Multiplication (e.g., EUR/USD × USD/JPY = EUR/JPY)
Division: Quote Common (e.g., EUR/USD ÷ GBP/USD = EUR/GBP)
Division: Base Common (e.g., USD/JPY ÷ USD/CHF = CHF/JPY)
Formula: Rate 1 × Rate 2
Please enter valid positive exchange rates.
Calculated Cross Rate
0.0000
function updateFxHints() {
var method = document.getElementById('fxCalcMethod').value;
var hint = document.getElementById('methodHint');
if (method === 'multiply') {
hint.innerHTML = "Use when the Common Currency is Quote in Pair 1 and Base in Pair 2 (or vice versa). Formula: Rate 1 × Rate 2";
} else if (method === 'divide_quote') {
hint.innerHTML = "Use when the Common Currency is the Quote (second) currency in BOTH pairs. Formula: Rate 1 ÷ Rate 2";
} else if (method === 'divide_base') {
hint.innerHTML = "Use when the Common Currency is the Base (first) currency in BOTH pairs. Formula: Rate 2 ÷ Rate 1 (to find Pair 2's Quote / Pair 1's Quote)";
}
}
function calculateCrossRate() {
// Get Inputs
var rate1Input = document.getElementById('fxRate1');
var rate2Input = document.getElementById('fxRate2');
var method = document.getElementById('fxCalcMethod').value;
var errorBox = document.getElementById('fxErrorMessage');
var resultBox = document.getElementById('fxResultBox');
var resultValue = document.getElementById('fxResultValue');
var r1 = parseFloat(rate1Input.value);
var r2 = parseFloat(rate2Input.value);
// Validation
if (isNaN(r1) || isNaN(r2) || r1 <= 0 || r2 100 (like JPY pairs), usually 2 decimals. If 100) {
displayString = finalRate.toFixed(3);
} else {
displayString = finalRate.toFixed(5);
}
resultValue.innerHTML = displayString;
resultBox.style.display = 'block';
}
Understanding Cross Rate Calculation
In the foreign exchange market, a Cross Rate is an exchange rate between two currencies that is calculated by reference to a third currency, typically the US Dollar (USD). While major currency pairs (like EUR/USD or USD/JPY) are traded directly, pairs that do not involve the US Dollar (like EUR/GBP or AUD/JPY) are known as cross currency pairs.
Traders and financial analysts calculate cross rates to determine arbitrage opportunities, set pricing for international transactions, or analyze the relative strength of two currencies without the influence of the USD. This calculator simplifies the mathematics involved in deriving these rates.
How the Calculation Works
There are three primary methods to calculate a cross rate depending on how the two currencies are quoted against the common bridge currency (usually USD).
1. The Multiplication Method
This method is used when the common currency is the Quote currency in one pair and the Base currency in the other. In simpler terms, the USD "cancels out" diagonally.
Example (EUR/JPY):
You want to find the rate for EUR/JPY.
1. Pair 1 (EUR/USD): 1.0850
2. Pair 2 (USD/JPY): 145.20 Formula: 1.0850 × 145.20 = 157.542 Result: 1 EUR = 157.542 JPY
2. The Division Method (Common Quote)
This is used when the common currency (USD) is the Quote currency in both pairs. To find the cross rate, you divide the Base pair rate by the Terms pair rate.
Example (EUR/GBP):
You want to find the rate for EUR/GBP.
1. Pair 1 (EUR/USD): 1.0900
2. Pair 2 (GBP/USD): 1.2500 Formula: 1.0900 ÷ 1.2500 = 0.8720 Result: 1 EUR = 0.8720 GBP
3. The Division Method (Common Base)
This scenario arises when the common currency (USD) is the Base currency in both pairs. To find the cross rate of the two quote currencies, you divide the rate of the currency you want as the numerator (Terms) by the rate of the currency you want as the denominator (Base).
Example (CHF/JPY):
You want to find the rate for CHF/JPY (How many Yen buy one Swiss Franc).
1. Pair 1 (USD/JPY): 145.00
2. Pair 2 (USD/CHF): 0.8900 Formula: 145.00 ÷ 0.8900 = 162.92 Result: 1 CHF = 162.92 JPY
Why Accurate Cross Rates Matter
For international businesses, understanding cross rates is vital for pricing goods correctly in local markets. If a European company imports goods from Japan, they need the EUR/JPY rate to calculate costs, even if the actual payment is settled via USD. Small discrepancies in the calculation method or rounding errors can lead to significant financial variance in large-volume trading.
Use the calculator above to quickly determine the theoretical market price for any cross pair based on the major pairs available to you.