Calculate the exchange rate between two currencies using a common bridge currency.
Step 1: Define Your Target Pair (A / B)
Step 2: Enter Known Rates vs Common Bridge (e.g., USD)
Quote is Base (e.g., Bridge/Base)
Quote is Bridge (e.g., Base/Bridge)
Is the rate [Bridge/A] or [A/Bridge]?
Quote is Quote (e.g., Bridge/Quote)
Quote is Bridge (e.g., Quote/Bridge)
Is the rate [Bridge/B] or [B/Bridge]?
Calculated Cross Rate
0.0000
function calculateCrossRate() {
// Get Inputs
var baseCode = document.getElementById('currencyBase').value || 'Base';
var quoteCode = document.getElementById('currencyQuote').value || 'Quote';
var rate1 = parseFloat(document.getElementById('rate1').value);
var rate2 = parseFloat(document.getElementById('rate2').value);
var type1 = document.getElementById('pairType1').value;
var type2 = document.getElementById('pairType2').value;
var resultBox = document.getElementById('resultBox');
var resultDisplay = document.getElementById('resultDisplay');
var resultExplanation = document.getElementById('resultExplanation');
// Validation
if (isNaN(rate1) || isNaN(rate2) || rate1 <= 0 || rate2 <= 0) {
alert("Please enter valid positive numbers for both exchange rates.");
resultBox.style.display = "none";
return;
}
// Logic: Calculate everything relative to the Bridge currency
// We want the price of Base (A) in terms of Quote (B).
// Formula: Value of A in Bridge / Value of B in Bridge
var valueOfBaseInBridge = 0;
var valueOfQuoteInBridge = 0;
// Determine Value of 1 Unit of Base Currency in terms of Bridge Currency
if (type1 === 'bridge_per_base') {
// Input is A/Bridge (e.g. EUR/USD = 1.10). 1 EUR = 1.10 USD.
valueOfBaseInBridge = rate1;
} else {
// Input is Bridge/A (e.g. USD/JPY = 110). 1 JPY = 1/110 USD.
valueOfBaseInBridge = 1 / rate1;
}
// Determine Value of 1 Unit of Quote Currency in terms of Bridge Currency
if (type2 === 'bridge_per_quote') {
// Input is B/Bridge (e.g. GBP/USD = 1.30). 1 GBP = 1.30 USD.
valueOfQuoteInBridge = rate2;
} else {
// Input is Bridge/B (e.g. USD/CHF = 0.90). 1 CHF = 0.90 USD.
valueOfQuoteInBridge = 1 / rate2;
}
// Calculate Cross Rate (Base/Quote)
var crossRate = valueOfBaseInBridge / valueOfQuoteInBridge;
// Display Results
// Precision logic: If rate is very small, show more decimals
var precision = 4;
if (crossRate 100) precision = 2;
resultDisplay.innerHTML = "1 " + baseCode + " = " + crossRate.toFixed(precision) + " " + quoteCode;
// Detailed Explanation Construction
var formulaText = "";
if (type1 === 'bridge_per_base' && type2 === 'bridge_per_quote') {
formulaText = "Formula: (" + baseCode + "/Bridge) ÷ (" + quoteCode + "/Bridge)";
} else if (type1 === 'base_per_bridge' && type2 === 'quote_per_bridge') {
formulaText = "Formula: (Bridge/" + quoteCode + ") ÷ (Bridge/" + baseCode + ")";
} else {
formulaText = "Formula derived via chain rule relative to the common bridge currency.";
}
resultExplanation.innerHTML = "Implied Bid/Ask calculation based on mid-market rates provided." + formulaText;
resultBox.style.display = "block";
}
Understanding Cross Exchange Rates
In the world of foreign exchange (Forex), not every currency pair is traded directly in high volumes. While major pairs like EUR/USD or USD/JPY have established, liquid markets, the exchange rate between two currencies that do not involve the US Dollar is known as a Cross Rate.
A Cross Exchange Rate Calculator is an essential tool for traders and businesses involved in international transactions where a direct quote is unavailable or when calculating arbitrage opportunities. By using a common third currency—usually the US Dollar (USD), Euro (EUR), or British Pound (GBP)—you can mathematically derive the fair market exchange rate between any two currencies.
How the Calculation Works
The logic behind a cross rate calculation relies on the "Chain Rule" of mathematics. To find the rate of Currency A relative to Currency B (written as A/B), you utilize their relationships with a common "bridge" currency (let's call it C).
There are generally three scenarios depending on how the rates are quoted:
Case 1: Both currencies are quoted against the bridge (e.g., A/USD and B/USD). To find A/B, you divide the rate of A by the rate of B. Formula: (A/USD) ÷ (B/USD) = A/B
Case 2: The bridge is the base for both (e.g., USD/A and USD/B). To find A/B, you divide the rate of B by the rate of A. Formula: (USD/B) ÷ (USD/A) = A/B
Case 3: Mixed quotes (e.g., A/USD and USD/B). To find A/B, you multiply the two rates. Formula: (A/USD) × (USD/B) = A/B
Example: Calculating EUR/GBP via USD
Suppose you want to find the exchange rate for Euros to British Pounds (EUR/GBP), but you only have the rates against the US Dollar.
Since both are quoted with USD as the "Counter" currency, you divide the Euro rate by the Pound rate:
1.0850 ÷ 1.2500 = 0.8680
Therefore, the cross rate is EUR/GBP 0.8680.
Why Use a Cross Rate Calculator?
1. Pricing Accuracy: For businesses importing goods from Japan (JPY) but holding funds in Swiss Francs (CHF), accurate cross rate calculation ensures you aren't losing money on bank conversion spreads.
2. Arbitrage Opportunities: Forex traders use these calculators to identify discrepancies. If the calculated cross rate differs significantly from the actual market price of that pair, an arbitrage opportunity may exist.
3. Travel Budgeting: If you are traveling between countries that don't use the standard global reserve currencies, knowing the cross rate helps in understanding the real cost of goods.