How to Calculate Probability Odds
What is Probability Odds?
A probability and odds converter switches between probability (0–1 or %), fractional odds (a:b), decimal odds, and frequency (1 in n). All express the same likelihood differently.
Formula
Probability (0-1 or %) = favourable outcomes / total outcomes; Odds = probability / (1 − probability)
- P
- Probability (0 to 1 or 0-100%)
- O
- Odds (ratio (a:b or a/b))
Step-by-Step Guide
- 1Probability p → Fractional odds: (1−p)/p
- 2Fractional odds a/b → Probability: b/(a+b)
- 3Decimal odds d → Probability: 1/d
- 4Frequency "1 in n" → Probability: 1/n
Worked Examples
Input
Probability 0.25 (25%)
Result
Fractional: 3/1 (3:1 against); Decimal: 4.0; Frequency: 1 in 4
Frequently Asked Questions
What's the difference between probability and odds?
Probability = likelihood (0-1). Odds = ratio of likelihood. P=0.25 = odds 1:3.
If probability is 50%, what are the odds?
Odds are 1:1 (50/50). Same as even odds or "even money".
How do I convert odds to probability?
If odds are a:b, then probability = a / (a+b). Odds 2:3 = 2/(2+3) = 40%.