Implied Probability Calculator
Convert odds to a probability and back — decimal, fractional and moneyline — and see the margin built into a set of quoted odds.
Odds and probabilities are the same information in different clothes.
How the implied probability calculator works
Odds and probabilities are the same information in different clothes. Decimal odds d imply 1 ÷ d; fractional odds a/b imply b ÷ (a + b); positive moneyline m implies 100 ÷ (m + 100), and negative implies |m| ÷ (|m| + 100).
When a bookmaker quotes both sides of a two-way market, the implied probabilities sum to more than 100%. That excess is the overround, and it is the margin.
Formula: P = 1 / decimal odds; overround = ΣP − 1
Worked examples
| Inputs | Implied probability | Note |
|---|---|---|
| Decimal 2.50 | 40% | 40% |
| Evens (2.00) | 50% | 50% |
| A two-way market at 1.90 each | 52.6316% | 5.26% overround |
FAQFrequently asked questions
How do I convert decimal odds to a probability?
Divide 1 by the odds. Decimal 4.00 implies 25%.
What is the overround?
The amount by which a book's implied probabilities exceed 100%. At 1.90 on both sides of a coin flip the book sums to 105.3%, so the margin is 5.3%.
What do positive and negative moneylines mean?
+150 means a 100 stake wins 150; −200 means you must stake 200 to win 100. The first implies 40%, the second 66.7%.
Are implied probabilities the true probabilities?
No — they include the margin. Dividing each by their sum removes it and gives the book's actual view.
What are "odds against"?
The ratio of ways to lose to ways to win. A 25% chance is 3 to 1 against.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.