Odds Calculator: convert fractional, decimal and moneyline odds

Odds describe how likely an event is and how much a winning bet pays. The same probability can be written three ways: as a fraction, as a decimal, or as American moneyline odds. Each format appears in a different corner of the world. Fractional odds are common in Britain and Ireland, decimal odds in Europe, South Africa and Australia, and moneyline odds in North America. This calculator converts between all three and shows the implied probability behind each set of odds, so you can read any bookmaker, exchange or accumulator and know exactly what the number means.

What odds actually mean

Odds carry two separate pieces of information at once. The first is the implied probability, which is the chance the market assigns to the event. The second is the payout, which is what you collect if the bet wins, including your original stake. A bet at even money, written 1/1 fractional, 2.00 decimal or +100 moneyline, implies a 50 percent chance and returns double your stake if it wins. Understanding both readings matters because the two are not independent: the payout is always slightly lower than a fair price would pay, and that gap is the bookmaker's margin.

It helps to separate the words. Probability is a number from 0 to 1, or 0 to 100 percent. Odds are a ratio or a price that expresses the same probability in betting language. When a bookmaker quotes 4/1, they are saying the event has a one in five chance, which is 20 percent, and a correct one unit stake pays four units profit plus your unit back.

The three formats

Fractional odds are written as two numbers separated by a slash, such as 4/1 or 6/5. The second number is your stake and the first is your profit. At 4/1, a one unit stake returns four units of profit plus the stake, five units in total. At 6/5, a five unit stake returns six units of profit plus the five back. Fractional odds below even, where the first number is smaller than the second, describe a favourite, and fractional odds above even describe an underdog.

Decimal odds are the simplest to work with. The number is the total return per one unit staked, profit included. Decimal odds of 5.00 mean a one unit stake returns five units in total, of which four are profit. Decimal odds of 2.00 are even money. Anything below 2.00 is a favourite and anything above 2.00 is an underdog. Decimal odds can never be below 1.00, because 1.00 would mean a stake returns only itself with no profit.

American moneyline odds use a plus or minus sign. A plus number is the profit on a 100 unit stake, so +400 means a 100 unit stake profits 400. A minus number is the stake required to profit 100, so -400 means you must stake 400 to profit 100. Plus numbers describe underdogs and minus numbers describe favourites. Moneyline odds never sit between -100 and +100, because that band would describe an event more likely than a coin flip as a favourite and would cross the even-money boundary.

How the conversion works

Every conversion passes through a single idea: the payout for one unit staked. Fractional odds of a over b convert to decimal odds with the rule decimal equals (a divided by b) plus 1. Moneyline odds convert to decimal by two rules depending on the sign.

For positive moneyline odds, decimal equals (moneyline divided by 100) plus 1. For negative moneyline odds, decimal equals (100 divided by the absolute value of the moneyline) plus 1.

The conversions in the other direction follow the same arithmetic in reverse. Decimal odds of d convert to fractional by subtracting one, then expressing the remainder as the simplest fraction that fits, so decimal 5.00 becomes 4/1. Decimal odds of d convert to moneyline by checking whether d is at least 2.00: if it is, moneyline equals 100 times (d minus 1); if not, moneyline equals negative 100 divided by (d minus 1).

Worked examples

Start with 4/1 fractional. The decimal is (4 divided by 1) plus 1, which is 5.00. The moneyline, because the decimal is at least 2.00, is 100 times (5.00 minus 1), which is +400. A 10 unit stake at 5.00 returns 50 units in total, 40 of them profit.

Now take the favourite 1/4. The decimal is (1 divided by 4) plus 1, which is 1.25. Because this is below 2.00, the moneyline is negative 100 divided by (1.25 minus 1), which is -400. A 10 unit stake at 1.25 returns 12.50 units in total, 2.50 of them profit.

A value in between, such as 6/5, works the same way. The decimal is (6 divided by 5) plus 1, which is 2.20. The moneyline is 100 times (2.20 minus 1), which is +120. A five unit stake at 2.20 returns 11 units in total, six of them profit.

