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Build the converter around decimal odds: parse the selected format, convert it to decimal, then calculate the other formats, implied probability, and—if entered—total payout and profit. This keeps the math consistent while making the key distinction clear: decimal odds include the returned stake in a winning payout; American and fractional odds describe profit relative to stake.
What the three odds formats mean
American, decimal, and fractional odds express the same price using different conventions. Decimal odds are a direct multiplier for the total payout on a win. Fractional odds state profit relative to stake. American odds use a positive or negative value around even money: positive odds state the profit on a $100 stake, while negative odds state how much must be staked to profit $100.
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| Format | Example | What it expresses | Common convention |
|---|---|---|---|
| American | +150 or −125 | Positive: profit per $100 staked. Negative: stake needed to profit $100. | Common in US-facing examples; regional usage is not universal. |
| Decimal | 2.50 | Total payout per unit staked, including the original stake. | Common in many European examples. |
| Fractional | 3/2 | Profit relative to stake: 3 units of profit for every 2 staked. | Common in UK contexts and horse-racing coverage. |
These regional labels are general conventions, not rules. Decimal odds are especially convenient for comparing prices because multiplying the stake by the decimal price gives the total return on a win.
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Use decimal odds, represented below by D, as the intermediate value. For American odds, A is the signed number; for fractional odds, A/B is the profit-to-stake ratio.
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American odds to decimal
- For positive American odds,
D = 1 + A/100. For example,+150becomes2.50. - For negative American odds,
D = 1 + 100/|A|. For example,−125becomes1.80.
Fractional odds to decimal
For fractional odds A/B, calculate D = 1 + A/B. Thus 3/2 becomes 2.50, and 4/5 becomes 1.80. The fraction represents profit, so the additional 1 accounts for the stake returned in decimal odds.
Decimal odds to American
- At even money or above, when
D ≥ 2, calculateA = 100 × (D − 1). For2.50, this gives+150. - Below even money, when
1 < D < 2, calculateA = −100/(D − 1). For1.80, this gives approximately−125.
Decimal odds of 2.00 are even money. Values above 2.00 produce positive American odds; values between 1 and 2 produce negative American odds.
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Decimal odds to fractional
Subtract 1 from decimal odds to get the profit-to-stake ratio, then express that ratio as a fraction and reduce it if desired. For example, 2.50 − 1 = 1.50, or 3/2. If the decimal value has been rounded for display, the fractional equivalent may only be approximate.
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Implied probability, payout, and profit
Calculate odds-implied probability
Convert the price to a raw implied probability using the matching formula:
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- Decimal odds:
p = 1/D. - Positive American odds:
p = 100/(A + 100)percent. - Negative American odds:
p = |A|/(|A| + 100)percent. - Fractional odds
A/B:p = B/(A + B).
For a browser display, multiply a decimal probability by 100 to show a percentage. Label this result “implied probability” or “odds-implied probability,” not the true chance of an outcome. Bookmaker prices can include a margin, so the displayed probability may not be a fair estimate. The World Lottery Association’s 2024 Code of Practice, section L.6, “Sports, esports, and horse race betting,” explains that “the odds-on display does not represent the true chances that the event will, or will not occur, but are the amount that the company will pay out on a winning bet, together with the required stake.”
Keep payout separate from profit
For stake S at decimal odds D, total payout on a win is S × D; profit is S × (D − 1). A $10 stake at 2.50 returns $25 total, of which $15 is profit. Another example: a $20 stake at American −125 is equivalent to 1.80 decimal and 4/5 fractional, producing a $36 total payout and $16 profit on a win.
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Implement the converter in JavaScript
The following single-file example runs in a browser without a library. It uses strict input checks, converts through decimal odds, and updates the result as the form is submitted. The accepted format is an implementation choice: American input may include a leading plus or minus sign, decimal input must be greater than 1, and fractional input uses a numerator and denominator separated by a slash.
