Probability to Odds Calculator
Probability and odds express the same chance in two different ways, and this calculator converts from the first to the second. A probability is the likelihood of an event on a scale from 0 to 1, or equivalently from 0 to 100 percent. Odds instead compare how often the event happens with how often it does not, written as a ratio such as 3 to 1. To turn a probability into odds in favor, you divide the probability by one minus the probability, the standard relationship taught in every introductory statistics course. You enter a probability as a decimal between 0 and 1, and the tool returns the odds in favor, both as a single decimal multiple and as a clean ratio. Every figure is computed deterministically from the formula shown below, never estimated, so the worked example reconciles exactly with the result on screen. This conversion matters whenever you compare a probability against a quoted betting line, or when reading research that reports findings as odds rather than plain probabilities. It is the inverse of converting odds back into a probability. Use this calculator to translate a percent into odds or to check a bookmaker's implied probability.
A probability converts to odds in favor with odds = p / (1 - p). For a probability of 0.75 (75 percent), the odds in favor are 3.00, that is 3 to 1, because 0.75 / 0.25 = 3.
Probability to odds formula
odds in favor = p / (1 - p)
p = probability (between 0 and 1)
1 - p = probability the event does not happen
ratio form = odds to 1
Odds in favor are the ratio of the chance an event happens to the chance it does not. Dividing the probability by its complement gives that ratio directly, which can then be written as a single multiple or as odds to one.
Worked example
Convert a probability of 0.75 into odds in favor.
- Probability p = 0.75
- Complement = 1 - 0.75 = 0.25
- Odds in favor = 0.75 / 0.25 = 3.00
- As a ratio: 3 to 1
A 75 percent chance is the same as odds of 3 to 1 in favor. This is the calculator's default input, so the result above matches the widget exactly.
Probabilities and their odds
| Probability | Percent | Odds in favor |
|---|---|---|
| 0.50 | 50.00% | 1 to 1 |
| 0.67 | 66.67% | 2 to 1 |
| 0.75 | 75.00% | 3 to 1 |
| 0.80 | 80.00% | 4 to 1 |
| 0.90 | 90.00% | 9 to 1 |
Reference: US National Institute of Standards and Technology (NIST).
Probability to odds: frequently asked questions
How do I convert a probability into odds?
Divide the probability by one minus the probability. If the chance of an event is p, the odds in favor are p divided by (1 minus p). A probability of 0.75 gives odds of 0.75 divided by 0.25, which is 3, written as odds of 3 to 1.
What is the difference between odds in favor and odds against?
Odds in favor compare the chance an event happens to the chance it does not, so 3 to 1 means three times as likely to happen as not. Odds against flip the ratio to 1 to 3. This calculator reports odds in favor; reverse the two numbers to read the odds against.
Can I enter a percent instead of a decimal?
Yes. A probability of 75 percent is the same as 0.75. Enter the value as a decimal between 0 and 1, so 75 percent becomes 0.75 and 5 percent becomes 0.05. The calculator then returns the matching odds in favor.
What happens at a probability of 0 or 1?
A probability of 1 means the event is certain, so the odds in favor are infinite and cannot be written as a finite ratio. A probability of 0 means it never happens, giving odds of 0. The formula is defined for every probability strictly between 0 and 1.
Why convert probability to odds at all?
Odds are the natural language of betting markets, and odds ratios are standard in medical and social statistics. Converting a probability you trust into odds lets you compare it directly with a quoted betting line or with results reported as odds in research.
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.