Odds & Probability Converter
Print PageAn Odds Calculator (also known as an Odds to Probability Converter, Betting Odds & Payout Utility, Odds Ratio Analyzer, or Fractional-Decimal-American Odds Converter) converts ratio odds in favor (a : b) and odds against (b : a) into exact mathematical probability percentages (P). It also converts between American Moneyline (+200 / -150), Decimal (3.00 / 1.67), and Fractional (2/1 / 2/3) formats while calculating net profit and total return for any custom wager amount.
A fundamental mistake in statistics is confusing Odds with Probability. Probability measures the ratio of favorable outcomes to total outcomes (a ÷ [a + b]), whereas Odds measure the ratio of favorable outcomes to unfavorable outcomes (a : b). For example, odds against of 4 : 1 mean that for every 5 attempts, you expect to lose 4 times and win 1 time (an exact 20.0% probability).
Our free online Odds Calculator provides instant conversions across all standard odds formats, probabilities, and wager payouts:
- Odds in Favor (a : b) to Probability (P):
P = a ÷ (a + b)(e.g. 3 : 2 in favor &implies; 3/5 = 60.00%). - Odds Against (b : a) to Probability (P):
P = a ÷ (a + b)(e.g. 4 : 1 against &implies; 1/5 = 20.00%). - Probability (P) to Odds in Favor:
Odds = P ÷ (1 - P)(e.g. 75% &implies; 0.75/0.25 = 3 : 1 in favor). - Probability (P) to Odds Against:
Odds = (1 - P) ÷ P(e.g. 20% &implies; 0.80/0.20 = 4 : 1 against). - Positive American Odds (+L e.g. +200):
Net Profit = Wager · (L ÷ 100)(e.g. $100 × 200/100 = $200 profit). - Negative American Odds (-L e.g. -150):
Net Profit = Wager · (100 ÷ |L|)(e.g. $150 × 100/150 = $100 profit).
Master Odds Conversion & Payout Reference Table
The table below displays the exact mathematical conversions across Odds Ratio Against, Probability %, American Moneyline, Decimal, Fractional, and Net Profit on a $100 Wager:
| Odds Ratio (Against) | Exact Win Probability P | American Moneyline | Decimal Odds | Fractional Odds | Net Profit ($100 Wager) | Total Payout ($100 Wager) |
|---|---|---|---|---|---|---|
| 5 : 1 Against | 16.67% | +500 | 6.00 | 5/1 | $500.00 | $600.00 |
| 4 : 1 Against | 20.00% | +400 | 5.00 | 4/1 | $400.00 | $500.00 |
| 3 : 1 Against | 25.00% | +300 | 4.00 | 3/1 | $300.00 | $400.00 |
| 2 : 1 Against | 33.33% | +200 | 3.00 | 2/1 | $200.00 | $300.00 |
| 3 : 2 Against | 40.00% | +150 | 2.50 | 3/2 | $150.00 | $250.00 |
| 1 : 1 (EVEN ODDS) | 50.00% | +100 (EVEN) | 2.00 | 1/1 | $100.00 | $200.00 |
| 1 : 1.1 (Standard Spread) | 52.38% | -110 | 1.909 | 10/11 | $90.91 | $190.91 |
| 1 : 2 (Favor 2:1) | 66.67% | -200 | 1.50 | 1/2 | $50.00 | $150.00 |
| 1 : 5 (Favor 5:1) | 83.33% | -500 | 1.20 | 1/5 | $20.00 | $120.00 |
Step-by-Step Horse Racing 5:1 Odds Payout & Probability Example
To calculate the win probability, net profit, and total payout for a $50 horse racing bet placed at 5 : 1 odds against:
Step 1 (Identify Odds Ratio): Odds Against = 5 : 1 &implies; a = 1 favorable outcome, b = 5 unfavorable outcomes
Step 2 (Calculate Win Probability P): P = a ÷ (a + b) = 1 ÷ (1 + 5) = 1 ÷ 6 = 0.166667 ≈ 16.67%
Step 3 (Calculate Net Profit): Net Profit = Wager × (Odds Ratio) = $50 × 5 = $250.00
Step 4 (Calculate Total Payout): Total Payout = Wager + Net Profit = $50 + $250 = $300.00
Thus, a winning $50 bet at 5:1 odds against returns a $250.00 net profit ($300.00 total payout) and represents a 16.67% probability of occurring.
Key Differences: Odds Ratio vs. Probability Percentage
Below is a comparative reference chart clarifying the fundamental differences between Odds and Probability:
| Measurement Feature | Probability (P) | Odds Ratio (a : b) |
|---|---|---|
| Denominator Reference | Total possible outcomes (Favorable + Unfavorable) | Unfavorable outcomes only |
| Mathematical Range | Bounded between 0.0 (0%) and 1.0 (100%) | Unbounded from 0 to infinity (∞) |
| Primary Application Field | Academic statistics, machine learning, physics | Sports betting, horse racing, medical odds ratios |
History & Mathematics: 16th Century Gerolamo Cardano to 18th Century British Turf Clubs
16th Century Gerolamo Cardano & Ratio Odds
In 1564, Italian polymath Gerolamo Cardano wrote Liber de Ludo Aleae (“Book on Games of Chance”), introducing the mathematical concept of Odds Ratio (a : b) as the ratio of favorable to unfavorable chances when rolling dice.
18th Century British Horse Racing & Fractional Payouts
In 18th-century England, bookmakers at British horse racing tracks developed fractional odds against (e.g. 5/1) to rapidly compute payout returns relative to bettors’ stakes.
Popular direct tools:
Frequently Asked Questions (FAQ)
What is the difference between Odds and Probability?
Probability measures favorable outcomes divided by total outcomes (e.g. 1 ÷ 5 = 20%). Odds measure favorable outcomes divided by unfavorable outcomes (e.g. 1 : 4 in favor or 4 : 1 against).
How do you convert 4 to 1 odds to probability?
For 4:1 odds against: P = 1 ÷ (4 + 1) = 1 ÷ 5 = 20.0% probability.
How much does a $50 bet at 5:1 odds pay?
A $50 bet at 5:1 odds against pays $250.00 in net profit, returning a $300.00 total payout.