AT A GLANCE
Betting odds conversion formulas let you compare prices expressed in decimal, fractional and American formats by reducing each one to implied probability.
- Decimal odds include your stake in the total return, so a £10 stake at 2.50 returns £25.
- Fractional odds show profit relative to your stake, so 3/2 returns £15 profit from £10, plus the £10 stake.
- American odds use a positive number for profit on £100 and a negative number for the stake needed to win £100.
- Implied probability equals 1 divided by decimal odds, before allowing for the bookmaker’s margin.
The format changes the display, not the underlying price, but rounding and overround can affect comparisons.
Odds Conversion Quick Reference Table
This table shows equivalent prices for commonly encountered odds. The implied probability is the break-even percentage suggested by the quoted price, not a guaranteed estimate of the actual chance.
| Fractional | Decimal | American | Implied probability |
|---|---|---|---|
| 1/1 | 2.00 | +100 | 50.0% |
| 1/2 | 1.50 | -200 | 66.7% |
| 2/1 | 3.00 | +200 | 33.3% |
| 5/2 | 3.50 | +250 | 28.6% |
| 4/1 | 5.00 | +400 | 20.0% |
For example, decimal odds of 3.00, fractional odds of 2/1 and American odds of +200 all describe the same gross return and the same 33.3% implied probability.
Understanding Betting Odds Formats
Decimal, fractional and American odds are three ways to state the same relationship between stake, profit and return. The conversion is mechanical, but each format highlights a different part of the calculation.
- Decimal odds: multiply the stake by the decimal price to calculate the total return. At 2.40, a £10 stake returns £24, including £14 profit.
- Fractional odds: multiply the stake by the fractional numerator divided by the denominator to calculate profit. At 7/4, a £10 stake produces £17.50 profit and £27.50 total return.
- American positive odds: show the profit from a notional £100 stake. At +150, £100 produces £150 profit and £250 total return.
- American negative odds: show the stake required to make £100 profit. At -150, a £150 stake produces £100 profit and £250 total return.
The UK Gambling Commission treats odds as a price attached to a possible outcome, so a displayed price should not be confused with certainty. A bookmaker can also build margin into a market, meaning the implied probabilities across all outcomes usually add up to more than 100%.
American Odds Conversion Formulas
American odds conversion formulas depend on whether the moneyline is positive or negative. The sign is not cosmetic: it determines whether the number describes potential profit from £100 or the amount needed to win £100.
- Positive American to decimal: decimal = 1 + (American odds ÷ 100).
- Negative American to decimal: decimal = 1 + (100 ÷ absolute American odds).
- Positive American to fractional: fractional profit = American odds ÷ 100.
- Negative American to fractional: fractional profit = 100 ÷ absolute American odds.
Converting American Odds to Decimal and Fractional
To convert positive American odds to decimal, divide by 100 and add 1. For +250, the calculation is 1 + (250 ÷ 100) = 3.50, which is 5/2 in fractional form.
To convert negative American odds, use the absolute value in the denominator. For -150, decimal odds are 1 + (100 ÷ 150) = 1.6667, while the fractional equivalent is 100/150, simplified to 2/3.
The decimal price includes the original stake, while the fractional price describes profit only. At -150, a £15 stake returns £25, consisting of £10 profit and the £15 stake.
Converting American Odds to Implied Probability
Positive American odds use this formula: implied probability = 100 ÷ (American odds + 100) × 100. At +150, the calculation is 100 ÷ 250 × 100 = 40%.
Negative American odds use this formula: implied probability = absolute American odds ÷ (absolute American odds + 100) × 100. At -300, the calculation is 300 ÷ 400 × 100 = 75%.
These percentages are unadjusted prices. If a two-outcome market shows +150 on one side and -180 on the other, the implied probabilities are 40.0% and 64.3%, adding to 104.3%. The extra 4.3 percentage points represent the approximate overround in that simplified market.
