Probability to Odds Calculator

More about the Probability to Odds Calculator so that you can better understand the elements used in this calculator. It is common for people to have a confusion between the concepts of odds and probability, and often times, they incorrectly use them, most typically interchanging probability by odds.

The odds for the occurrence of an event are simply the probability of occurrence of an event, divided by the probability that the event does not occur. Or for example, if there are 8 equally likely individual outcomes, and 6 of them favor of an event, and 2 are against the event, then the odds for the occurrence of the event are "6 to 2", or "6/2" or simply 3. So, the odds can be any positive number, it does not have to be a number between 0 and 1.

How do you convert probability to odds?

The idea of probability and odds are sometimes used as the same thing by people, but they are actually two different things. The probability of an even is the likelihood of an event occurring, whereas the odds is the likelihood of an event occurring RELATIVE to the likelihood of it not occurring

As this definition suggests then, the odds are computed by dividing the probability of occurrence of an even (p) by the probability of the event not occurring (1 - p).

So then, how do you calculate the odds of something happening? First, you identify the probability that the event occurs, which you call p. Second, you identify the probability of the event not occurring, which is 1 - p.

Then, the odds are obtained by dividing these two probabilities, this is, by computing p/(1 - p)

The Probability to Odds Formula

The formula that is used to compute the odds for the occurrence of an event, \(p\), given its probability is shown below:

\[ Odds = \displaystyle \frac{p}{1 - p}\]

The conversion from probability to odds is usually referred also as a risk to odds conversion.

If, on the other hand, instead of knowing the probability you know the odds, you can use this odds to probability calculator .

Example: Probability to Odds Calculation

Suppose that an event has a probability of p = 0.4 of happening. What are the odds for this event to happen?

The first step is to identify the probability, which in this case is directly provided as p = 0.4. Then, we plug this value into the probability to odds formula:

\[ Odds = \displaystyle \frac{p}{1 - p} = \displaystyle \frac{0.4}{1 - 0.4} = \displaystyle \frac{0.4}{0.6} = 0.667\]

How do you interpret this? It is perfectly valid to say that odds are 0.667, and that is the end of the story. But when you see other people talking about odds, you hear this "2:1 odds" type of thing.

In which case, you can say "the event happens 0.667 for every 1 time it does not happen", or simply say, the odds are 0.667:1, or more elegantly 2:3 if that is the notation that you are interested in.