Methodology
How we convert odds
The formulas behind /tools/odds-converter. Last updated 2026-05-04.
Sportsbook odds tell you two things: what payout you get if you win, and what probability the bookmaker assigns to the outcome. Four common formats — American, Decimal, Fractional, and Implied Probability — encode the same underlying numbers differently. This page explains each format, the formulas to convert between them, and what bookmaker margin (“vig”) does to the implied probabilities you read.
The four formats
- American (US odds): positive numbers (e.g.
+150) show how much you win on a $100 stake. Negative numbers (e.g.−200) show how much you must risk to win $100. - Decimal (European): the multiplier on your stake including the stake (e.g.
2.50means $1 returns $2.50 total — $1.50 profit + the $1 back). - Fractional (UK): profit-to-stake ratio (e.g.
3/2means $2 staked returns $3 profit + $2 stake = $5 total). - Implied probability: the probability of the outcome that breaks even on a fair bet at those odds.
Conversion formulas
American → Decimal:
if american > 0: decimal = (american / 100) + 1
if american < 0: decimal = (100 / |american|) + 1Decimal → American:
if decimal >= 2.0: american = (decimal − 1) × 100
if decimal < 2.0: american = −100 / (decimal − 1)Decimal → Fractional:
profit_ratio = decimal − 1
fraction = simplify(profit_ratio_numerator / profit_ratio_denominator)We use Euclidean GCD reduction to keep fractions in lowest terms. Continued-fraction approximation for irrational decimal values (very rare in published odds; usually a rounding artifact).
Decimal → Implied Probability:
implied_prob = 1 / decimalImplied Probability → Decimal:
decimal = 1 / probabilityVig and what implied probability really means
Implied probability from sportsbook odds is notthe bookmaker’s belief about the outcome. It includes the bookmaker’s margin (the “vig” or “juice”). On a coin flip, fair odds are 2.00 on each side (50% implied each); a bookmaker offering 1.91 on each side is quoting 52.4% implied each — total 104.8% — with the 4.8% being their margin.
To get the bookmaker’s “true” estimate, you can normalize implied probabilities so they sum to 100%: true_prob_i = implied_i / sum(implied_j for all outcomes). This assumes the vig is split evenly across outcomes; in reality bookmakers shade lines, so the assumption is approximate.
Worked examples
- +150 (American) → 2.50 (Decimal) → 3/2 (Fractional) → 40% (Implied)
- −200 (American) → 1.50 (Decimal) → 1/2 (Fractional) → 66.7% (Implied)
- 2.00 / +100 / 1/1 / 50% — the canonical even-money bet
- 1.91 / −110 / 10/11 / 52.4% — standard NFL spread; the 2.4% above 50% is the vig
Limitations
- Fractional rounding: irrational decimals (e.g.
2.333…) approximate to nearby simple fractions (7/3) for readability. The implied probability shown is computed from the original decimal, not the rounded fraction. - Implied probability does not equal market probability. See §3 — it includes vig.
- We don’t support negative-decimal or push handling; standard sportsbook odds are always positive decimal.
Run a conversion
The converter at /tools/odds-converter handles all four formats interchangeably. Type in any field; the others update.
Frequently asked questions
What's the easiest odds format to read?
What does −110 mean?
−110 means risk $110 to win $100. Equivalent in decimal: 1.91. Implied probability: 52.4%. The 2.4% above 50% is the bookmaker’s vig.What is vig (or juice) on a sportsbook line?
2.00. A book offering 1.91 on each side is implying 52.4% on each — total 104.8%. The 4.8% above 100% is the vig: profit the book keeps regardless of outcome.How do I convert American to Decimal odds?
+150 → 1.50 + 1 = 2.50.Negative American: divide 100 by the absolute value, add 1.
−200 → 100/200 + 1 = 0.5 + 1 = 1.50.