How to Convert Odds: Decimal, Fractional & American Explained

The Three Odds Formats

Betting odds are just a compact way of writing a payout, and the world uses three formats for the same number. Convert between them and you can read any odds, in any market, anywhere.

• Decimal (Europe, Australia, Canada) — your total return per 1 staked, stake included. 2.50 means stake 1, get back 2.50 (profit 1.50).
• Fractional (UK, Ireland) — profit per stake, as a fraction. 3/2 means stake 2, profit 3 (return 5).
• American (US, Canada) — anchored at 100. Positive: profit on a 100 stake (+150 → profit 150). Negative: stake needed to profit 100 (−200 → stake 200, profit 100).

The Conversion Formulas

• Decimal → fractional: d − 1. (2.50 → 3/2)
• Fractional a/b → decimal: 1 + a/b. (3/2 → 2.50)
• American +A → decimal: 1 + A/100. (+150 → 2.50)
• American −B → decimal: 1 + 100/B. (−200 → 1.50)
• Decimal d → American: if d ≥ 2, +100(d − 1); if d < 2, −100/(d − 1). (2.50 → +150; 1.50 → −200)

Worked example: one event, three formats

Take 3/2. Decimal: 1 + 3/2 = 2.50. American: 100 × (2.50 − 1) = +150. So 3/2, +150 and 2.50 are the same price. A few more: 5/2 = 3.50 = +250; 10/1 = 11.00 = +1000; −200 = 1.50 = 1/2.

Implied Probability: What the Odds Say

Every price implies a probability: implied probability = 1 ÷ decimal. So 2.50 implies 40%, −200 implies 1/1.50 ≈ 66.67%, and 5/2 implies 1/3.50 ≈ 28.57% (equivalently b/(a+b) for fractional a/b).

On a two-outcome market the bookmaker's prices sum to more than 100% — the excess is the juice (vig). Example: 1.90 and 2.10 imply 52.63% and 47.62%, summing to 100.25%. Divide each by the total to strip the vig: 52.63/100.25 = 52.5% and 47.62/100.25 = 47.5%. Those are the "no-vig" (fair) probabilities; the matching fair decimals are 1/0.525 ≈ 1.905 and 1/0.475 ≈ 2.105.

Finding Value

A bet has value when your estimated probability beats the implied one. If you believe an outcome is 55% likely and the price is 1.90 (implied 52.63%), the edge is 0.55 × 1.90 − 1 = +4.5%. Small positive edges are why serious bettors convert odds rather than eyeball them. Once value is established, stake sizing is a separate problem — the Kelly criterion gives the mathematically optimal fraction.

Tools That Do the Converting

The Odds Converter turns any price into all three formats at once, with the implied probability alongside. The Implied Probability Calculator goes further: feed it both sides of a market and it returns each probability plus the bookmaker's margin. For stake sizing after you've found an edge, the Kelly Criterion Calculator computes the optimal fraction and a half-Kelly variant. All three run in your browser.

Common Pitfalls

• Mixing up profit and return — decimal odds are total return, not profit; fractional and American are profit only.
• Forgetting the sign — +150 and −150 are very different prices (2.50 vs 1.667).
• Comparing raw prices across formats — 10/1 "looks bigger" than +1000 but they are identical; always normalize to decimal first.
• Ignoring the vig — comparing your estimate to a vigged price overstates edge; compare to the no-vig probability instead.