Quick answer
Odds convert to probability: decimal 1 ÷ odds; American positive 100 ÷ (odds + 100), negative |odds| ÷ (|odds| + 100); fractional a/b gives b ÷ (a + b). Decimal odds of 2.50 imply a 40% probability.
Choose the odds format and enter the odds. The calculator returns the implied probability and decimal odds.
Related tools: Probability Calculator: Probability of A and B, and A or B, for independent or mutually exclusive events. Dice Average Calculator: Average, minimum and maximum of rolling several dice. Permutation and Combination Calculator: Number of permutations and combinations of r items from n.
How to use the Implied Probability Calculator
- Choose odds format: Decimal (2.50), American (+150 / −200) and Fractional (3/2).
- Type odds, for example 2.50, +150 or 3/2.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Odds format | Choose one: Decimal (2.50); American (+150 / −200); Fractional (3/2) | Starts at Decimal (2.50) |
| Odds | Text, such as 2.50, +150 or 3/2 | — |
Formula and method
Formula
decimal: 1 ÷ odds; American +: 100 ÷ (odds + 100), −: |odds| ÷ (|odds| + 100); fractional a/b: b ÷ (a + b)
IEEE-754 double precision; shown to at most 6 decimal places.
Implied probability includes the bookmaker's margin, so a market's implied probabilities typically sum to more than 100%.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Odds format = Decimal (2.50); Odds = 2.5.
| Result | Value |
|---|---|
| Implied probability | 40% |
| Decimal odds | 2.5 |
Example 2
Inputs: Odds format = American (+150 / −200); Odds = -200.
| Result | Value |
|---|---|
| Implied probability | 66.6667% |
| Decimal odds | 1.5 |
The first line is the headline result (implied probability). Below it the implied Probability Calculator lists decimal odds, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
More worked cases
+150 American is 100 ÷ 250 = 40%, the same as 2.5 decimal and 3/2 fractional. −200 implies 200 ÷ 300 = 66.7%.
The bookmaker's margin
Implied probabilities across all outcomes of an event add to more than 100%; the excess is the bookmaker's margin (the 'overround'). Decimal odds must exceed 1. This is not betting advice.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Odds: entering "1" shows "Decimal odds must be greater than 1." beside that field and no result.
Choosing between the Implied Probability Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Probability Calculator](/statistics/probability-calculator/) | p, p and events are | P(A and B) |
| [Dice Average Calculator](/statistics/dice-average/) | number of dice and sides per die | Average roll |
| [Permutation and Combination Calculator](/statistics/permutation-and-combination-calculator/) | total items and chosen items | Combinations (nCr) |
| [Expected Value Calculator](/statistics/expected-value/) | values and probabilities | Expected value E[X] |
| [Bayes' Theorem Calculator](/statistics/bayes-theorem-calculator/) | prior P, p and p | P(A | B) |
Background: probability and distributions
A probability model only applies when its conditions hold. The binomial model needs a fixed number of independent trials with two outcomes and a constant success probability; its mass function gives the chance of exactly k successes. The normal density is f(x) = 1 ÷ (σ√(2π)) × e^(−(x − μ)² ÷ (2σ²)).
A cumulative probability adds up everything at or below a value, a density or mass function gives the value at a point. For a standard normal variable, z = −1.96 leaves 0.025 in the lower tail, which is why ±1.96 bounds a 95% interval.
Assumptions and limitations
- Decimal odds must exceed 1
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for odds to confirm this.
Frequently asked questions
What does +100 imply?
American odds of +100 mean you win as much as you stake, an implied probability of 100 ÷ 200 = 50%.
What is the implied probability of 4/1?
Fractional odds of 4/1 imply 1 ÷ (4 + 1) = 20%.
How do I remove the margin?
Divide each by their total.
What does the Implied Probability Calculator calculate?
Probability implied by betting odds. It returns Implied probability and Decimal odds.
What formula does the Implied Probability Calculator use?
decimal: 1 ÷ odds; American +: 100 ÷ (odds + 100), −: |odds| ÷ (|odds| + 100); fractional a/b: b ÷ (a + b). Implied probability includes the bookmaker's margin, so a market's implied probabilities typically sum to more than 100%.
What do I need to enter in the implied Probability Calculator?
You enter Odds format and Odds.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Decimal odds must exceed 1.
What does the “Odds format” option change?
It sets how the implied Probability is worked out. The choices are Decimal (2.50), American (+150 / −200) and Fractional (3/2).
What is an example of a implied Probability result?
With odds format Decimal (2.50) and odds 2.5, the implied probability is 40%.
Where does the method come from?
The method follows: OpenStax, Introductory Statistics 2e (Rice University): measures of center and spread, correlation and regression.
Related calculators
- Probability Calculator — Probability of A and B, and A or B, for independent or mutually exclusive events.
- Dice Average Calculator — Average, minimum and maximum of rolling several dice.
- Permutation and Combination Calculator — Number of permutations and combinations of r items from n.
- Expected Value Calculator — Expected value and variance of a discrete distribution.
- Bayes' Theorem Calculator — Posterior probability from a prior and test accuracy.
- Geometric Probability Calculator — Probability the first success occurs on trial k.
Sources
- OpenStax, Introductory Statistics 2e (Rice University): measures of center and spread, correlation and regression
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.