Betting odds come in three formats — American, decimal and fractional — and all of them encode the same idea: how much a bet pays, and therefore what chance of winning the price implies. This calculator converts any price into every format, shows the implied probability, works out the payout for your stake, and, if you enter the other side of the market, calculates the bookmaker’s margin and the fair odds without it.
How to use the odds calculator
- Choose the odds format you are starting from: American, decimal, fractional, implied probability, or odds in favor (A to B).
- Enter the odds, for example +150, −110, 2.5, 5/2 or 40.
- Enter a stake to see the profit and total payout if the bet wins.
- Optional: enter the other side’s odds in the same format to see the margin and the no-vig probability.
Odds conversion formulas
Everything converts through decimal odds D, the total return per unit staked:
| American | Decimal | Fractional | Implied probability |
|---|---|---|---|
| −300 | 1.33 | 1/3 | 75.0% |
| −200 | 1.50 | 1/2 | 66.7% |
| −110 | 1.91 | 10/11 | 52.4% |
| +100 | 2.00 | 1/1 (evens) | 50.0% |
| +150 | 2.50 | 3/2 | 40.0% |
| +200 | 3.00 | 2/1 | 33.3% |
| +500 | 6.00 | 5/1 | 16.7% |
Fractional odds are “odds against”: 3/2 means 3 units of profit for every 2 staked. When a price doesn’t reduce to a simple fraction, the calculator shows the nearest fraction with a denominator up to 100 and marks it as approximate.
Worked example: removing the vig
A game is priced −150 on the favorite and +130 on the underdog.
- Favorite: 150 ÷ 250 = 60.00%. Underdog: 100 ÷ 230 = 43.48%.
- The total is 103.48%, so the bookmaker’s margin (overround) is 3.48%.
- Fair probabilities: 60.00 ÷ 103.48 = 57.98% for the favorite and 43.48 ÷ 103.48 = 42.02% for the underdog.
- As fair American odds those are about −138 and +138.
If you believe the favorite wins more than 60% of the time, the −150 price offers value; if you think it is closer to 58%, the market price is slightly against you.
Expected value of a bet
Implied probability is the break-even win rate. If your own estimate of the chance is q, the expected profit per $1 staked is
At +150 (D = 2.50), a 45% estimate gives EV = 0.45 × 1.5 − 0.55 = +$0.125 per dollar; a 38% estimate gives −$0.05. Without an edge over the implied probability, the margin guarantees a long-run loss.
Probability, odds against and odds in favor
- A probability of 25% is 3 to 1 against (three failures for every success) and 1 to 3 in favor.
- To convert odds against a to b into a probability: p = b ÷ (a + b).
- To convert odds in favor a to b: p = a ÷ (a + b).
These are the same ratios used for dice, cards and lotteries — compare with the jackpot odds in the lottery number generator or the hand odds in poker hand rankings. For general percentage work, see the percentage calculator.
This calculator is for information and education. Odds express a price, not a prediction, and sports betting is legal only in some states and for adults. Bet only what you can afford to lose; the National Council on Problem Gambling offers free, confidential help.
Frequently asked questions
How do I convert American odds to probability?
For positive odds, probability = 100 ÷ (odds + 100): +150 gives 100 ÷ 250 = 40%. For negative odds, probability = |odds| ÷ (|odds| + 100): −200 gives 200 ÷ 300 = 66.7%.
What does −110 mean?
You must stake $110 to win $100 profit. The implied probability is 110 ÷ 210 = 52.38%. When both sides of a game are −110, the two probabilities add up to 104.76%, and the extra 4.76% is the bookmaker's margin.
What is the difference between odds and probability?
Probability compares successes with all outcomes (a 1-in-5 chance is 20%). Odds against compare failures with successes (4 to 1 against). Betting odds also show how much a winning bet pays, so they bake in the bookmaker's margin.
What are decimal odds?
Decimal odds give the total return per $1 staked, including the stake. Odds of 2.50 return $2.50 for every $1, a profit of $1.50. Implied probability is 1 ÷ decimal odds.
How do I remove the vig?
Enter the prices for both sides. The calculator converts each to an implied probability, adds them, and divides each by the total so they sum to 100%. Those are the fair, no-vig probabilities.