How to Convert Between Odds Formats
Every conversion between decimal, fractional, American odds and implied probability — with the exact formula, a worked example, and the logic behind each one. Whether you need to convert a single price or build an intuition for how formats relate, this is the complete reference.
Why You Need to Convert Odds
Decimal 4.00, fractional 3/1 and American +300 are identical odds. Converting between them doesn't change the value of the bet — it just changes how it's written.
You'll need to convert odds in several common situations. You might be comparing prices across bookmakers where one displays decimal and another fractional. You might be using a calculator or tool that requires a specific format. You might be looking at US sports data expressed in American odds while your bookmaker shows decimal. Or you might simply want to check whether odds represent fair value by converting to implied probability.
In all of these cases the conversion is straightforward once you know the formula. This guide covers every direction — and if you'd rather not do the arithmetic, our free Odds Converter handles all conversions instantly.
Use Decimal as Your Hub Format
The easiest way to convert between any two formats is to treat decimal odds as a stepping stone. Rather than memorising six separate conversion paths (fractional to American, American to fractional, and so on), you only need to remember two things: how to get to decimal, and how to get from decimal to your target format.
Convert to Decimal First
Whatever format you're starting with — fractional or American — convert it to decimal first using the formulas in this guide. Decimal is the universal intermediate format.
Convert Decimal to Target
Once you have the decimal equivalent, use the decimal → fractional or decimal → American formula to reach your target format. Two simple steps cover every possible conversion.
This approach works because decimal odds have the cleanest mathematical relationship to probability and payout. All the other formats are essentially different ways of expressing the same underlying decimal number.
Fractional → Decimal
This is the most common conversion UK bettors need to make — taking a traditional fractional price and turning it into a decimal for use in calculations or matched betting tools.
Decimal = (Numerator ÷ Denominator) + 1
The +1 accounts for your stake being returned alongside the profit.
Worked Examples
5/1 → Decimal
(5 ÷ 1) + 1
= 5.0 + 1
= 6.00
7/2 → Decimal
(7 ÷ 2) + 1
= 3.5 + 1
= 4.50
1/4 → Decimal
(1 ÷ 4) + 1
= 0.25 + 1
= 1.25
11/8 → Decimal
(11 ÷ 8) + 1
= 1.375 + 1
= 2.375
Fractional odds only express profit. Decimal odds express total return including your stake. The +1 adds your stake back in. Without it, decimal 5.00 would mean you profit 5× your stake — but in reality decimal 5.00 means your total return is 5× your stake, giving you 4× in profit. Always add 1.
Decimal → Fractional
Going the other direction — from decimal to fractional — requires one extra step: simplifying the resulting fraction into a clean, standard form.
Step 1: Subtract 1 from the decimal odds
Step 2: Express the result as a fraction
Step 3: Simplify the fraction to its lowest terms
Worked Examples
6.00 → Fractional
6.00 − 1 = 5.0
5.0 = 5/1
= 5/1
3.50 → Fractional
3.50 − 1 = 2.5
2.5 = 5/2
= 5/2
1.80 → Fractional
1.80 − 1 = 0.8
0.8 = 4/5
= 4/5
2.375 → Fractional
2.375 − 1 = 1.375
1.375 = 11/8
= 11/8
Some decimal odds — particularly those generated by exchanges or precise probability models — produce fractions that don't simplify neatly. For example, decimal 1.91 produces a fraction of approximately 91/100, which bookmakers would display as 10/11 (a common standard rounding). In practice, bookmakers round to the nearest standard fractional price. When precision matters, stick with decimal.
American → Decimal
American odds use two different formulas depending on whether the number is positive or negative. Always check the sign first before applying the formula.
Positive American odds (underdogs):
Decimal = (American ÷ 100) + 1
Negative American odds (favourites):
Decimal = (100 ÷ |American|) + 1
(The | | symbols mean use the absolute value — ignore the minus sign)
Positive Odds — Worked Examples
+200 → Decimal
(200 ÷ 100) + 1
= 2.0 + 1
= 3.00
+350 → Decimal
(350 ÷ 100) + 1
= 3.5 + 1
= 4.50
+1200 → Decimal
(1200 ÷ 100) + 1
= 12.0 + 1
= 13.00
Negative Odds — Worked Examples
−200 → Decimal
(100 ÷ 200) + 1
= 0.5 + 1
= 1.50
−150 → Decimal
(100 ÷ 150) + 1
= 0.667 + 1
= 1.67
−400 → Decimal
(100 ÷ 400) + 1
= 0.25 + 1
= 1.25
Decimal → American
Converting decimal to American requires checking whether the decimal is above or below 2.00 — the equivalent of evens. Above 2.00 produces a positive American number. Below 2.00 produces a negative one.
If decimal ≥ 2.00 (odds-against):
American = (Decimal − 1) × 100
If decimal < 2.00 (odds-on):
American = −100 ÷ (Decimal − 1)
Odds-Against Examples (Decimal ≥ 2.00)
3.00 → American
(3.00 − 1) × 100
= 2.0 × 100
= +200
4.50 → American
(4.50 − 1) × 100
= 3.5 × 100
= +350
2.00 → American
(2.00 − 1) × 100
= 1.0 × 100
= +100
Odds-On Examples (Decimal < 2.00)
1.50 → American
−100 ÷ (1.50 − 1)
= −100 ÷ 0.5
= −200
1.25 → American
−100 ÷ (1.25 − 1)
= −100 ÷ 0.25
= −400
1.67 → American
−100 ÷ (1.67 − 1)
= −100 ÷ 0.67
= −149
Odds → Implied Probability
Implied probability is the percentage chance of winning that a set of odds represents. Converting odds to probability is one of the most useful skills in betting — it lets you instantly assess whether a price reflects genuine value or whether the bookmaker's margin is distorting the picture.
