Odds conversion: two prices, four formats

Why this matters

A price can look different without changing its meaning. Decimal 2.50, fractional 3/2 and American +150 express the same return before fees. Start with the format printed by the source; entering an American price in the decimal field produces a different calculation.

Before entering the numbers

A price can look different without changing its meaning. Decimal 2.50, fractional 3/2 and American +150 express the same return before fees. Start with the format printed by the source; entering an American price in the decimal field produces a different calculation.

Open the calculator: Odds Converter. All figures below are hypothetical. CU denotes a consistent currency unit, not a named currency. Field and result names match the English calculator interface.

Example 1: the starting assumptions

Use a decimal price of 2.50 to check how the converter moves between formats. No event probability has been independently estimated here. The percentage comes entirely from the entered price.

Entered fields: Input format: Decimal · Odds or probability: 2.50 (Decimal >1; fraction a/b with a,b >0; American ≤−100 or ≥100; probability >0 and <100%)

Calculated results: Decimal: 2.500000 · Fractional (approximate): 3/2 · American: +150.00 · Implied probability: 40.0000 %

• d = 2.50; fractional = 2.50 − 1 = 1.50 = 3/2
• American = 100 × (2.50 − 1) = +150
• 100 / 2.50 = 40%

Example 2: change the inputs

Switch the input format to American and enter −125. The minus sign changes the conversion rule; it does not mean a negative decimal price or a negative chance.

Entered fields: Input format: American · Odds or probability: -125 (Decimal >1; fraction a/b with a,b >0; American ≤−100 or ≥100; probability >0 and <100%)

Calculated results: Decimal: 1.800000 · Fractional (approximate): 4/5 · American: -125.00 · Implied probability: 55.5556 %

• d = 1 + 100 / 125 = 1.80
• fractional = 0.80 = 4/5
• 100 / 1.80 = 55.5556%

What the result leaves out

The reciprocal of one price does not remove bookmaker margin. Prices for every mutually exclusive outcome are needed to inspect the whole market. Neither example establishes the likelihood of an event.

Arithmetic uses unrounded intermediate values; displayed numbers are rounded. These examples document the model, not a provider quote or an observed transaction.

18+. Educational information only. This is not financial, investment, legal or tax advice, and it is not a guarantee of any result. Betting, gambling and crypto involve a risk of losing money. Estimates depend on your inputs; verify current provider terms and local rules.

Practical checklist

• Record the source, units and time of each input.
• Keep fees and principal in their stated units.
• Reproduce both examples before comparing other inputs.
• Read the stated limitations and current provider terms.