The Mathematics
For fractional odds a/b, decimal odds are 1 + a/b. Decimal prices include the returned cash stake; fractions describe profit relative to stake. American positive odds state profit on a 100-unit stake, while negative odds state the stake needed to win 100 units. Above or at decimal 2.00, American odds are +100 × (decimal − 1). Below 2.00 they are −100 ÷ (decimal − 1). The units may be pounds or another currency without changing the price relationship.
Fractional a/b → decimal = 1 + a/b
Positive American A → decimal = 1 + A/100
Negative American A → decimal = 1 + 100/|A|
Implied percentage = 100 ÷ decimal odds
Cash win return = stake × decimal odds
Worked Example
Enter fractional 5/2. The equivalent decimal price is 3.50 and American price is +250. The odds-implied percentage is 100 ÷ 3.50 = 28.57% before rounding. A £10 winning cash bet at this price returns £35 with £25 profit. For the odds-on contrast, 1/2 is decimal 1.50 and American −200: £10 returns £15 and profits £5.
How do I use the odds converter fields?
Select Fractional, Decimal or American in Input Format, then type the price in Enter Odds. Fractional examples include 11/4 and 4/6; evens can be written 1/1. Decimal examples include 3.75 and 1.50. American prices require their sign to preserve meaning: +200 is decimal 3.00 while −200 is decimal 1.50. Changing the format clears the old value so a fractional string is not accidentally reinterpreted as an American or decimal quote.
There is no stake field, because converting a price does not depend on stake size. Use the single calculator after conversion if you want a cash payout. The displayed decimal and implied percentage are rounded for readability, and American prices are rounded to whole numbers. Preserve the accepted original price when checking a bookmaker settlement rather than repeatedly converting rounded displays between formats.
What does the implied percentage actually mean?
At decimal 4.00, the reciprocal is 25%. If a cash bet at that price genuinely won exactly one time in four over comparable trials, it would break even before fees and other adjustments. This is a mathematical threshold, not evidence that a particular horse wins one race in four. A market's quoted prices can reflect margin, liquidity, information and judgement; none of those factors makes one reciprocal price an independently measured probability.
To examine a whole race's quoted book, enter every runner's price in the margin calculator. The implied percentages can sum above 100%, indicating overround. Dividing each by the total is a proportional normalization, not a validated probability model. Do not use this converter's percentage as a reason to stake a fixed fraction of a bankroll, and do not describe it as a RaceCards prediction.
How can conversion errors affect payout comparisons?
Fractional 11/4 is decimal 3.75, not 2.75. The latter omits the returned stake and understates a £10 winning return by £10. Decimal 2.50 corresponds to fractional 3/2 and American +150, while decimal 1.50 corresponds to fractional 1/2 and American −200. The sign convention is why simply attaching a plus sign to an odds-on quote is incorrect.
A decimal price need not match a familiar bookmaker fraction. Decimal 3.37 corresponds to 237/100 in exact fractional arithmetic, not the nearest traditional price such as 12/5. The converter preserves the numeric decimal relationship rather than replacing it with a convenient price. American rounding can still create a small discrepancy on a round trip; compare the underlying decimal numbers when precision matters.
Which factors does an odds converter leave out?
The tool converts one quoted price only. It does not find the best available odds, retrieve a live market, remove commission, settle a Rule 4, calculate a dead heat, approve an accumulator or handle promotional stake-not-returned bets. Two offers with the same displayed price can have different net outcomes if their fees or terms differ. A larger decimal price gives a larger gross winning return for the same cash stake, but that observation alone does not decide which offer is suitable.
For multiples, first convert every component to decimal, then multiply. A double at 5/2 and 2/1 has decimal 3.50 × 3.00 = 10.50, equivalent to fractional 19/2. Multiplying the raw fractions 2.5 × 2 gives the wrong payout basis. For each way, apply the place fraction to decimal minus one before adding one back. The separate calculators perform those structures; the converter does not construct them.
Popular questions about this calculator
What is 5/2 in decimal and American odds?
Fractional 5/2 equals decimal 3.50 and American +250. All represent £25 profit on a £10 winning cash stake, with £35 total return. The implied percentage is approximately 28.57%, which describes the quoted price rather than a verified chance of winning.
How do I convert fractional odds to decimal?
Divide the numerator by the denominator and add one. For 11/4, 11 ÷ 4 + 1 = 3.75. The added one represents the returned cash stake, which is why multiplying £10 by 3.75 already gives the full £37.50 winning return.
What is evens in all three odds formats?
Evens is fractional 1/1, decimal 2.00 and American +100. A £10 cash winner returns £20 with £10 profit. The reciprocal decimal price is 50%, but that number alone does not establish an actual fifty-fifty outcome.
What does −200 mean in American odds?
It means staking 200 units to win 100 units of profit. The equivalent fractional price is 1/2 and decimal price is 1.50. It does not mean negative winnings or a negative stake; the minus sign identifies the American odds-on convention.
Does implied probability equal the horse's true probability?
No. It is 100 divided by decimal odds, a market-implied break-even percentage before fees. True chances require an independently justified model or assessment. Bookmaker margin means the implied percentages across a race may exceed 100%.
Why does a decimal conversion add one?
Fractional odds quote profit; decimal odds quote total return per unit including the stake. At 3/1, a winning £1 cash bet makes £3 profit and returns £4. Decimal 4.00 therefore includes one stake unit as well as three profit units.
Can I convert an unusual decimal price exactly?
Yes, its profit multiple can be expressed as a fraction rather than forced to the nearest familiar quote. Decimal 3.37 has a profit multiple of 2.37, or fractional 237/100. Display rounding and very long inputs can still limit precision, so retain the accepted original quote.
Do I multiply fractional odds for an accumulator?
No. Convert each price to decimal before multiplying. A 5/2 and 2/1 double has decimal 3.5 × 3 = 10.5, or fractional 19/2. Multiplying 2.5 by 2 omits stake rollover and gives the wrong combined return.
Does converting odds include exchange commission?
No. Conversion preserves the gross quoted price. Exchange fees depend on the account and net market result, not only one selection's displayed odds. Use the accepted price for gross arithmetic and apply the operator's applicable commission rules separately.
Why do converted American odds sometimes differ on a round trip?
American prices are displayed as whole numbers, so rounding can change a later conversion slightly. For example, fractional 4/6 gives decimal 1.666… and American −150, while using rounded decimal 1.67 produces a slightly different intermediate value. Keep full precision for settlement checks.
Official rules and further reading
These operator references explain bet structures and settlement rules. They are not endorsements, and the terms attached to your accepted bet take precedence. Worked amounts on this page are illustrative arithmetic, not live odds or promised outcomes. Only gamble money you can afford to lose; a returns tool does not make a bet safe.