Negative moneyline odds reverse cleanly. At -200, the decimal is (100 divided by 200) plus 1, which is 1.50. At +200, the decimal is (200 divided by 100) plus 1, which is 3.00. Notice that +200 and -200 are not mirrors of each other: one describes a 33 percent chance and the other a 67 percent chance, and the difference is where the margin hides.

Implied probability

The implied probability is the reciprocal of the decimal odds, written as a percentage: implied probability equals 1 divided by decimal odds. Decimal odds of 5.00 imply 1 divided by 5.00, which is 20 percent. Decimal odds of 1.25 imply 1 divided by 1.25, which is 80 percent. Decimal odds of 2.00 imply 50 percent.

The same result can be read from fractional odds without converting first. For fractional odds of a over b, the implied probability is b divided by (a plus b). At 4/1 that is 1 divided by (4 plus 1), which is 20 percent. At 1/4 it is 4 divided by (1 plus 4), which is 80 percent.

Moneyline odds imply probability through two rules. For a positive moneyline m, implied probability is 100 divided by (m plus 100). For a negative moneyline m, implied probability is the absolute value of m divided by (absolute value of m plus 100). At +400 the probability is 100 divided by 500, or 20 percent. At -400 it is 400 divided by 500, or 80 percent.

Implied probability is the bookmaker's view of the event, margin included, so the probabilities on all outcomes in a market always add up to more than 100 percent. The excess is the overround, also called the vig or the juice. A market where two outcomes are each priced at 1.90 decimal has an implied probability of 52.63 percent on each side, a total of 105.26 percent, and the extra 5.26 percent is the bookmaker's margin.

Common odds at a glance

Each row is the same event written four ways. The table makes the pattern clear: as the implied probability falls, the decimal and fractional odds rise, and the moneyline flips from negative to positive at the even-money line of 2.00.

Reading the results

The calculator shows three things for any odds you enter: the same price in the other two formats, the implied probability, and the payout on your stake. The payout is stake multiplied by decimal odds, and it always includes the stake. If you want profit rather than total return, subtract the stake from the payout.

Keep two points in mind when you use the result. First, odds are a price, not a promise: a 20 percent implied probability means the event wins roughly once in five attempts over the long run, not that any single attempt will win. Second, the implied probability is always shaded by the margin, so it reads slightly higher than the true chance the bookmaker believes in. Both points matter when you compare odds across bookmakers, which is the most practical use of this converter.

Frequently Asked Questions

What is the difference between probability and odds? Probability is a fraction of one, usually shown as a percentage, that states how likely an event is. Odds are a ratio or a price that expresses the same probability in betting language. A 20 percent probability is 4/1 fractional, 5.00 decimal and +400 moneyline. Odds also carry the payout, which probability does not.

Why do decimal odds always sit above 1.00? Decimal odds are the total return per one unit staked, profit included. A value of exactly 1.00 would mean the stake is returned with no profit, which no bookmaker offers. Real prices start just above 1.00 for heavy favourites and rise without limit for long shots.

What does the plus and minus sign mean in American odds? The plus sign shows the profit on a 100 unit stake, so +400 profits 400 on a 100 stake. The minus sign shows the stake needed to profit 100, so -400 needs a 400 stake to profit 100. Plus describes an underdog and minus describes a favourite.

How do I work out my profit from decimal odds? Multiply your stake by the decimal odds to get the total return, then subtract the stake. A 20 unit stake at 2.20 returns 44 units in total, which is 24 units of profit. The stake is always included in the decimal number.

Why do the implied probabilities add up to more than 100 percent? The bookmaker prices every outcome slightly short of fair value so that the market pays out less than it takes in over the long run. The amount by which the probabilities exceed 100 percent is the margin, also called the overround or the vig. It is how a bookmaker earns, and it is why the odds never match the true probability exactly.

Can I convert any fractional odds to a moneyline? Yes. Convert the fraction to a decimal first, then apply the moneyline rule. If the decimal is at least 2.00 the moneyline is positive, and if it is below 2.00 the moneyline is negative. Every valid price in one format has an exact equivalent in the other two.