Odds Calculator
Convert between probability and odds, and calculate odds ratio. Odds express the ratio of favorable to unfavorable outcomes and are commonly used in betting, epidemiology, and research. Enter either a probability or odds value, and the calculator shows the conversion and odds ratio interpretation. Understanding odds is essential for interpreting research findings, medical statistics, and betting information.
Odds conversion formulas
Probability to Odds: odds = p / (1 - p)
Odds to Probability: p = odds / (1 + odds)
Odds Ratio: OR = odds₁ / odds₂
Examples
- Probability 0.5: Odds = 1:1 (equal chance).
- Probability 0.75: Odds = 3:1 (3 favorable per unfavorable).
- Probability 0.1: Odds = 1:9 (1 favorable per 9 unfavorable).
- Odds 5:1: Probability = 5/6 ≈ 0.833.
Odds: frequently asked questions
What are odds?
Odds express the ratio of favorable to unfavorable outcomes. If odds are 3:1, there are 3 favorable outcomes for every 1 unfavorable outcome. Odds = p/(1-p), where p is probability.
How do odds differ from probability?
Probability ranges from 0 to 1 and measures likelihood. Odds range from 0 to infinity and compare favorable to unfavorable outcomes. Probability 0.75 equals odds of 3:1.
What is odds ratio?
Odds ratio compares odds of an outcome in two groups. OR = (odds in group 1) / (odds in group 2). Used in epidemiology and research to compare risk.
How do I convert odds to probability?
If odds are k:1, then probability = k/(k+1). If odds are 3:1, probability = 3/(3+1) = 0.75.
Official sources
- NIST/SEMATECH e-Handbook: NIST Handbook.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.