Comprehensive Calculator Guide
This calculator converts a probability into odds for and against, a ratio such as 1:3, and the log-odds used in statistics. 25% is odds of 1:3. Odds are used in medical studies and logistic regression.
Odds vs probability
Probability is part over whole; odds are part over part: 25 ÷ 75 = 0.333. Back again: p = odds ÷ (1 + odds). Logistic regression models ln(odds), which spans all real numbers.
How to Use
- Enter the probability as a percentage.
- The odds for, against and the logit are derived.
- Press “Convert” to see the results.
Formula Used
Odds = p ÷ (1 − p) | p = odds ÷ (1 + odds) | logit = ln(odds)
Practical Examples
- Example 1
- 25%: 1:3, logit −1.099.
- Example 2
- 80%: 4:1, logit 1.386.
Important Tips
- Odds ≈ probability only when small.
- Odds ratio ≠ relative risk.
- Logit is 0 at 50%.
Common Mistakes to Avoid
- Reading 1:3 as one third.
- Entering a decimal.
- Mixing odds for and against.
Frequently Asked Questions
- Odds vs probability?
- Part over part vs part over whole.
- Odds to probability?
- odds ÷ (1 + odds).
- What is the logit?
- ln(odds).