Odds Calculator
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About Odds
'The odds are 3 to 1' and 'a 75% chance' say the same thing — yet mixing the two frames is a reliable source of confusion in games, medicine (odds ratios), and betting alike. The distinction is one denominator: odds exclude the successes from the comparison base; probability includes them.
Convert either direction, and get the decimal and American betting equivalents alongside. Dice, cards, sports lines, and statistics homework all reduce to the same three-way translation this tool performs.
Percent problems more generally live in the Percentage Calculator
The Conversions
One division each way, two betting dialects on top:
Probability = A ÷ (A + B) (odds A : B in favor) Odds = P : (100 − P) Decimal = 100 ÷ P% American = −(P/(100−P))×100 if P ≥ 50, else +((100−P)/P)×100
Worked examples: 3:1 in favor = 75%, decimal 1.33, American −300. The reverse: 25% = 1:3 in favor, decimal 4.00, +300. And 60% = 3:2 — the halfway-common case where odds stop being round numbers.
Odds ↔ Probability ↔ Betting Formats
The translation table — every row from this calculator's formulas:
| Odds (for) | Probability | Decimal | American |
|---|---|---|---|
| 1 : 9 | 10% | 10.00 | +900 |
| 1 : 4 | 20% | 5.00 | +400 |
| 1 : 2 | 33.3% | 3.00 | +200 |
| 1 : 1 (evens) | 50% | 2.00 | ±100 |
| 3 : 2 | 60% | 1.67 | −150 |
| 3 : 1 | 75% | 1.33 | −300 |
| 9 : 1 | 90% | 1.11 | −900 |
Evens (1:1, 50%) is the pivot: American odds flip sign there, and decimal odds cross 2.00 — every format agrees where the coin lands.
Reading Betting Lines Honestly
Bookmaker odds aren't pure probability — they embed the vig (margin). Convert every outcome's line to implied probability and the sum runs 104–110%: the excess is the house's cut, which is why 'the odds say 55%' really means 'the market plus margin says 55%'. Sharp bettors deflate lines proportionally before comparing to their own estimates.
Statistics' version matters in health news: an odds RATIO of 2.0 between groups is not 'twice as likely' when the outcome is common — odds exaggerate relative to probability as events get likelier (75% vs 25% is 3:1 vs 1:3, a nine-fold odds ratio for a three-fold probability ratio). When a headline says 'doubles the odds', check the base rates before alarm.
Frequently Asked Questions
How do I convert odds to probability?
For odds A:B in favor, probability = A ÷ (A+B): 3:1 gives 3⁄4 = 75%. Odds AGAINST swap the roles — 3:1 against means 25%. The 'in favor / against' direction is half of every odds confusion.
What do +200 or −150 mean in betting?
American odds: +200 pays $200 profit per $100 staked (implied 33.3%); −150 requires $150 staked per $100 profit (implied 60%). Minus marks favorites, plus marks underdogs; the calculator converts both directions.
What are decimal odds?
The total-return multiplier per unit staked: decimal 4.00 returns $4 per $1 (including the stake) — implied probability 1 ÷ 4 = 25%. Europe's default format, and the cleanest for math: implied % is just 100 ÷ decimal.
What's the difference between odds and probability?
Denominators: odds = successes : failures; probability = successes ÷ all outcomes. A die shows 'six' at 1:5 odds but 1⁄6 ≈ 16.7% probability. Same chance, two dialects — this tool is the interpreter.
Why do bookmaker probabilities sum over 100%?
The margin (vig): a fair coin priced at −110 both sides implies 52.4% + 52.4% = 104.8% — the extra 4.8% is the book's edge. Implied probability from any line includes it; true probability is always a bit lower for every outcome.
What are the odds of common dice and card events?
A specific die face: 1:5 (16.7%). Two dice totaling 7: 1:5 (16.7%, the commonest total). Drawing an ace: 1:12 (7.7%). A specific poker hand pre-flop, pocket aces: 1:220 (0.45%). Enter any of them above to see all four formats.
Methodology. This calculator uses standard, peer-reviewed mathematical formulas. It is reviewed and maintained by the Vast Calculators editorial team.
Last updated · July 11, 2026
Results are estimates for general use; verify critical figures independently.