# The Difference Between Odds and Probability

## Odds and Probability Conversion Calculator

Odds-Probability Conversion
Check one button. Enter either a probability to convert to odds, or an odds to convert to probability.
probability as a decimal (ex: 0.85)

probability as a fraction (ex: 2/15)

odds (ex: 5:3)

Odds and probability are two different ways to describe the chance of an even occurring. Odds expresses chance as a ratio of success to failure, the number of desired outcomes to the number of undesired outcomes. Probability expresses chance as a ratio of the number of desired outcomes to the total number of possible outcomes.

As an example, consider a coin flip. The odds of getting heads is 1:1 because there is one way to get heads and one way to not get heads, i.e. getting tails. Odds are read "x to y." where x is the number of successes and y is the number of failures.

The probability of getting heads is 1/2 or 0.5. There is one desired event (heads) and two events total (heads and tails). Probability is read "x out of z," where x is the number of successes and z is the total number of possible outcomes.

Converting Odds to Probability:

To convert odds to probability, add the successes and failures to find the total. Then divide the number of successes by the total to calculate the probability.

Example: Suppose the odds of a casino game are 2:3. Since 2+3 = 5 we take 5 as the total. Thus the probability is 2/5 = 0.4 = 40%.

Converting Probability to Odds:

First express the probability as a fraction with the numerator equal to the number of successes and the denominator equal to the total. Subtract the numerator from the denominator to find the number of failures. Then you have the two numbers needed to express odds.

Example. Suppose the probability of winning a game is 1/5. Since 5-1 = 4, we take 4 as the number of unsuccessful events. Thus, the odds are 1:4.