Odds Calculator
Convert any odds format to implied probability, find your potential payout on a stake, and strip out the bookmaker margin to see the fair-odds probability underneath. Choose American (moneyline), decimal, fractional, or ratio odds, then enter an optional stake to see profit and total return in one step.
Formula
Worked example
Ratio 1:4 gives P = 1/(1+4) = 20%. Decimal 2.50 gives P = 1/2.50 = 40%. Fractional 6/4 gives P = 4/(6+4) = 40%. American +150 gives P = 100/(150+100) = 40%. American -200 gives P = 200/(200+100) = 66.67%.
Odds versus probability: the same chance, two languages
Probability counts how many outcomes are favorable out of all possible outcomes, so it always sits between 0% and 100%. Odds compare favorable outcomes against unfavorable ones, a ratio of "wins" to "losses." Odds of 1 to 4 mean one way to succeed for every four ways to fail. Both describe the same underlying chance; the bridge is simple division: divide the favorable count by the total (for plus against) to get the probability. Sportsbooks almost never quote raw ratios. They use three main shorthand systems: decimal, fractional, and American (moneyline), each just a different way of expressing the same ratio.
Decimal, fractional, and American odds explained
Decimal odds (e.g. 2.50) state the total return per unit staked, stake included, so inverting them gives the probability directly: 1 / 2.50 = 40%. Fractional odds like 6/4 show profit over stake, so the probability is the stake divided by the total: 4 / (6+4) = 40%. American moneyline odds work in two directions. A positive value like +150 is an underdog: the number is profit on a 100-unit stake, and probability = 100 / (150+100) = 40%. A negative value like -200 is a favorite: the number is the stake needed to win 100, and probability = 200 / (200+100) = 66.67%. Despite the different arithmetic, all four formats encode the same underlying probability.
Payout, profit, and total return
Once you know the decimal odds equivalent (which this calculator always shows), payout math is straightforward. Your profit equals your stake multiplied by (decimal odds minus 1), because decimal odds include the stake return. Your total return is simply stake multiplied by the decimal odds. On a 10-unit stake at decimal odds of 2.50 the profit is 10 x 1.50 = 15 units and the total return is 25 units. Enable the stake section to have the calculator work these numbers out live as you adjust the odds.
The bookmaker margin: overround and fair-odds probability
Bookmakers make money by offering odds that imply a total probability above 100% across all outcomes in a market. That surplus above 100% is the overround, also called the vig or juice. For a two-outcome market, add the implied probabilities of both sides: if they sum to 105%, the overround is 5%. To find the true fair-odds probability for one side, divide its implied probability by that total: if side A has implied 60% and the total is 105%, the fair probability is 60 / 1.05 = 57.14%. Removing the vig lets you compare the bookmaker estimate to your own and decide whether the offered odds represent value.
Consecutive outcomes and compound probability
When the same independent event repeats, the probability of it occurring n times in a row is p raised to the power n, where p is the single-event probability. Flip a fair coin (50%) three times: the chance of three heads is 0.50^3 = 12.5%. Bet on a 40% implied-probability outcome five times: the chance of winning all five is 0.40^5 = 1.02%. Each event must be truly independent for this formula to apply. If the events are not independent (e.g. drawing cards without replacement), you would need to multiply the changing conditional probabilities at each step instead.
Common odds across all four formats
| Ratio (for:against) | Fractional | Decimal | American | Implied probability |
|---|---|---|---|---|
| 1:9 | 1/9 | 1.11 | -900 | 90.00% |
| 1:4 | 1/4 | 1.25 | -400 | 80.00% |
| 2:3 | 2/3 | 1.67 | -150 | 60.00% |
| 1:1 | 1/1 (evens) | 2.00 | +100 | 50.00% |
| 2:3 | 3/2 | 2.50 | +150 | 40.00% |
| 1:2 | 2/1 | 3.00 | +200 | 33.33% |
| 1:4 | 4/1 | 5.00 | +400 | 20.00% |
| 1:9 | 9/1 | 10.00 | +900 | 10.00% |
Exact conversions between ratio, fractional, decimal, and American odds with implied probability.
Frequently asked questions
How do I convert odds to a probability?
For ratio odds, divide the odds-for by the sum of for and against: 1/(1+4) = 20%. For decimal odds, divide 1 by the decimal: 1/2.50 = 40%. For fractional odds a/b, divide the denominator by the total: b/(a+b). For positive American odds, use 100/(odds+100). For negative American odds, use |odds|/(|odds|+100).
What is implied probability?
Implied probability is the win chance encoded in a set of odds. It is called "implied" because it includes the bookmaker margin, so it slightly overstates the genuine estimate. To find it, convert any odds format to a 0-to-100 percentage using the formulas above.
How do positive and negative American odds work?
Positive American odds (e.g. +150) show the profit you would collect on a 100-unit stake if you win. +150 means win 150 on a 100 stake, for a total return of 250. Negative American odds (e.g. -200) show how much you must stake to win 100 units. -200 means you stake 200 to win 100, for a total return of 300.
What is the overround and why does it matter?
The overround (also called vig or juice) is the bookmaker margin. Add up the implied probabilities of every outcome in a market and the total exceeds 100%. That excess is the overround. A 5% overround means for every 100 you bet across the market the bookmaker keeps about 5. Knowing the overround lets you see how much the implied probability is inflated above the fair-odds probability.
How do I calculate profit and total return from a stake?
Once you have the decimal odds equivalent, profit = stake x (decimal odds - 1) and total return = stake x decimal odds. At decimal 3.00 and a 20-unit stake: profit = 20 x 2 = 40, total return = 60. The stake section in this calculator does this automatically.
What is the probability of winning n times in a row?
For independent events, raise the single-event probability to the power n. If the implied probability of one outcome is 40% (0.40), the chance of it occurring three times in a row is 0.40^3 = 0.064, or 6.4%. The consecutive section calculates this automatically.
Why do implied probabilities in a market add up to more than 100%?
Bookmakers build in a margin known as the overround. Add the implied probabilities for all outcomes and the total exceeds 100%. The excess is the house edge. A fair-odds probability, with the vig removed, is always slightly lower than the implied figure shown in quoted odds.