Gambling terms, explained straight

Odds, Probability & Bankroll

American odds to European

A method for restating a betting line from the American moneyline format into the European decimal format, where the number shown is the total payout per unit staked, including the original stake.

Positive formula
1 + (a / 100)53
Negative formula
1 + (100 / |a|)53
Even money
+100 American = 2.00 decimal3

Key points

  • Positive American odds (e.g., +400) convert to decimal odds by adding 1 to the odds divided by 100, giving 5.0.24
  • Negative American odds (e.g., −400) convert by adding 1 to 100 divided by the absolute value of the odds, giving 1.25.53
  • The decimal format represents the full payout including the original stake per unit staked, unlike American odds which show profit or required stake.15

Where this term is used

Not the same as

Odds & probability American odds Explains the American moneyline format itself. Odds & probability Odds General overview of betting odds and their meaning. Odds & probability Betting odds Covers the different formats used to display betting odds. Odds & probability Fractional odds to decimal Conversion from UK fractional odds to European decimal odds. Odds & probability Odds vs probability Distinguishes between odds and implied probability. Odds & probability Royal flush odds The probability of being dealt a royal flush in poker.

Sources

  1. Odds en.wikipedia.org Provides the definition of decimal odds and the context of odds conversion.
  2. Fixed-odds betting en.wikipedia.org Supports the application of this conversion to fixed-odds betting markets.
  3. Sports betting - Wikipedia en.wikipedia.org Gives the formulas for converting both positive and negative American odds to decimal.
  4. Sports: Straight Bet - Calculators wizardofodds.com Provides example conversions such as +400 = 5.0.
  5. Sports - FAQ - Wizard of Odds wizardofodds.com Establishes the definition and the conversion formulas used on this page.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.

Written and maintained by Ellis Warrender, writer and maintainer.

Last updated 28 July 2026. Spotted an error? Tell me and it gets fixed and logged on the corrections page.