Cross Rate Calculation Formula

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Forex Cross Rate Calculator

Same Base Currency (Divide) Same Quote Currency (Divide) Chain / Crossing (Multiply) Calculate A/B given A/USD and B/USD.
Calculated Cross Rate
0.0000
Formula Used: Rate 1 / Rate 2

What is the Cross Rate Calculation Formula?

A cross rate is an exchange rate between two currencies that is derived from their individual relationship with a third, common currency—most often the US Dollar (USD) or the Euro (EUR). In the world of foreign exchange (Forex), not every currency pair is traded actively enough to have a direct market price. The cross rate formula allows traders and businesses to calculate the exact exchange rate between any two currencies by "crossing" them through a common liquid currency.

How to Calculate Cross Rates

The calculation method depends entirely on how the two currencies are quoted relative to the common currency. There are three primary scenarios you will encounter:

1. Same Base Currency (Division)

This scenario occurs when the common currency is the denominator (bottom) of both pairs. For example, if you have Currency A / USD and Currency B / USD, and you want to find Currency A / Currency B.

Formula: Cross Rate = Rate 1 / Rate 2

Example:
EUR/USD = 1.1000 (Rate 1)
GBP/USD = 1.3000 (Rate 2)
To find EUR/GBP: 1.1000 / 1.3000 = 0.8461

2. Same Quote Currency (Division)

This occurs when the common currency is the numerator (top) of both pairs. For example, USD / Currency A and USD / Currency B. To find Currency A / Currency B, the division order flips.

Formula: Cross Rate = Rate 2 / Rate 1

Example:
USD/JPY = 110.00 (Rate 1 – Quote A)
USD/CHF = 0.9200 (Rate 2 – Quote B)
To find JPY/CHF: 0.9200 / 110.00 = 0.00836

3. Chain / Crossing the Bridge (Multiplication)

This is the most intuitive method. It occurs when the common currency is the denominator of the first pair and the numerator of the second pair (or vice versa). E.g., Currency A / USD and USD / Currency B.

Formula: Cross Rate = Rate 1 × Rate 2

Example:
EUR/USD = 1.1000 (Rate 1)
USD/JPY = 110.00 (Rate 2)
To find EUR/JPY: 1.1000 × 110.00 = 121.00

Why Use This Calculator?

While major pairs like EUR/USD are traded heavily, pairs like GBP/JPY or AUD/CAD are considered "crosses." Understanding the mathematical relationship between these pairs helps arbitrageurs spot inefficiencies in the market. If the calculated cross rate differs significantly from the actual market price offered by a broker, an arbitrage opportunity may exist.

function updateLabels() { var method = document.getElementById("calcMethod").value; var label1 = document.getElementById("labelRate1"); var label2 = document.getElementById("labelRate2"); var desc = document.getElementById("methodDescription"); var rate1Input = document.getElementById("rate1"); var rate2Input = document.getElementById("rate2"); if (method === "base") { label1.innerText = "Pair 1 (Target / Common) [e.g., EUR/USD]"; label2.innerText = "Pair 2 (Counter / Common) [e.g., GBP/USD]"; desc.innerText = "Formula for Target/Counter: Rate 1 / Rate 2"; rate1Input.placeholder = "1.1050"; rate2Input.placeholder = "1.3100"; } else if (method === "quote") { label1.innerText = "Pair 1 (Common / Target) [e.g., USD/JPY]"; label2.innerText = "Pair 2 (Common / Counter) [e.g., USD/CHF]"; desc.innerText = "Formula for Target/Counter: Rate 2 / Rate 1"; rate1Input.placeholder = "110.50"; rate2Input.placeholder = "0.9250"; } else if (method === "chain") { label1.innerText = "Pair 1 (Target / Common) [e.g., EUR/USD]"; label2.innerText = "Pair 2 (Common / Counter) [e.g., USD/JPY]"; desc.innerText = "Formula for Target/Counter: Rate 1 × Rate 2"; rate1Input.placeholder = "1.1050"; rate2Input.placeholder = "110.00"; } } function calculateCrossRate() { var method = document.getElementById("calcMethod").value; var r1 = parseFloat(document.getElementById("rate1").value); var r2 = parseFloat(document.getElementById("rate2").value); var resultDisplay = document.getElementById("result"); var crossRateValue = document.getElementById("crossRateValue"); var formulaText = document.getElementById("formulaUsed"); // Error Handling if (isNaN(r1) || isNaN(r2)) { alert("Please enter valid numeric exchange rates for both fields."); resultDisplay.style.display = "none"; return; } if (r1 <= 0 || r2 <= 0) { alert("Exchange rates must be greater than zero."); resultDisplay.style.display = "none"; return; } var result = 0; var formulaStr = ""; if (method === "base") { // Formula: Rate 1 / Rate 2 // Example: (EUR/USD) / (GBP/USD) = EUR/GBP result = r1 / r2; formulaStr = r1 + " / " + r2; } else if (method === "quote") { // Formula: Rate 2 / Rate 1 // Example: (USD/CHF) / (USD/JPY) = JPY/CHF // Note: If finding JPY/CHF, we need (1/Rate1) * Rate2. // 1 JPY = (1/r1) USD. 1 USD = r2 CHF. // 1 JPY = (1/r1) * r2 CHF = r2/r1. result = r2 / r1; formulaStr = r2 + " / " + r1; } else if (method === "chain") { // Formula: Rate 1 * Rate 2 // Example: (EUR/USD) * (USD/JPY) = EUR/JPY result = r1 * r2; formulaStr = r1 + " × " + r2; } // Format result to 5 decimal places for precision crossRateValue.innerText = result.toFixed(5); formulaText.innerText = formulaStr; resultDisplay.style.display = "block"; } // Initialize labels on load updateLabels();

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