Odds Converter & Payout Calculator
In this Odds Calculator, enter any odds value (American, Decimal, Fractional, or Probability) to convert it to all other formats and calculate potential returns based on your stake.
Guide to Betting Odds
Types of Odds Explained
Odds represent the ratio between the amounts staked by parties to a wager or bet. Here is how to understand the three main types:
- American Odds (+/-): Positive figures indicate how much profit you win on a $100 stake. Negative figures indicate how much you must stake to win 100 profit.
- Decimal Odds: The most common format globally. It represents the total return (Stake + Profit) for every $1 wagered. Formula:
Total Payout = Stake × Decimal Odds. - Fractional Odds: Common in the UK/Ireland. The numerator is the profit, and the denominator is the stake required to earn that profit.
Quick Formulas
Understanding Implied Probability
Implied probability is a percentage that shows the likelihood of an outcome as suggested by the odds. It helps bettors find “value” in a market.
- Decimal to Probability:
(1 / Decimal) × 100 - Negative American to Probability:
Negative Odds / (Negative Odds + 100) - Positive American to Probability:
100 / (Positive Odds + 100)
* Note: This calculator assumes a fair market. Real bookmaker odds include a “vig” or margin which makes the total probability exceed 100%.
The Mathematics of Chance: Understanding Betting Odds
In probability theory and finance, “odds” are simply a way of expressing the likelihood of an event occurring relative to the likelihood of it not occurring. However, in the world of sports betting and prediction markets, odds serve a dual purpose: they represent the implied probability of an outcome and the price a bookmaker is willing to pay for that risk.
This calculator acts as a universal translator. Different regions of the world use different mathematical dialects to express the same risk/reward ratio. Whether you are looking at a Moneyline in Las Vegas or a Fractional line in London, this tool unifies them into a single, comparable set of data, allowing you to calculate your potential payout and the implied “break-even” percentage.
The Three Dialects of Risk
To use this calculator effectively, you must understand the input formats it accepts.
1. American Odds (Moneyline)
Used primarily in the US.
- Positive (+): Indicates the profit on a $100 bet.
- +150: You bet $100 to win $150. (Underdog).
- Negative (-): Indicates how much you must bet to win $100.
- -110: You bet $110 to win $100. (Favorite).
- Base: Always centered around the number 100.
2. Decimal Odds (European)
Used in Europe, Canada, and Australia. This is the most mathematically straightforward format.
- Definition: It represents the Total Payout (Stake + Profit) for every $1 wagered.
- 2.50: For every $1 you bet, you get back $2.50 total ($1.50 profit).
- Formula: $\text{Total Payout} = \text{Stake} \times \text{Decimal Odds}$.
3. Fractional Odds (British)
Used in the UK and Ireland.
- Format: Profit / Stake.
- 5/2: For every $2 you bet, you win $5 in profit.
- 1/1: “Evens.” You win exactly what you staked.
The Hidden Metric: Implied Probability
The most critical output of this calculator is the Implied Probability. This percentage answers the question: “How often does this event need to happen for me to break even?”
- The Math: $\text{Probability} = (1 / \text{Decimal Odds}) \times 100$.
- Example:
- Odds: +100 (American) / 2.00 (Decimal).
- Probability: $50\%$.
- Analysis: If you believe the team has a $55\%$ chance of winning, and the odds imply only $50\%$, you have found “Value.” If you believe they have a $45\%$ chance, it is a bad bet.
Calculating the Payout
The calculator computes two financial outcomes based on your Stake (wager amount):
- Total Payout: The total amount returned to your account if you win.
$$\text{Total Payout} = \text{Stake} + \text{Profit}$$ - Net Profit: The actual earnings from the wager.
$$\text{Net Profit} = \text{Total Payout} – \text{Stake}$$
Practical Examples
Scenario A: The Longshot
- Input: American Odds
+300. Stake$50. - Calculator Output:
- Decimal:
4.00 - Probability:
25% - Net Profit:
$150 - Total Payout:
$200
- Decimal:
Scenario B: The Sure Thing
- Input: Decimal Odds
1.20. Stake$1,000. - Calculator Output:
- American:
-500 - Probability:
83.3% - Net Profit:
$200 - Total Payout:
$1,200
- American:
Frequently Asked Questions (FAQ)
Q: Why do the probabilities sum to more than 100%?
A: In a real betting market, if you calculate the implied probability of every possible outcome (e.g., Team A wins + Team B wins), the sum will often be 104% to 110%. This extra percentage is the Vig (or Vigorish/Juice)—the bookmaker’s profit margin. This calculator shows the raw probability for the specific odds you entered, without accounting for the bookmaker’s margin.
Q: What does “Push” mean?
A: A “Push” is a tie where no money is lost or won. The calculator assumes a binary Win/Loss outcome.
Q: Can I enter probability to find the odds?
A: Yes. If you want to know what the odds should be for a coin flip (50%), enter 50 in the Implied Probability field. The calculator will tell you the “Fair Odds” are +100 / 2.00 / 1/1.
Scientific Reference and Citation
For the mathematical foundations of probability in gaming and economics:
Source: Thorpe, E. O. (1966). “Beat the Dealer: A Winning Strategy for the Game of Twenty-One.” Vintage Books.
Relevance: While focused on Blackjack, Edward Thorp’s work is the foundational text for quantitative gambling. It established the principles of the Kelly Criterion and the mathematical relationship between edge (probability vs. odds) and optimal stake sizing.