Odds to Probability Calculator
Odds and probability describe the same uncertainty in two different languages, and converting between them is a frequent source of confusion. Probability states the chance of an event directly, as a value between 0 and 1 or as a percent. Odds instead compare the chance an event happens with the chance it does not, written as a ratio such as 4 to 1. This calculator translates odds in favor into the equivalent probability, returning both a decimal and a percent so you can read the figure in whichever form you need. The method is the standard one taught in probability courses: divide the favorable count by the total of favorable and unfavorable outcomes. You can enter odds as two numbers, favorable and unfavorable, or as a single number understood as that many to one. Every result is computed deterministically from the formula shown below, never estimated, so the worked example reconciles exactly with the figures on screen. Understanding this conversion matters in betting, where quoted odds imply a probability, and in fields like genetics and epidemiology. Use the calculator to sanity-check a quoted line or to translate a probability you trust. A companion tool converts probability back into odds.
Odds in favor of a to b convert to probability with P = a / (a + b). For odds of 4 to 1, the probability is 0.80, equal to 80.00%, since 4 / (4 + 1) = 0.80.
Odds to probability formula
P = a / (a + b)
a = favorable outcomes (odds in favor)
b = unfavorable outcomes
For odds of o to 1: P = o / (1 + o)
The probability of an event is the number of favorable outcomes divided by the total number of outcomes. Because odds split that total into favorable and unfavorable parts, dividing the favorable part by their sum recovers the probability.
Worked example
Convert odds of 4 to 1 in favor into a probability.
- Favorable a = 4, unfavorable b = 1
- Total outcomes = a + b = 4 + 1 = 5
- Probability = 4 / 5 = 0.80
- As a percent: 0.80 x 100 = 80.00%
Odds of 4 to 1 in favor correspond to an 80.00 percent chance. These are the calculator's default inputs, so the result above matches the widget exactly.
Odds and their probabilities
| Odds in favor | Probability | Percent |
|---|---|---|
| 1 to 1 | 0.5000 | 50.00% |
| 2 to 1 | 0.6667 | 66.67% |
| 3 to 1 | 0.7500 | 75.00% |
| 4 to 1 | 0.8000 | 80.00% |
| 9 to 1 | 0.9000 | 90.00% |
Reference: US National Institute of Standards and Technology (NIST).
Odds to probability: frequently asked questions
What is the difference between odds and probability?
Probability is the chance an event happens, expressed as a number from 0 to 1 or as a percent. Odds compare the chance it happens to the chance it does not. Odds of 4 to 1 mean four favorable outcomes for every one unfavorable outcome, which is a probability of four out of five, or 0.80.
How do I convert odds to a probability?
If the odds in favor are written as a to b, the probability is a divided by the sum of a and b. When odds are given as a single number o (meaning o to 1), the probability is o divided by one plus o. This calculator accepts either form and returns the decimal probability and the equivalent percent.
What are odds in favor versus odds against?
Odds in favor of 4 to 1 describe four chances something happens for each chance it does not. Odds against are simply the reverse, 1 to 4, describing the same event from the opposite side. Always confirm which direction is meant, because the resulting probability is very different.
Why use odds rather than probability?
Odds are common in betting, genetics and some statistical models because they make ratios and multiplication of independent chances convenient. Odds also have no upper bound, which suits comparisons of rare or very likely events, whereas a probability is always capped between 0 and 1.
Can probability exceed one?
No. A valid probability is always between 0 and 1 inclusive, equivalent to 0 and 100 percent. Because the formula divides favorable outcomes by all outcomes, the result of any genuine odds conversion stays within that range automatically.
Official sources
- Probability and statistics reference: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.