KEY TAKEAWAYS
American odds, decimal odds, and fractional odds are three ways sportsbooks express a betting price. For example, -150 in American odds equals 1.6666… in decimal odds and 2/3 in fractional odds. A decimal display rounded to 1.67 is a close approximation, rather than an exact equivalent. Knowing how to convert helps readers compare prices across sportsbooks, understand international betting coverage, and check potential payouts. The formulas below explain each conversion, with a comparison table and a worked example showing where rounding matters.
Why Three Odds Formats Exist
The three formats reflect regional conventions. American odds use a 100-unit reference amount and are common in the United States. A negative number shows how much must be staked to win 100 units in profit; a positive number shows the profit from a 100-unit stake. The examples in this article use dollars, but the same ratios apply in other currencies.
Decimal odds are common in continental Europe, Australia, and other markets. They represent the total return per unit staked, including the original stake. Fractional odds are traditionally associated with the United Kingdom and Ireland and remain common in horse racing. They express potential profit as a ratio to the stake.
Exact equivalents in all three formats have the same payout and implied probability. American odds express the relationship using a signed number, decimal odds show the total-return multiplier, and fractional odds show the profit ratio. None changes the underlying bet simply by displaying it differently.
Implied probability is the probability represented by the quoted price. It is not necessarily the outcome’s actual chance of occurring, because sportsbook prices include a margin. Converting the format does not remove that margin.
How to Convert Between Odds Formats
Converting American odds to decimal odds depends on whether the American number is negative or positive. For negative odds, divide 100 by the absolute value of the American odds, then add 1. For positive odds, divide the American odds by 100, then add 1. The absolute value is the number without its minus sign.
Negative American odds: Decimal = 1 + (100 ÷ |American odds|).
Positive American odds: Decimal = 1 + (American odds ÷ 100).
For example, -150 becomes 1 + (100 ÷ 150) = 1.6666…, approximately 1.67. A price of +150 becomes 1 + (150 ÷ 100) = 2.50 exactly.
American Odds to Decimal Odds (and Back)
Converting decimal odds back to American odds depends on whether the decimal value is at least 2.00 or below it. For decimal odds of 2.00 or higher, subtract 1 and multiply by 100, then show the result with a plus sign. For decimal odds greater than 1.00 but below 2.00, divide -100 by the decimal value minus 1.
Decimal odds of 2.00 or higher: American = (Decimal − 1) × 100.
Decimal odds between 1.00 and 2.00: American = -100 ÷ (Decimal − 1).
A decimal price of 2.50 becomes +150, while 1.50 becomes -200. Even money, or 2.00, is conventionally written as +100. Some conversions produce non-integer American values: an exact decimal price of 1.67 converts to approximately -149.25, not exactly -150.
Decimal and Fractional Odds
Fractional odds express the profit ratio, while decimal odds include the returned stake. To convert decimal odds to fractional odds, subtract 1 and write the result as a simplified fraction. A decimal price of 2.50 becomes 1.50, or 3/2. To convert fractional odds to decimal odds, divide the numerator by the denominator and add 1: 3/2 becomes 2.50.
American odds also convert directly to fractional odds. For negative American odds, use 100/|American odds| and simplify: -150 becomes 100/150, or 2/3. For positive American odds, use American odds/100: +150 becomes 150/100, or 3/2.
To convert fractional odds a/b directly to American odds, use +100 × (a ÷ b) when a is at least b. When a is smaller than b, use -100 × (b ÷ a). For example, 3/2 becomes +150 and 2/3 becomes -150.
Preserve precision when converting. An exact decimal price of 1.67 converts to 67/100 in fractional odds, whereas the recurring decimal 1.6666… converts to 2/3. Replacing one with the other introduces rounding.
The table below applies these formulas to common price points:
| American Odds | Decimal Odds | Fractional Odds |
|---|---|---|
| -200 | 1.50 | 1/2 |
| -150 | 1.67 (rounded) | 2/3 |
| -110 | 1.91 (rounded) | 10/11 |
| +100 (Even) | 2.00 | 1/1 |
| +110 | 2.10 | 11/10 |
| +150 | 2.50 | 3/2 |
| +200 | 3.00 | 2/1 |
The decimal equivalents of -150 and -110 are rounded to two decimal places in this table. Their exact values are 1.6666… and 1.909090…, respectively. The fractional equivalents shown are exact.
For an exact row such as -200, 1.50, and 1/2, all three formats represent the same payout and an implied probability of approximately 66.67%. Different-looking numbers can therefore express the same price, provided the conversion preserves their full value.
