Convert American Odds to Decimal and Fractional Odds

To convert American odds to decimal, divide a positive price by 100 and add 1, or divide 100 by a negative price (ignoring the minus sign) and add 1. So +150 becomes 2.50 and −200 becomes 1.50. Decimal odds are the easiest format to work with because the implied probability is simply 1 ÷ decimal odds.

Sportsbooks quote the same price in three styles: American (moneyline), decimal and fractional. They look different but carry identical information: how much a winning bet pays and how likely the market says the outcome is. Converting between them is arithmetic, and once you can do it, any quoted price can be compared with any other.

This guide gives the conversion formulas with every symbol defined, three worked examples with the steps shown, a table of common prices in all formats, and the checks that catch mistakes. All prices here are hypothetical and are used only to teach the math, not to suggest a bet.

The Three Odds Formats and What They Say

American odds are quoted around a $100 stake. A positive number such as +150 is the profit on a $100 stake, so +150 means a $100 winning bet returns $150 profit plus the stake. A negative number such as −200 is the stake needed to win $100, so a $200 winning bet returns $100 profit plus the stake.

Decimal odds show the total return per $1 staked, including the stake. A price of 2.50 returns $2.50 for every $1 wagered, which is $1.50 of profit and the $1 back. This is why decimal odds can never be below 1.00.

Fractional odds show profit relative to the stake. A price of 3/2 (said “three to two”) pays $3 of profit for every $2 staked. The stake is not part of the fraction, which is the most common source of confusion when comparing it with decimal odds.

Every price also implies a probability. The implied probability is the chance of winning that the price is equivalent to, and the break-even win rate for a bettor is exactly the same number. It is not a forecast of what will happen, and it includes the bookmaker’s margin, a point covered in the table section below.

Because the three formats describe one price, converting is lossless apart from rounding. The convention used here is that all percentages are rounded to two decimals and marked with ≈.

Odds Conversion Formulas

Start with American to decimal. The formula depends on the sign.

where:

A is the American price without its sign, for example 150 for +150 or 200 for −200.

decimal is the total return per $1 staked.

Fractional to decimal adds the stake back to the profit ratio.

where:

a is the numerator (profit) and b is the denominator (stake) of the fraction a/b.

To go the other way, decimal to American, solve the same equations for A.

where:

decimal − 1 is the profit per $1 staked.

Finally, the implied probability comes straight from decimal odds, or directly from the American price.

where:

decimal is the decimal price.

A is the American price without its sign.

For payouts at decimal price D and stake S, total return = S × D and profit = S × (D − 1).

Worked Examples, Step by Step

Example 1: +150. Suppose a hypothetical price is +150 on a $50 stake.

Step 1: decimal = 1 + 150 ÷ 100 = 2.50.

Step 2: implied probability = 1 ÷ 2.50 = 0.40, or 40.00%.

Step 3: profit = 50 × (2.50 − 1) = $75, and total return = 50 × 2.50 = $125.

Step 4: fractional = 2.50 − 1 = 1.5 = 3/2.

Example 2: −200. Suppose a price is −200 on a $50 stake.

Step 1: decimal = 1 + 100 ÷ 200 = 1.50.

Step 2: implied probability = 1 ÷ 1.50 ≈ 66.67%.

Step 3: profit = 50 × (1.50 − 1) = $25, and total return = $75.

Step 4: fractional = 1.50 − 1 = 0.5 = 1/2.

Example 3: 5/2. Step 1: decimal = 5 ÷ 2 + 1 = 3.50. Step 2: American = +100 × (3.50 − 1) = +250. Step 3: implied probability = 1 ÷ 3.50 ≈ 28.57%.

The implied probability is a price, not a prediction: a 40.00% implied chance means the bet breaks even only if it wins 40.00% of the time.

Odds Compared Across Formats

The table converts several hypothetical American prices into the other formats. Every row is derived with the formulas above.

Now add the bookmaker’s margin. In a two-sided market priced at −110 on each side, the implied probabilities are 52.38% + 52.38% = 104.76%. The 4.76% above 100% is the overround, and the theoretical hold is 1 − 1 ÷ 1.0476 ≈ 4.55%.

To remove the margin, divide each implied probability by their sum. For −110 on both sides, 52.38 ÷ 104.76 = 50.00%, so the fair price is 2.00 (+100). For an uneven market of −150 and +130, the implied probabilities are 60.00% and 43.48%, summing to 103.48%, so the no-vig probabilities are 57.98% and 42.02%. This proportional method is a simple convention, not the only one.

Common Mistakes and Misconceptions

The biggest error is treating implied probability as the true probability. It includes the margin, which is why both sides of a market add to more than 100%. A price of −110 implies 52.38%, but the fair chance in a balanced market is 50.00%.

A second error is reading fractional odds as decimal odds. The price 3/2 is not 1.5 in decimal terms for the return; it is 2.50 because the stake is added back. Forgetting the +1 makes every payout look smaller than it is.

Third, many people read negative American odds as a loss. The minus sign only marks a price that risks more than it wins, and a −200 bet that wins still pays a profit.

Finally, rounding too early distorts results. Keep four decimals through the calculation and round only the final answer. A short price like 1.33 for −300 is the rounded form of 1.3333.

Quick Reference and How to Check Your Answer

Check every conversion by going back to the original price. Starting from +150, you get 2.50, and converting 2.50 back gives +100 × (2.50 − 1) = +150. If you do not land on the same number, there is an arithmetic slip.

Also check direction. A short price should give a high implied probability and a long price a low one: −200 gives 66.67% while +400 gives 20.00%. And in any two-sided market, the two implied probabilities should add to a little over 100%, never under it.

Related Concepts and Next Steps

Odds are only one half of the picture. To see how a quoted probability is built from counting outcomes, read how probability is calculated and the formulas behind it. Those formulas are what let you compare a price with a real chance.

The natural next steps are expected value, which combines a probability and a payout into the average result per bet, and the math of parlays, which multiplies decimal odds together. Both rely on the conversions above, so practice them until moving between formats feels automatic.