<form id="odds-form">
<label>
Input format
<select id="format">
<option value="american">American</option>
<option value="decimal">Decimal</option>
<option value="fractional">Fractional</option>
</select>
</label>
<label>
Odds
<input id="odds" type="text" inputmode="decimal" placeholder="+150, 2.50, or 3/2">
</label>
<label>
Stake (optional)
<input id="stake" type="text" inputmode="decimal" placeholder="10.00">
</label>
<button type="submit">Convert</button>
</form>
<p id="error" role="alert"></p>
<section id="result" aria-live="polite"></section>
<script>
function parseOdds(format, raw) {
const text = raw.trim();
if (!text) throw new Error("Enter odds to convert.");
if (format === "american") {
if (!/^[+-]?d+(?:.d+)?$/.test(text)) {
throw new Error("Enter American odds as a number, such as +150 or -125.");
}
const american = Number(text);
if (!Number.isFinite(american) || american === 0) {
throw new Error("American odds must be a nonzero number.");
}
return american > 0
? 1 + american / 100
: 1 + 100 / Math.abs(american);
}
if (format === "decimal") {
if (!/^d+(?:.d+)?$/.test(text)) {
throw new Error("Enter decimal odds as a number greater than 1.");
}
const decimal = Number(text);
if (!Number.isFinite(decimal) || decimal <= 1) {
throw new Error("Decimal odds must be greater than 1.");
}
return decimal;
}
if (format === "fractional") {
const match = /^(d+(?:.d+)?)/(d+(?:.d+)?)$/.exec(text);
if (!match) throw new Error("Enter fractional odds as numerator/denominator, such as 3/2.");
const numerator = Number(match[1]);
const denominator = Number(match[2]);
if (!Number.isFinite(numerator) || !Number.isFinite(denominator) || denominator <= 0) {
throw new Error("Use a nonnegative numerator and a positive denominator.");
}
const decimal = 1 + numerator / denominator;
if (!Number.isFinite(decimal) || decimal <= 1) {
throw new Error("These odds must produce a decimal value greater than 1.");
}
return decimal;
}
throw new Error("Choose a supported odds format.");
}
function formatAmerican(decimal) {
if (decimal >= 2) return `+${(100 * (decimal - 1)).toFixed(0)}`;
return `-${(100 / (decimal - 1)).toFixed(0)}`;
}
function formatFractional(decimal) {
const profit = decimal - 1;
const denominator = 1000;
const numerator = Math.round(profit * denominator);
function gcd(a, b) {
return b === 0 ? a : gcd(b, a % b);
}
const divisor = gcd(Math.abs(numerator), denominator);
return `${numerator / divisor}/${denominator / divisor}`;
}
const form = document.querySelector("#odds-form");
const error = document.querySelector("#error");
const result = document.querySelector("#result");
form.addEventListener("submit", (event) => {
event.preventDefault();
error.textContent = "";
result.replaceChildren();
try {
const format = document.querySelector("#format").value;
const decimal = parseOdds(format, document.querySelector("#odds").value);
const impliedProbability = 100 / decimal;
const values = [
["Decimal", decimal.toFixed(2)],
["American", formatAmerican(decimal)],
["Fractional (approx.)", formatFractional(decimal)],
["Odds-implied probability", `${impliedProbability.toFixed(2)}%`]
];
const stakeText = document.querySelector("#stake").value.trim();
if (stakeText) {
if (!/^d+(?:.d+)?$/.test(stakeText)) {
throw new Error("Enter a stake as a nonnegative amount, such as 10 or 10.50.");
}
const stake = Number(stakeText);
if (!Number.isFinite(stake)) throw new Error("Enter a finite stake amount.");
values.push(["Total payout on a win", (stake * decimal).toFixed(2)]);
values.push(["Profit on a win", (stake * (decimal - 1)).toFixed(2)]);
}
const list = document.createElement("dl");
for (const [label, value] of values) {
const term = document.createElement("dt");
const description = document.createElement("dd");
term.textContent = label;
description.textContent = value;
list.append(term, description);
}
result.append(list);
} catch (exception) {
error.textContent = exception.message;
}
});
</script>Why the implementation validates and rounds
Reject malformed or unusable values
Reading the field as text and validating the whole string prevents permissive parsing from accepting a valid-looking prefix while ignoring trailing characters. The code rejects zero American odds, decimal odds at or below 1, malformed fractions, and fractions with a zero denominator. Those checks prevent invalid values, division by zero, and NaN or infinity from flowing into the display. The stake field is optional and, when supplied, accepts a nonnegative numeric amount.
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Choose display precision deliberately
The example rounds decimal odds to two places, American odds to whole numbers, and the fractional display to a ratio based on a denominator of 1000 before reduction. These are display choices, not universal standards; rounding means a converted value may not reproduce the original exactly. The fractional label marks the result approximate for that reason.
For production use, consider a more sophisticated fraction-reduction strategy if you need simple conventional fractions rather than a bounded approximation. Also consider currency formatting if the utility supports specific currencies; the example treats stake and payout as plain numeric amounts and does not assume a currency.
What the converter can and cannot tell you
The tool can translate odds formats and calculate arithmetic consequences of a stated price and stake. Its implied probability is a transformation of that price, not an independent assessment of an event. A bookmaker’s margin may be embedded in quoted odds, so a converter should not present the result as a prediction or “true” chance.
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