional a/b gives d = 1 + a ÷ b; probability p% gives d = 100 ÷ p. Implied probability = 100 ÷ d percent.

Implied probability is 1 ÷ decimal odds. It includes the bookmaker’s margin, so the implied probabilities of all outcomes of one event add up to more than 100%.
Conversions are exact fractions. Only American odds and the displayed decimals are rounded.
Decimal odds must be above 1 and at most 1,000,001 (American +100,000,000).
Results are mathematics, not betting advice.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

Odds format American, Odds +150 gives American odds +150, Decimal odds 2.5, Fractional odds 3/2, Implied probability 40%, Chance of losing 60%.Source: hand calculation in content.mdx: 1 + 150 ÷ 100 = 2.5; 1 ÷ 2.5 = 40%
Odds format American, Odds -110 gives American odds -110, Decimal odds 1.909091, Fractional odds 10/11, Implied probability 52.380952%.Source: hand calculation in content.mdx: 1 + 100 ÷ 110 = 21/11; 11/21 = 52.380952…%
Odds format Fractional, Odds 5/2 gives American odds +250, Decimal odds 3.5, Fractional odds 5/2, Implied probability 28.571429%.Source: hand calculation in content.mdx: 1 + 5/2 = 7/2; 2/7 = 28.571428…%
Odds format Decimal, Odds 1.8 gives American odds -125, Fractional odds 4/5, Implied probability 55.555556%.Source: hand calculation in content.mdx: 100 ÷ 0.8 = 125; 0.8 = 4/5; 1 ÷ 1.8 = 55.5…%
Odds format Probability, Odds 75% gives American odds -300, Decimal odds 1.333333, Fractional odds 1/3, Implied probability 75%.Source: hand calculation in content.mdx: 100 ÷ 75 = 4/3; 4/3 − 1 = 1/3; −100 ÷ (1/3) = −300
Odds format Decimal, Odds 1.91 gives American odds -109.89, Fractional odds 91/100.Source: hand calculation in content.mdx: 100 ÷ 0.91 = 109.890…, rounded to 109.89

How it works

Every format is turned into decimal odds d, the total return for each 1 staked (stake included). The calculator keeps d as an exact fraction.

You type	Decimal odds d
American +A (A ≥ 100)	d = 1 + A ÷ 100
American −A (A ≥ 100)	d = 1 + 100 ÷ A
Fractional a/b	d = 1 + a ÷ b
Implied probability p%	d = 100 ÷ p

From d it writes every format:

Decimal odds: d, shown to at most 4 decimals.
American odds: when d ≥ 2, +100 × (d − 1); when d < 2, −100 ÷ (d − 1). The number is rounded to 2 decimals (halves away from 0), trailing zeros are dropped, and it always carries its sign (+150, -110). Even money (d = 2) is written +100.
Fractional odds: the exact fraction d − 1 in lowest terms, written numerator/denominator (3/2, 10/11, 1/1).
Implied probability: 100 ÷ d percent. The chance of losing is 100% minus that.

What you can type

Spaces are ignored, and the minus sign − reads as -.
Each format has its own shape, so odds typed in another format are never read as the chosen one. The page says which format they are in and gives the same price in the chosen format (with Decimal chosen, +110 gives “The same price as decimal odds is 2.1”).
American: a number with a + or − sign whose size is at least 100, such as +150, -110 or +1,000 (commas are thousands commas). Numbers between −100 and +100, and numbers with no sign, are not American odds.
Decimal: a plain number above 1 with no sign, such as 2.5. A single comma with no point is a decimal comma (2,5 is 2.5) unless exactly 3 digits follow it (1,000 is 1000); any other comma is a thousands comma.
Fractional: a/b, a:b, a-b or a to b with a and b above 0, or evens, even or evs (any letter case, to too). A bare number is not fractional odds.
Probability: a percentage above 0 and below 100 written with %, such as 40%. A single comma with no point is a decimal comma (66,6%).
Decimal odds above 1,000,001 (American +100,000,000) give no answer; the message says so.
Shapes that older odds pages accept get a hint instead: a number with no sign as American odds (100 or more): “type +150 or -150”; a whole number as fractional odds: “type 4/1”; a number below 100 as a probability: “type 40%”.
In the “the same price” message, decimal odds and probabilities are rounded to 4 decimals and American odds to 2, halves away from 0.

Assumptions

Implied probability comes straight from the odds. It includes the bookmaker’s margin (the vig), so the implied probabilities of every outcome of one event add up to more than 100%. The no-vig calculator removes the margin.
The result is exact arithmetic on the odds you type; only American odds and the shown decimals are rounded.

Worked examples by hand

American +150. d = 1 + 150 ÷ 100 = 2.5. Fractional: 2.5 − 1 = 1.5 = 3/2. Implied probability: 100 ÷ 2.5 = 40%, so the chance of losing is 60%.

American −110. d = 1 + 100 ÷ 110 = 1 + 10/11 = 21/11 = 1.9091. Fractional: 10/11. Implied probability: 100 × 11 ÷ 21 = 52.38%.

Fractional 5/2. d = 1 + 5/2 = 7/2 = 3.5. Since d ≥ 2, American: +100 × 2.5 = +250. Implied probability: 100 × 2 ÷ 7 = 28.57%.

Decimal 1.8. d − 1 = 0.8 = 4/5. Since d < 2, American: −100 ÷ 0.8 = −125. Implied probability: 100 ÷ 1.8 = 55.56%.

Probability 75%. d = 100 ÷ 75 = 4/3 = 1.3333. Fractional: 4/3 − 1 = 1/3. American: −100 ÷ (1/3) = −300.

Decimal 1.91. Fractional: 91/100. American: −100 ÷ 0.91 = −109.8901…, rounded to −109.89.

A note on betting

These results are mathematics, not advice. Every bet can lose, and the odds include the bookmaker’s margin. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).

Other questions people ask

How do I convert American odds to decimal odds?

For positive American odds, divide by 100 and add 1: +150 is 1 + 150 ÷ 100 = 2.5. For negative American odds, divide 100 by the number without its sign and add 1: −110 is 1 + 100 ÷ 110 = 1.9091.

How do I convert decimal odds to fractional odds?

Subtract 1 and write the result as a fraction in lowest terms. Decimal 2.5 gives 1.5 = 3/2, and decimal 1.8 gives 0.8 = 4/5. The fraction is the profit for each 1 you stake.

What is implied probability?

It is the win chance that the odds stand for: 1 ÷ decimal odds. Decimal 2.5 implies 1 ÷ 2.5 = 40%. It includes the bookmaker’s margin, so it is usually a little higher than the true chance.

What do plus and minus mean in American odds?

A plus number is the profit on a 100 stake: +150 wins 150 for 100 staked. A minus number is the stake you need to win 100: −110 means you stake 110 to win 100. Plus odds are for the less likely side, minus odds for the favourite.

Why do +100 and −100 give the same odds?

Both mean an even-money bet: you win as much as you stake. Both are decimal 2.0, fractional 1/1, and a 50% implied probability. The calculator writes even money as +100.

Why is the fractional answer sometimes a large fraction?

The calculator keeps the exact value. Decimal 1.91 is exactly 91/100 in fractional odds, and a 52.38% probability is exactly 2381/2619. Bookmakers round such odds to a nearby simple fraction such as 10/11.