Common Currency is Quote in BOTH (e.g., EUR/USD & GBP/USD)
Common Currency is Quote in First, Base in Second (e.g., EUR/USD & USD/JPY)
Common Currency is Base in BOTH (e.g., USD/JPY & USD/CHF)
Select how your known pairs are structured relative to the shared currency (usually USD).
Enter the current market rate for the first pair.
Enter the current market rate for the second pair.
Calculated Cross Rate
0.0000
Inverse Rate:0.0000
Understanding Cross Exchange Rates
A Cross Exchange Rate (or simply "cross rate") is the currency exchange rate between two currencies, both of which are not the official currency of the country in which the exchange quote is given. In most major forex markets, the US Dollar (USD) is the primary reserve currency. When a transaction does not involve the USD, the rate is calculated through a "cross" calculation using USD as the common bridge.
For example, if a trader wants to exchange Euros (EUR) for Japanese Yen (JPY), they typically use the EUR/USD rate and the USD/JPY rate to determine the fair market price for EUR/JPY. This calculator automates that mathematical process based on the position of the common currency.
How to Calculate Cross Rates
The formula for calculating a cross rate depends entirely on how the two currencies are quoted against the common currency (usually USD). There are three main scenarios:
1. Both Currencies are Quoted Against the Common Currency (Indirect Quotes)
This scenario occurs when the common currency is the "Quote" currency (the second currency in the pair) for both rates. This is common for major pairs like EUR/USD and GBP/USD.
Goal: Find EUR/GBP.
Knowns: EUR/USD (Rate A) and GBP/USD (Rate B).
Formula: Rate A ÷ Rate B.
Example: If EUR/USD = 1.20 and GBP/USD = 1.40, then EUR/GBP = 1.20 ÷ 1.40 = 0.8571.
2. The Common Currency is the Base in Both (Direct Quotes)
This scenario occurs when the common currency is the "Base" currency (the first currency in the pair). This is typical for pairs like USD/JPY and USD/CHF.
Goal: Find JPY/CHF.
Knowns: USD/JPY (Rate A) and USD/CHF (Rate B).
Formula: Rate B ÷ Rate A.
Example: If USD/JPY = 110.00 and USD/CHF = 0.9200, then JPY/CHF = 0.9200 ÷ 110.00 = 0.00836. (Note: Usually CHF/JPY is the preferred quote, which would be Rate A ÷ Rate B).
3. One is Base, One is Quote (Multiplication)
This is the most straightforward calculation, used when the common currency links the two pairs like a chain (e.g., A/USD and USD/B).
Goal: Find EUR/JPY.
Knowns: EUR/USD (Rate A) and USD/JPY (Rate B).
Formula: Rate A × Rate B.
Example: If EUR/USD = 1.15 and USD/JPY = 105.00, then EUR/JPY = 1.15 × 105.00 = 120.75.
Why Use a Cross Rate Calculator?
While major pairs are quoted instantly by brokers, exotic crosses or specific arbitrage opportunities often require manual calculation. Traders use cross rate calculations to:
Identify arbitrage opportunities where the calculated cross rate differs from the market quote.
Determine exchange rates for currencies that do not have a direct trading pair.
Hedge portfolio risk across multiple currency exposures.
function updateLabels() {
var mode = document.getElementById('calcMode').value;
var label1 = document.getElementById('labelRate1');
var label2 = document.getElementById('labelRate2');
var help1 = document.getElementById('helpRate1');
var help2 = document.getElementById('helpRate2');
if (mode === 'divide1') {
// Common is Quote in BOTH
label1.innerHTML = "Base Pair Rate (e.g., EUR/USD)";
label2.innerHTML = "Target Pair Rate (e.g., GBP/USD)";
help1.innerHTML = "Enter the rate where Common Currency is the second currency (Quote).";
help2.innerHTML = "Enter the rate where Common Currency is the second currency (Quote).";
} else if (mode === 'multiply') {
// Chain
label1.innerHTML = "First Pair Rate (e.g., EUR/USD)";
label2.innerHTML = "Second Pair Rate (e.g., USD/JPY)";
help1.innerHTML = "Enter the rate where Common Currency is the Quote (2nd).";
help2.innerHTML = "Enter the rate where Common Currency is the Base (1st).";
} else if (mode === 'divide2') {
// Common is Base in BOTH
label1.innerHTML = "Base Pair Rate (e.g., USD/JPY)";
label2.innerHTML = "Target Pair Rate (e.g., USD/CHF)";
help1.innerHTML = "Enter the rate where Common Currency is the first currency (Base).";
help2.innerHTML = "Enter the rate where Common Currency is the first currency (Base).";
}
}
function calculateCrossRate() {
// 1. Get Elements
var rate1Input = document.getElementById('rate1');
var rate2Input = document.getElementById('rate2');
var mode = document.getElementById('calcMode').value;
var errorDiv = document.getElementById('errorDisplay');
var resultBox = document.getElementById('resultBox');
var finalResultDiv = document.getElementById('finalResult');
var inverseResultDiv = document.getElementById('inverseResult');
var formulaDiv = document.getElementById('formulaUsed');
// 2. Parse Values
var r1 = parseFloat(rate1Input.value);
var r2 = parseFloat(rate2Input.value);
// 3. Reset UI
errorDiv.style.display = 'none';
resultBox.style.display = 'none';
// 4. Validation
if (isNaN(r1) || isNaN(r2)) {
errorDiv.innerHTML = "Please enter valid numerical exchange rates.";
errorDiv.style.display = 'block';
return;
}
if (r1 <= 0 || r2 Want EUR/GBP
// Formula: r1 / r2
result = r1 / r2;
formulaText = "Formula: Rate 1 ÷ Rate 2";
} else if (mode === 'multiply') {
// Scenario: EUR/USD (r1) and USD/JPY (r2) -> Want EUR/JPY
// Formula: r1 * r2
result = r1 * r2;
formulaText = "Formula: Rate 1 × Rate 2";
} else if (mode === 'divide2') {
// Scenario: USD/JPY (r1) and USD/CHF (r2) -> Want JPY/CHF (Cross)
// Wait, standard is usually Target/Base.
// If we want Base/Target (e.g. JPY/CHF), it's (USD/CHF) / (USD/JPY) = r2 / r1
result = r2 / r1;
formulaText = "Formula: Rate 2 ÷ Rate 1";
}
// 6. Display Result
// Formatting to 5 decimal places for precision
finalResultDiv.innerHTML = result.toFixed(5);
// Calculate Inverse
var inverse = 1 / result;
inverseResultDiv.innerHTML = inverse.toFixed(5);
formulaDiv.innerHTML = formulaText;
resultBox.style.display = 'block';
}
// Initialize labels on load
updateLabels();