Convert between fractional, decimal, American odds and implied probability with payout tables, profit calculations, and a comprehensive odds reference chart.
Fractional odds are the traditional UK and Irish format for expressing betting probabilities. Written as "5/1" (spoken "five-to-one"), the numerator represents potential profit and the denominator represents the stake required. This calculator converts fractional odds to and from decimal, American, and implied probability formats, and computes exact payouts at any stake amount.
Enter odds in any of four formats and get instant conversion to all others, with a payout table showing returns at standard stake levels. The implied probability reveals the true likelihood embedded in the odds, the profit calculation shows exact returns, and the comprehensive conversion reference table covers odds from 1/10 favorites to 100/1 longshots.
Beyond simple conversion, understanding the relationship between fractional odds and implied probability is essential for identifying value bets — situations where the true probability differs from what the odds imply. This calculator makes that comparison straightforward. Check the example with realistic values before reporting.
Fractional odds remain the dominant format in UK and Irish betting markets, but most online platforms now offer all three formats. Quick, accurate conversion between formats is essential for comparing odds across bookmakers, calculating exact payouts, and computing implied probabilities for value assessment.
This calculator provides the complete conversion in one place, with a payout table that eliminates manual multiplication and a reference chart covering the most common odds. The implied probability output is particularly valuable for comparing the "true" likelihood suggested by the market.
Fractional to Decimal: decimal = (num/den) + 1 Fractional to American: if num/den ≥ 1: +100×(num/den); if < 1: −100/(num/den) Fractional to Probability: probability = den / (num + den) Payout = stake × decimal odds Profit = stake × (decimal − 1) ROI = profit / stake × 100%
Result: Decimal: 6.000, American: +500, Probability: 16.67%, Payout: $600, Profit: $500
Fractional odds of 5/1 mean for every $1 staked, you win $5 profit if successful. The equivalent decimal odds are 6.00 (total return including stake). In American format, +500 means $500 profit on a $100 bet. The implied probability of 16.67% means the odds suggest the event has about a 1-in-6 chance of occurring.
Fractional odds originated in 18th-century British horse racing, where bookmakers would call out odds in the paddock. The format naturally expresses the profit-to-stake ratio: "five-to-one" means five units of profit for one unit risked. This verbal tradition persists at UK racecourses today, though online betting increasingly favors decimal odds for their mathematical simplicity.
UK and Ireland primarily use fractional odds, with traditional "board prices" at racecourses. Continental Europe uses decimal odds almost universally. The United States uses American (moneyline) odds for most sports. Asian markets often use Hong Kong odds (decimal minus 1) or Malay/Indonesian formats. Converting between these formats is a daily necessity for anyone comparing global betting markets.
Expected Value (EV) is the fundamental concept in probability-based decision making. EV = (probability of winning × profit) − (probability of losing × stake). If odds are 3/1 (implied 25%) but the true probability is 30%, EV = (0.30 × 3) − (0.70 × 1) = 0.20, meaning a positive return of $0.20 per dollar wagered on average. Professional bettors and traders seek positive EV systematically.
In X/Y fractional odds, you profit X for every Y staked. So 5/1 means $5 profit per $1 wagered; 1/5 means $1 profit per $5 wagered. You always get your stake back too. "Odds-on" (numerator < denominator, like 1/3) means the event is favored; "odds-against" (like 3/1) means it's less likely.
Evens (1/1) means you profit the same amount as your stake — a $100 bet returns $200 total. The implied probability is exactly 50%. In decimal format it's 2.00; in American it's +100.
The sum of implied probabilities across all outcomes exceeds 100% — this excess is called the overround or "vig" (vigorish). It's the bookmaker's built-in profit margin. If a coin flip is priced at 10/11 each way, each side has 52.4% implied probability, totaling 104.8%. The 4.8% is the margin.
Fractional odds are traditional in UK horse racing and football. Decimal odds (popular in Europe and Asia) are easier for calculating exact payouts and comparing odds. American odds are standard in US sports. Most professionals prefer decimal for clarity, but fractional remains culturally important in the UK.
Short odds (like 1/5) mean the event is very likely — low risk, low reward. Long odds (like 50/1) mean the event is unlikely — high risk, high reward. "Shortening" means the odds are getting smaller (event becoming more likely); "drifting" means odds are getting longer (less likely).
Compare the implied probability with your own estimate. If odds are 3/1 (25% implied) but you believe the true probability is 35%, the bet has positive expected value. Value = (your probability × decimal odds) − 1. If this is positive, the bet is theoretically profitable long-term.