Odds Calculator — Convert Between Probability and Odds Formats

Formula

How this is calculated

All odds formats express the same underlying probability; they differ only in how bookmakers and different markets quote it. Decimal odds (popular in Europe, Australia, and Canada) equal 1 / probability — so a 40% chance has decimal odds of 2.50, meaning a $1 stake returns $2.50 in total (including the stake back). Fractional odds (common in the UK and Ireland) express the net profit relative to the stake: 3/2 means you win $3 for every $2 staked, implying a probability of 2/(3+2) = 40%. American or moneyline odds use positive figures for underdogs and negative figures for favourites — +150 means a $100 stake earns $150 profit, giving an implied probability of 100/(150+100) = 40%; −200 means you stake $200 to earn $100 profit, giving 200/(200+100) ≈ 67%.

The "implied probability" is what the odds say the fair chance of the outcome is. In practice, bookmakers build in a margin (overround or vig) so the implied probabilities of all outcomes in an event sum to more than 100%, guaranteeing a long-run profit regardless of the result. This calculator converts pure (fair) odds with no margin applied, so the implied probabilities of opposing outcomes will sum to exactly 100%.

To go the other direction — from probability to odds — use decimal = 1/p; fractional = (1−p)/p; American: +((1−p)/p)×100 when p < 0.5 (underdog), −(p/(1−p))×100 when p ≥ 0.5 (favourite). For example, a 60% implied probability gives decimal 1.667, fractional 2/3, and American −150.