Decimal Odds Conversion Formulas
Decimal odds are the most direct format for calculating returns because the quoted number is the total return per unit stake. A price of 2.00 means the total return is twice the stake, not that the profit is twice the stake.
- Decimal to implied probability: probability = 1 ÷ decimal odds × 100.
- Decimal to fractional: fractional profit = decimal odds – 1.
- Decimal to positive American: (decimal odds – 1) × 100.
- Decimal to negative American: -100 ÷ (decimal odds – 1), when the decimal price is below 2.00.
Converting Decimal Odds to American and Fractional
Subtract 1 from decimal odds to isolate the profit component. Decimal odds of 2.75 produce 2.75 – 1 = 1.75, or 7/4 fractional odds, and convert to +175 American odds.
For a decimal price below 2.00, the American equivalent is negative. At 1.40, the calculation is -100 ÷ (1.40 – 1) = -250. The fractional equivalent is 0.40, usually written as 2/5.
Converting Decimal Odds to Implied Probability
Divide 1 by the decimal odds and multiply by 100. For 2.40, the calculation is 1 ÷ 2.40 × 100 = 41.67%.
To calculate payouts by hand, multiply the stake by the decimal price. A £25 stake at 2.40 returns £60, so the profit is £35 after subtracting the £25 stake. This calculation does not remove any tax, commission or market-specific settlement adjustment that may apply.
Fractional Odds Conversion Formulas
Fractional odds express profit as a ratio of stake. The numerator shows profit units and the denominator shows stake units, so 5/1 means £5 profit for every £1 staked.
- Fractional to decimal: decimal = (numerator ÷ denominator) + 1.
- Fractional to American: multiply the fractional profit by 100, using a positive sign when the profit exceeds 1 stake unit.
- Fractional to implied probability: probability = 1 ÷ (fractional odds + 1) × 100.
- Fractional payout: profit = stake × (numerator ÷ denominator), then add the stake for total return.
Converting Fractional Odds to Decimal and American
For 7/4, divide 7 by 4 and add 1: 7 ÷ 4 + 1 = 2.75. The American equivalent is +175 because 7/4 represents 1.75 units of profit per unit staked.
For a fractional price below evens, such as 2/5, the decimal conversion is 2 ÷ 5 + 1 = 1.40. The American conversion is negative because the profit is less than the stake: -100 ÷ (2/5) = -250.
Converting Fractional Odds to Implied Probability
Add 1 to the fractional profit, then divide 1 by that result. For 3/1, the calculation is 1 ÷ (3 + 1) × 100 = 25%.
For 2/5, the calculation is 1 ÷ (0.40 + 1) × 100 = 71.43%. The same answer can be reached directly as denominator ÷ (numerator + denominator) × 100, giving 5 ÷ 7 × 100.
Implied Probability to Odds Formulas
Convert a probability into odds by first turning the percentage into a decimal, then applying the formula for the required display format. These calculations produce fair, margin-free odds only if the probability itself is a fair estimate.
- Probability to decimal: decimal = 1 ÷ probability as a decimal. For 40%, 1 ÷ 0.40 = 2.50.
- Probability to fractional: fractional profit = (1 ÷ probability as a decimal) – 1. For 40%, 2.50 – 1 = 1.50, or 3/2.
- Probability to positive American: American = (1 ÷ probability as a decimal – 1) × 100. For 40%, this gives +150.
- Probability to negative American: American = -100 × probability as a decimal ÷ (1 – probability as a decimal). For 60%, this gives -150.
To check a market’s margin, convert every selection to implied probability and add the results. A three-outcome market priced at 50%, 30% and 25% has a total of 105%, indicating a 5% overround before any rounding effect.
Rounding can create small discrepancies. A displayed price of 1.67 implies 59.88%, while the exact equivalent of 3/5 is 1.6667 and implies 60%, so retain extra decimal places when comparing prices.
GambleAware advises setting spending and time limits before gambling, and its guidance also supports taking a break when gambling stops feeling controlled. Conversion formulas describe price mechanics only; they do not make an outcome more likely or remove variance.