Converting Odds: A Worked Example
Suppose a hypothetical sportsbook lists a selection at -150. Its exact decimal equivalent is 1 + (100 ÷ 150) = 1.6666…, where the six repeats indefinitely. Its fractional equivalent is 100/150, simplified to 2/3.
For a winning $100 stake, the American-odds calculation gives profit = 100 × (100 ÷ 150) = $66.6666…. Rounded to the nearest cent, that is $66.67 in profit and $166.67 in total return.
The exact decimal calculation gives the same result: total return = 100 × (1 + 100/150) = $166.6666…. Fractional odds confirm it: profit = 100 × (2/3) = $66.6666…. The original stake is then added to obtain the total return.
An accepted decimal price of exactly 1.67 is slightly different. At that price, a winning $100 stake returns $167, including $67 in profit. That is approximately $0.33 more than the return at -150. A rounded conversion displayed for reference should therefore be distinguished from the actual price accepted on a bet.
The implied probability at -150 is 150 ÷ (150 + 100) × 100 = 60%. For equal-stake wagers at that fixed price, all settled as wins or losses, a 60% win rate is the break-even point before any additional fees or commissions. A higher win rate produces a profit under those assumptions. The sportsbook’s margin is already reflected in the offered odds; it is not a separate charge to subtract again.
When to Convert Betting Odds
A common reason to convert is comparing prices across sportsbooks that use different formats. A bettor familiar with American odds may see -110 at one sportsbook and 1.91 at another. The exact decimal equivalent of -110 is 1.909090…, so an accepted price of exactly 1.91 offers a slightly higher return. If 1.91 is only a rounded display of another underlying price, the accepted bet details and settlement rules determine the payout.
Conversion also helps when reading odds-comparison tools, international sports coverage, or data feeds that use an unfamiliar format. The same formulas translate fractional prices in racing coverage or decimal prices in a statistics table into a format the reader understands.
For a meaningful comparison, check that the prices refer to the same selection, market, and settlement conditions. For example, a market including overtime is not necessarily equivalent to one covering regulation time only.
Conversion does not create value by itself. It makes prices easier to compare. Exact equivalents offer the same gross payout for the same stake, while genuinely different prices remain different after conversion.
Common Mistakes When Converting Odds
Treating a rounded conversion as an exact equivalent is a common source of errors. -150 converts to 1.6666…, not exactly 1.67. Similarly, 1.6667 is still a rounded approximation, even though it uses more decimal places. Keep full precision during calculations where possible, and round the final monetary result as required.
Do not assume every sportsbook handles display rounding and settlement identically. A rounded reference value and an accepted decimal price are different things. Check the confirmed odds, listed potential return, and applicable settlement rules.
Confusing decimal odds with a probability is another mistake. A price of 1.67 does not mean a 1.67% chance. Its implied probability is (1 ÷ 1.67) × 100, or approximately 59.88%. That percentage is derived from the price and is not necessarily the outcome’s actual probability.
Confusing profit with total return also leads to incorrect payouts. Fractional odds of 2/3 mean $2 in profit for every $3 staked if the bet wins. The $3 stake is returned as well, producing a $5 total return. Decimal odds already include that returned stake in their multiplier.
The plus and minus signs in American odds describe payout ratios, not a universal favorite/underdog rule. Both sides of a closely priced two-way market can have negative odds. Compare the available prices within the same market to determine which selection is favored.
Finally, simplifying a fraction makes it easier to recognize, but does not change its value. The fractions 100/150 and 2/3 are mathematically identical.
Where Bettors Encounter Mixed Odds Formats
Sportsbooks may offer a choice of display formats, but that preference applies only to the platform where it is selected. Other sportsbooks, comparison tools, and media outlets may show the same event using a different notation.
Mixed formats also appear in betting records, spreadsheets, and historical data. Converting prices to a consistent format makes payout calculations and comparisons easier, provided rounded values are identified and the original price is retained when precision matters.
Being able to convert a price means a reader can interpret the number already on the screen without relying on a particular display setting. The key is to distinguish a change in notation from a genuine difference in price.
Related Concepts
Converting between formats is most useful once a reader understands how at least one format expresses payouts. For the 100-unit reference calculations behind negative and positive American odds, see how to read American odds. For the total-return multiplier used in decimal pricing, see decimal odds explained, and for the profit-ratio format associated with the UK and Ireland, see fractional odds explained. Readers comparing prices can also explore how sportsbook vig affects a quoted price. An exact format conversion preserves the margin already reflected in the odds.