From decimal:
Probability = (1 ÷ Decimal) × 100
From fractional:
Probability = Denominator ÷ (Numerator + Denominator) × 100
From positive American:
Probability = 100 ÷ (American + 100) × 100
From negative American:
Probability = |American| ÷ (|American| + 100) × 100
Worked Examples
Decimal 4.00
(1 ÷ 4.00) × 100
= 25.0%
Fractional 3/1
1 ÷ (3 + 1) × 100
= 1 ÷ 4 × 100
= 25.0%
American +300
100 ÷ (300 + 100) × 100
= 100 ÷ 400 × 100
= 25.0%
American −200
200 ÷ (200 + 100) × 100
= 200 ÷ 300 × 100
= 66.7%
All four examples above confirm that decimal 4.00, fractional 3/1 and American +300 are the same odds — they all produce exactly 25% implied probability. Our Implied Probability Calculator converts any odds and also shows the fair odds with the bookmaker's margin stripped out.
Implied Probability → Odds
Going in the other direction — converting a probability percentage into odds — is equally useful. If you've assessed that a team has a 35% chance of winning, you can instantly calculate what the fair odds should be and compare them to what's on offer.
To decimal:
Decimal = 100 ÷ Probability
To fractional:
Fractional = (100 − Probability) ÷ Probability, then simplify
To American (probability < 50%):
American = (100 ÷ Probability − 1) × 100 — expressed as positive
To American (probability > 50%):
American = −(Probability ÷ (100 − Probability)) × 100
Worked Examples — 35% Probability
35% → Decimal
100 ÷ 35
= 2.86
(Fair odds for a 35% chance)
35% → Fractional
(100 − 35) ÷ 35
= 65 ÷ 35
≈ 13/7
35% → American
(100 ÷ 35 − 1) × 100
= (2.857 − 1) × 100
= +186
Worked Examples — 70% Probability
70% → Decimal
100 ÷ 70
= 1.43
(Fair odds for a 70% chance)
70% → Fractional
(100 − 70) ÷ 70
= 30 ÷ 70
≈ 3/7
70% → American
−(70 ÷ 30) × 100
= −2.333 × 100
= −233
Quick Reference Table
The most common odds values expressed across all three formats with implied probability — bookmark this as your conversion cheat sheet.
1.25 / 1/4 / −400
Implied probability: 80.0%
£10 profit: £2.50
1.50 / 1/2 / −200
Implied probability: 66.7%
£10 profit: £5.00
1.80 / 4/5 / −125
Implied probability: 55.6%
£10 profit: £8.00
2.00 / 1/1 / +100
Implied probability: 50.0%
£10 profit: £10.00
2.50 / 6/4 / +150
Implied probability: 40.0%
£10 profit: £15.00
3.00 / 2/1 / +200
Implied probability: 33.3%
£10 profit: £20.00
4.00 / 3/1 / +300
Implied probability: 25.0%
£10 profit: £30.00
6.00 / 5/1 / +500
Implied probability: 16.7%
£10 profit: £50.00
11.00 / 10/1 / +1000
Implied probability: 9.1%
£10 profit: £100.00
21.00 / 20/1 / +2000
Implied probability: 4.8%
£10 profit: £200.00
51.00 / 50/1 / +5000
Implied probability: 2.0%
£10 profit: £500.00
101.00 / 100/1 / +10000
Implied probability: 1.0%
£10 profit: £1,000.00
Our free Odds Converter handles any price in any format — type in any decimal, fractional or American odds and get all three outputs plus implied probability instantly.
Common Questions
No. Converting between formats is purely cosmetic — like converting miles to kilometres. The underlying number, the payout and the implied probability are all identical regardless of which format the odds are displayed in. Decimal 3.00, fractional 2/1 and American +200 represent exactly the same bet.
Fractional odds are often set based on precise probability models that produce non-round results. Historically bookmakers rounded to convenient fractions — 5/4, 6/4, 7/4 — but as markets became more competitive and models more accurate, more precise fractions like 11/8, 13/5 and 15/8 entered common use, particularly in horse racing. These fractions are mathematically equivalent to specific decimal prices (11/8 = 2.375, 13/5 = 3.60) and there's nothing wrong with them — they're just less intuitive to calculate mentally.
This is the bookmaker's overround — their built-in profit margin. If you add the implied probabilities of all outcomes in any market, the total will always exceed 100% because the bookmaker shortens every price slightly to ensure they profit regardless of the result. The amount by which the total exceeds 100% is the overround percentage. A total of 106% means a 6% overround. See our guide on What Is Overround? for a full explanation.
No — implied probability is the probability that the bookmaker's odds suggest, which includes their margin. True probability is the genuine likelihood of the outcome occurring. Because of the overround, implied probability is always slightly higher than the bookmaker's true assessment. To get closer to true probability you need to remove the margin — our Implied Probability Calculator does this automatically by calculating fair odds alongside the raw implied probability.
Yes — the conversion formulas work identically for in-play odds. The format and maths are the same whether the event is about to start or is already underway. The only practical difference is that in-play odds move rapidly, so any manual conversion you do may be slightly out of date by the time you use it. For in-play betting it's generally best to work directly in the format your bookmaker displays rather than converting.
Want to skip the maths entirely? Our free Odds Converter handles every conversion instantly — decimal, fractional, American and implied probability in a single step.
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