Odds Calculator

What the odds calculator does

Odds are another way of expressing chance, stated as a ratio of the ways something can happen to the ways it cannot. This calculator takes the chances for and against an outcome and turns them into a probability, into the three common odds formats, and into the return on a stake if you are placing a bet.

Odds and probability describe the same thing but look different, and confusing the two is a common trap. Below is how they relate and how the calculator moves between them.

How to use it

1. Enter the chances for success and the chances against success, as whole numbers.
2. Enter a stake to see the return a bet at these odds would pay.
3. Press Calculate for the probability, the odds formats, and the payout, or Reset to clear it.

Odds are not the same as probability

This is the distinction worth getting straight. Probability compares the ways something can happen to the total number of outcomes, so a 1-in-5 chance is a probability of one fifth, or 20 percent. Odds instead compare the ways it can happen to the ways it cannot, so that same event has odds of 1 to 4, one way for it against four ways against it.

The difference is the denominator: probability is measured out of the whole, while odds set the ways for against the ways against. That is why odds of 1 to 4 and a probability of 20 percent describe exactly the same chance in different language. Mixing them up, reading 1 to 4 as a 25 percent chance, is an easy and costly slip, which is why the calculator shows both side by side.

How the conversions work

From the chances for and against, the probability of success is the chances for divided by the total of both:

Probability of success = chances for ÷ (chances for + chances against)

The odds themselves are just the ratio of the two chances, reduced to their simplest whole-number form. From there the calculator also works out the betting return: at these odds, a winning stake is multiplied by the decimal odds to give the total returned, and subtracting the stake leaves the profit.

The three odds formats

The same odds get written three ways around the world. Fractional odds, common in the UK, show the ratio as a fraction like 4/1, read as four to one. Decimal odds, common in Europe, show the total return per unit staked, so 5.0 means a winning bet returns five times the stake, the original plus four in profit.

American, or moneyline, odds show how much you win on a set stake, or must stake to win a set amount, depending on whether the outcome is a favourite or an underdog. The calculator reports all three, so a figure quoted in one format can be understood in the others.

A worked example

Suppose an outcome has 1 chance for and 4 chances against. The probability of success is 1 ÷ (1 + 4) = 20 percent, and the odds against are 4 to 1, or 5.0 in decimal form.

Stake 100 rupees on it and, if it wins, the total returned is the stake times the decimal odds, 100 × 5.0 = 500 rupees, of which 400 is profit. Notice the probability is 20 percent, not 25: the 1 to 4 odds compare one way to win against four to lose, not one against a total of four.

Entering your values

Enter the chances for and against as positive whole numbers, and a stake to see the payout. The calculator returns the win and loss probabilities as percentages, shown alongside a pie chart, the fractional, decimal, and American odds, and the total return and profit for your stake.

Questions people ask

What are odds?

A ratio of the ways an outcome can happen to the ways it cannot. Odds of 4 to 1 against mean four ways to lose for every one way to win.

How are odds different from probability?

Probability is the ways to win out of all outcomes; odds are the ways to win against the ways to lose. Odds of 1 to 4 equal a probability of 20 percent, not 25.

What do fractional, decimal, and American odds mean?

Fractional shows the ratio as a fraction, decimal shows the total return per unit staked, and American shows the win or stake on a fixed amount. All three describe the same odds.

How is the payout worked out?

A winning stake is multiplied by the decimal odds to get the total returned, and subtracting the stake gives the profit.

References

A quick note on where the methods here come from. Odds and their relationship to probability are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook covering probability and odds.

1. NIST/SEMATECH e-Handbook of Statistical Methods (probability and odds). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (probability topics). https://openstax.org/details/books/introductory-statistics-2e