What Is the Odds to Probability Calculator?
Odds and probability are two different ways of describing the same uncertainty, and they are easy to confuse. This calculator converts odds expressed in the form a:b into a clear probability — both as a decimal between 0 and 1 and as a percentage. It works for odds stated in favor of an event and for odds stated against it.
How to Use It
Enter the two numbers of your odds. For example, if you read "odds of 3:2", type 3 as the first number (a) and 2 as the second number (b). Then choose whether those odds are in favor of the event or against it, and the calculator returns the probability and its complement.
The Formula Explained
Odds in favor of a:b mean there are a favorable outcomes for every b unfavorable outcomes. The total number of outcomes is a + b, so the probability of the event is:
$$P = \frac{\text{a}}{\text{a} + \text{b}} \times 100\%$$
If the odds are stated against the event, the favorable and unfavorable parts swap, giving $$P = \frac{\text{b}}{\text{a} + \text{b}} \times 100\%$$ The probability of the event not happening is simply \(1 - P\).
Worked Example
Suppose a horse has odds in favor of 3:1. The probability of winning is $$P = \frac{3}{3 + 1} = \frac{3}{4} = 0.75,$$ or 75%. The chance of not winning is \(1 - 0.75 = 0.25\), or 25%.
FAQ
What is the difference between odds and probability? Probability is the ratio of favorable outcomes to all outcomes (a number from 0 to 1). Odds is the ratio of favorable to unfavorable outcomes (e.g. 3:1).
How do I convert a probability back to odds? If P is the probability, the odds in favor are \(P : (1 - P)\), which simplifies to a:b once scaled to whole numbers.
Are betting "odds against" the same as this? Yes. Bookmaker odds like 5:1 are usually odds against, meaning the implied probability of winning is \(1 / (5 + 1) \approx 16.7\%\).
