🎲 Odds to Probability Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
Read as a:b. With "odds in favor", a is the chance for and b is against. Example: 1:3 means 1 chance for, 3 against.
Enter a value from 0 to 100. Example: 25 means a 25% chance.
Odds a:b imply a probability of a ÷ (a + b). Decimal odds = 1 ÷ probability.
Odds and probability describe the same chance in two different languages, and this calculator translates between them in both directions. Enter odds as a ratio like 1:3 to see the implied probability and the matching decimal odds, or type a probability percent to get the odds back. It is handy for sports, games, statistics homework, or any time someone quotes a chance one way when you think in the other.
What is the Odds Calculator?
Probability and odds both measure how likely something is, but they slice the same number differently. Probability is the share of all outcomes that count as a win: a value from 0 (never) to 1, or 0% to 100%. Odds compare the winning outcomes to the losing ones as a ratio a:b. Odds in favor of 1:3 mean 1 way to win for every 3 ways to lose, which is 1 winning outcome out of 4 total, so the probability is 1 ÷ (1 + 3) = 0.25, or 25%.
To go from odds a:b to probability you compute a ÷ (a + b). To go the other way, a probability p becomes odds in favor of p : (1 - p), which you can scale to whole numbers. A 25% chance is 0.25 : 0.75, and dividing both sides by 0.25 gives the tidy ratio 1:3. Decimal odds, common in betting, are simply 1 ÷ probability: a 25% chance has decimal odds of 4.0, meaning a winning stake returns four times itself (the original stake plus three times profit).
The most common confusion is mixing up odds in favor with odds against. Odds in favor of 1:3 are the same event as odds against of 3:1, just read from the other side. Gamblers usually quote odds against (the bigger number first for an unlikely event), while statisticians often state odds in favor. Always confirm which way a ratio is written before you trust it, because 3:1 and 1:3 describe very different chances.
When to use it
- Turning a sportsbook line like 3:1 against into a plain probability so you can judge whether a bet is fair value.
- Converting a forecast probability (such as a 70% chance of rain) into odds to explain it to someone who thinks in ratios.
- Checking statistics or epidemiology coursework where odds, odds ratios, and probabilities are used side by side.
- Comparing decimal odds across bookmakers by first reducing them all to a single implied probability percent.
How to use the Odds Calculator
- Choose a direction: "Odds to probability" or "Probability to odds".
- For odds, enter the two parts of the ratio a:b (for example 1 and 3 for 1:3 in favor).
- For probability, enter a percent from 0 to 100 (for example 25 for a 25% chance).
- Read off the implied probability, the odds in favor, and the decimal odds, which update as you type.
Formula & method
Worked examples
Convert odds of 1:3 in favor into a probability and decimal odds.
- Sum the parts: a + b = 1 + 3 = 4
- probability = a ÷ (a + b) = 1 ÷ 4 = 0.25
- as a percent: 0.25 x 100 = 25%
- decimal odds = 1 ÷ probability = 1 ÷ 0.25 = 4.0
Result: Probability 25%, odds 1:3 in favor, decimal odds 4.0
Convert a probability of 80% into odds in favor and decimal odds.
- as a fraction: p = 80 ÷ 100 = 0.8
- odds in favor = p : (1 - p) = 0.8 : 0.2
- scale by dividing both sides by 0.2: 4 : 1
- decimal odds = 1 ÷ p = 1 ÷ 0.8 = 1.25
Result: Odds 4:1 in favor, probability 80%, decimal odds 1.25
Common odds in favor, their probability, and decimal odds
| Odds (in favor) | Probability | Decimal odds |
|---|---|---|
| 1:1 | 50% | 2.0 |
| 1:3 | 25% | 4.0 |
| 1:4 | 20% | 5.0 |
| 2:1 | 66.67% | 1.5 |
| 3:1 | 75% | 1.333 |
| 4:1 | 80% | 1.25 |
| 9:1 | 90% | 1.111 |
Common mistakes to avoid
- Confusing odds in favor with odds against. Odds in favor of 1:3 are the same as odds against of 3:1. Bookmakers usually quote odds against, statisticians often quote odds in favor, so always confirm the direction before converting.
- Treating odds like a probability. Odds of 1:3 do not mean a one-third chance. The probability is a ÷ (a + b) = 1 ÷ 4 = 25%, not 1 ÷ 3. The ratio counts wins against losses, not wins against the total.
- Forgetting decimal odds include the stake. Decimal odds of 4.0 return four times the stake in total, which is three times the stake as profit plus the original stake back. They are not the same as fractional profit odds.
- Using a probability above 100% or below 0%. Probability must sit between 0% and 100%. A value outside that range is invalid, and at exactly 0% or 100% the odds become 0:1 or 1:0 with the decimal odds undefined or equal to 1.
Glossary
- Probability
- The chance of an outcome expressed from 0 to 1 (or 0% to 100%), equal to favorable outcomes divided by all outcomes.
- Odds in favor
- A ratio a:b comparing the number of winning outcomes (a) to losing outcomes (b).
- Odds against
- The same ratio written the other way, b:a, comparing losing outcomes to winning ones.
- Implied probability
- The probability that a given set of odds corresponds to, found with a ÷ (a + b).
- Decimal odds
- A betting format equal to 1 ÷ probability, showing the total return per unit staked including the stake.
Frequently asked questions
How do I convert odds to probability?
For odds a:b in favor, the probability is a ÷ (a + b). For example, 1:3 gives 1 ÷ (1 + 3) = 0.25, which is a 25% chance. This calculator does it automatically when you enter the two parts of the ratio.
How do I convert probability to odds?
A probability p becomes odds in favor of p : (1 - p). A 25% chance is 0.25 : 0.75, which scales to 1:3. Switch to the "Probability to odds" mode and enter your percent to see the reduced ratio.
What is the difference between odds and probability?
Probability compares favorable outcomes to all outcomes, while odds compare favorable outcomes to unfavorable ones. Odds of 1:3 mean 1 win for every 3 losses, which is a 25% probability, not 33%.
What are decimal odds?
Decimal odds equal 1 ÷ probability and show the total return per unit staked, including your stake. A 25% chance is 4.0 decimal odds: a winning $1 stake returns $4 in total ($3 profit plus the $1 back).
Are 3:1 and 1:3 the same thing?
No. 1:3 in favor is a 25% chance, while 3:1 in favor is a 75% chance. They are only equal if one is read as odds in favor and the other as odds against the same event, so always confirm the direction.
What odds mean a 50% chance?
Even odds of 1:1 mean a 50% probability: one way to win for every one way to lose. The decimal odds for a 50% chance are 2.0, returning double the stake on a win.