Three formats. One probability. The UK betting market has long run on fractional odds, but online platforms and exchanges now default to decimals, and apps covering American sports quote moneylines. If you've ever loaded a site showing 6.00 where you expected 5/1, or seen +500 on an American sportsbook and had no idea how that compared to a price you already know, you're not alone. The maths connecting all three formats is actually quite short once you see the pattern.

The Core Idea

These three odds formats all describe the same relationship between stake, return, and probability. Fractional odds show profit relative to stake, decimal odds show total return per unit staked, and American odds use separate rules for favourites and underdogs. Every format implies the same underlying probability. Moving between them takes a short calculation. Once you've worked through the formulas below, you'll be able to read any odds format with confidence.

Three Formats, One Underlying Idea

Each format asks the same question: if you stake a certain amount on this outcome, what do you get back if it wins? They just answer it differently.

Fractional odds are the traditional British format. Written as two numbers separated by a slash, like 5/1 or 7/2, the left number is your profit and the right is your stake. At 5/1, a £1 stake returns £5 profit. Add back the original £1 and the total return is £6.

Decimal odds show the total return per £1 staked, stake included. That same 5/1 price is 6.00 in decimal. Stake £10 at 6.00 and you receive £60 back if it wins. Your £10 stake is within that £60, making your profit £50. Most exchanges and European bookmakers use decimals by default because they're easier to compare at a glance.

American odds, also called moneyline odds, work on a £100 reference point. Positive odds tell you how much profit a £100 bet would make. Negative odds tell you how much you'd need to stake to win £100. A price of +200 means a £100 bet wins £200 profit. A price of -150 means you'd need to stake £150 to win £100. All licensed betting operators in the UK sit under the oversight of the UK Gambling Commission, and regulated platforms may present odds in any of these three formats depending on the sport, market, or account settings the customer has chosen.

Converting Fractional to Decimal, Step by Step

The formula here is clean and consistent. Divide the numerator by the denominator, then add 1. That's the whole thing.

5/1: divide 5 by 1 to get 5, then add 1. Decimal odds are 6.00.

7/2: divide 7 by 2 to get 3.5, then add 1. Decimal odds are 4.50.

2/5: divide 2 by 5 to get 0.4, then add 1. Decimal odds are 1.40.

The "+1" compensates for the fact that fractional odds only show profit, while decimal odds include the returned stake. Adding 1 brings that stake return back into the figure.

Reversing the direction, from decimal to fractional, means subtracting 1 first. Decimal 4.50 minus 1 gives 3.5, which is 7/2. Decimal 3.00 minus 1 gives 2.0, which is 2/1. The calculation is simple. Simplifying the resulting fraction can take a moment with unusual prices, but standard bookmaker prices follow a short, familiar list and rarely throw up anything awkward.

How American Odds Work and Why They Split into Two Rules

Positive American odds apply to underdogs. Negative odds apply to favourites. The split happens because the reference is how much you'd win or need to risk relative to £100, and that relationship runs in opposite directions depending on which side of the market you're on.

With positive odds, converting to decimal means dividing by 100 and adding 1.

+200: divide 200 by 100 to get 2, then add 1. Decimal odds are 3.00.

+500: divide 500 by 100 to get 5, then add 1. Decimal odds are 6.00.

With negative odds, the formula flips. Divide 100 by the absolute value of the American odds (ignoring the minus sign), then add 1.

-200: divide 100 by 200 to get 0.5, then add 1. Decimal odds are 1.50.

-150: divide 100 by 150 to get 0.667, then add 1. Decimal odds are 1.667.

To convert American odds directly to fractional, use the same logic and express as a fraction. For positive odds, divide by 100 and simplify: +500 = 500/100 = 5/1. For negative odds, divide 100 by the absolute value: -200 = 100/200 = 1/2.

Skipping the Arithmetic with a Conversion Tool

The formulas above are worth knowing because they show you what the numbers actually represent. But there's no reason to work through the calculations manually every time you come across an unfamiliar price. An odds converter lets you type any format in and returns the equivalent across all three instantly. It's particularly useful when comparing prices across platforms that display different defaults, or when you want to see a moneyline expressed as a familiar decimal figure without the working-out.

Implied Probability and What It Tells You

Every set of odds implies a probability. That's the bookmaker's estimate of how likely the outcome is, embedded in the price. Knowing how to extract that number turns an abstract price into meaningful information.

For decimal odds: divide 1 by the decimal price, then multiply by 100 for a percentage. Decimal 6.00 implies 16.67%. Decimal 1.50 implies 66.67%.

For fractional odds: divide the denominator by the sum of both numbers (numerator plus denominator), then multiply by 100. At 5/1, that's 1 divided by 6, multiplied by 100, giving 16.67%. This matches the decimal result exactly, which confirms the two prices are equivalent.

For American odds, positive and negative each have their own version. For positive odds, divide 100 by (the odds plus 100), then multiply by 100. For negative odds, divide the absolute value by (the absolute value plus 100), then multiply by 100.

+500 implies: 100 divided by 600, multiplied by 100 = 16.67%. Again, the same result. All three formats point to the same underlying number. If your conversions produce matching implied probabilities, the arithmetic is right.

One thing worth knowing: bookmaker prices build in a margin, sometimes called the overround. This means the implied probabilities across all outcomes in a market will add up to more than 100%. That margin is how bookmakers secure their edge regardless of the result. The conversion formulas give you the implied probability per outcome, not an adjusted figure that accounts for the overround.

The Conversion Formulas at a Glance

A brief reference for when you need to check a specific formula:

  • Fractional to decimal: (numerator ÷ denominator) + 1. Example: 5/1 becomes (5 ÷ 1) + 1 = 6.00.
  • Decimal to fractional: subtract 1, then express as a simplified fraction. Example: 4.50 minus 1 = 3.5 = 7/2.
  • Positive American to decimal: (odds ÷ 100) + 1. Example: +500 becomes (500 ÷ 100) + 1 = 6.00.
  • Negative American to decimal: (100 ÷ |odds|) + 1. Example: -200 becomes (100 ÷ 200) + 1 = 1.50.
  • Decimal to implied probability: (1 ÷ decimal) × 100. Example: 6.00 becomes 16.67%.
  • Fractional to implied probability: denominator ÷ (numerator + denominator) × 100. Example: 5/1 gives 1 ÷ 6 × 100 = 16.67%.

Reading Any Odds Format with Confidence

The three formats feel like separate systems until you trace them back to the same question: how much do you win, and how likely does the bookmaker think the outcome is? Fractional odds answer the profit question directly. Decimal odds fold the stake return in. American odds anchor everything to a £100 reference point and split on whether you're backing the favourite or the underdog.

Once you've worked through the formulas a handful of times, the translations start to feel instinctive. Seeing 6.00, +500, and 5/1 starts to look like the same price written in three different scripts rather than three different things. The implied probability check ties them all together. Run that number across formats and it confirms whether your conversion landed correctly.

The arithmetic is short and repeatable. And for the times you'd rather not carry the working in your head, a conversion tool handles it in a keystroke.