How this calculation works
Convert entered decimal, fractional or American odds into implied probability and equivalent numerical representations. Decimal implied probability = 1 / decimal odds; fractional a/b implies b/(a+b); American +A implies 100/(A+100)
Decimal implied probability = 1 / decimal odds; fractional a/b implies b/(a+b); American +A implies 100/(A+100)A worked example
Decimal odds of 2 correspond to 50% implied probability, fractional odds 1 to 1 and American odds +100. A different notation does not create a different underlying chance.
Good to know
Mathematical representation only, not a true-probability estimate, betting recommendation, stake planner or prediction. No bookmaker-margin removal. Zero and 100% excluded because equivalent odds become singular. Fractional output is a decimal ratio to one rather than an exact reduced integer fraction.
Odds and probability describe a ratio differently
Decimal odds include a returned unit in their usual convention, so a decimal quote of two implies one divided by two, or fifty percent. Fractional odds describe the other part of that same ratio.
Here the fractional quote is a net-return ratio, not the statistical odds in favor of an event. For numerator a and denominator b, the implied probability is b divided by a plus b. Treating a divided by b as the probability would confuse a ratio with a share of a total.
The sign in American odds changes the formula
A positive American number A maps to 100 divided by A plus 100. A negative number maps to its absolute magnitude divided by that magnitude plus 100. The tool rejects values between minus one hundred and plus one hundred.
Both plus one hundred and minus one hundred correspond to fifty percent. At exactly fifty percent the output chooses the positive convention; that formatting choice does not change the probability.
Implied is not the same as established
A quoted price does not measure the true chance of an event. This page only converts the entered representation. It does not use team data, market history, injuries, experimental observations or any other forecasting evidence.
It also does not remove a margin across mutually exclusive outcomes. Comparing one isolated implied probability with a prediction requires additional justified assumptions, not just another notation.
Why zero and one hundred percent are excluded
Some equivalent representations become infinite or degenerate at the probability endpoints. The supported input range stays strictly inside zero and one hundred percent so every returned representation remains finite.
Fractional output is displayed as a numerical ratio to one. A value such as 0.5 to one can be written as one to two, but this output does not promise an exact reduced rational number from arbitrary floating-point input.
Use probability arithmetic for the follow-up
The percentage calculator helps turn a percentage into a count under a stated model. The binomial probability calculator addresses repeated independent trials with a fixed probability, which is a different question from converting a quote.
This page does not calculate stakes, place wagers or recommend a bet. Its side-by-side table is useful for checking notation and avoiding sign mistakes in a mathematical explanation.
A few questions, answered
Are implied probabilities true probabilities?
Not necessarily. They are mathematical conversions of a quoted representation, without a forecasting model.
Can I enter negative American odds?
Yes, values at or below minus one hundred are supported; values at or above plus one hundred use the positive convention.
Does the output remove bookmaker margin?
No. It converts one quote and does not adjust a set of outcomes or recommend any wager.