Odds Calculator
Convert between probability (%) and odds formats.
Calculate odds for/against, decimal odds, and "1 in N" from probability or event counts.
Odds & Probability
Probability vs Odds — what is the difference?
Probability is the chance something happens, expressed as a fraction of all outcomes.
P = favourable outcomes / total outcomes
Example: rolling a 6 on a die → P = 1/6 ≈ 16.67%
Odds express the ratio of favourable to unfavourable outcomes.
Odds for = favourable : unfavourable
Example: rolling a 6 → odds are 1:5 (one way to win, five ways to lose)
Converting between them:
- Probability → Odds for: P / (1 − P) e.g. 0.25 → 0.25/0.75 = 1:3
- Odds X:Y → Probability: X / (X + Y) e.g. 1:3 → 1/4 = 25%
Odds formats:
- Fractional (UK): 3/1 means you win 3 units per 1 staked
- Decimal (Europe): 4.0 means your total return per 1 staked (includes stake)
- Moneyline (US): +300 means win $300 on a $100 bet (underdog)
- “1 in N”: “1 in 4 chance” — the total number of outcomes needed for one success
Real-world examples:
- A fair coin: P = 50%, odds = 1:1 (evens), decimal = 2.0, 1 in 2
- Drawing an ace from a deck: P = 4/52 ≈ 7.69%, odds = 4:48 = 1:12
- Rolling any number ≤ 3 on a die: P = 50%, odds = 1:1