Fx Cross Rate Calculator

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FX Cross Rate Calculator

Calculate currency cross rates using major pair exchange rates.

Common Currency is Quote for Both (e.g., EUR/USD & GBP/USD) Common Currency is Base for Both (e.g., USD/JPY & USD/CHF) Bridging / Chained (e.g., EUR/USD & USD/JPY)
Select this if both pairs end in the same currency (like USD).
Calculated Cross Rate: 0.0000
Inverse Rate: 0.0000

Understanding FX Cross Rates

In the foreign exchange market, a Cross Rate is an exchange rate between two currencies that are not the official currency of the country where the exchange quote is given. More commonly, it refers to a currency pair that does not involve the US Dollar (USD).

Since most major currencies are quoted against the US Dollar, calculating the cross rate (e.g., EUR/GBP or EUR/JPY) requires a mathematical derivation based on their individual relationships with the USD.

How to Calculate Cross Rates

There are three primary scenarios for calculating cross rates, depending on how the two currencies are quoted against the common currency (usually USD):

  • Scenario 1: Common Quote Currency (Division)
    When both currencies are quoted against the dollar (e.g., EUR/USD and GBP/USD), you divide the base pair by the target pair to find the cross rate (EUR/GBP).
    Formula: Cross Rate = (Base/USD) / (Target/USD)
  • Scenario 2: Common Base Currency (Division)
    When the dollar is the base currency for both (e.g., USD/JPY and USD/CHF), you divide the rate of the target currency's pair by the rate of the base currency's pair to find the cross.
    Formula: Cross Rate = (USD/Target) / (USD/Base)
  • Scenario 3: Chained / Multiplication
    When one pair has USD as the quote currency and the other has USD as the base currency (e.g., EUR/USD and USD/JPY), you multiply the two rates to bridge them (finding EUR/JPY).
    Formula: Cross Rate = (EUR/USD) * (USD/JPY)

Why Cross Rates Matter

Cross rates allow traders to identify arbitrage opportunities and trade currencies directly without converting to US Dollars first. This reduces transaction costs and spreads. For businesses, understanding cross rates is essential for pricing goods in international markets where the USD is not the primary medium of exchange.

Example Calculation

Suppose you want to find the rate for EUR/JPY. You have the following market data:

  • EUR/USD: 1.1000
  • USD/JPY: 145.00

Since the USD is the quote currency in the first pair and the base currency in the second, you multiply the rates:

1.1000 × 145.00 = 159.50. Therefore, 1 Euro is worth 159.50 Japanese Yen.

// Initial label update updateLabels(); function updateLabels() { var method = document.getElementById('crossMethod').value; var label1 = document.getElementById('labelRate1'); var label2 = document.getElementById('labelRate2'); var hint = document.getElementById('methodHint'); var r1 = document.getElementById('rate1'); var r2 = document.getElementById('rate2'); if (method === 'quote_match') { label1.innerText = "Base Currency vs USD (e.g., EUR/USD)"; label2.innerText = "Target Currency vs USD (e.g., GBP/USD)"; hint.innerText = "Use when both pairs have USD as the second currency (Quote). Result is Base/Target."; r1.placeholder = "1.0850"; r2.placeholder = "1.2650"; } else if (method === 'base_match') { label1.innerText = "USD vs Target Currency (e.g., USD/JPY)"; label2.innerText = "USD vs Base Currency (e.g., USD/CHF)"; hint.innerText = "Use when both pairs have USD as the first currency (Base). Logic is inverted division."; r1.placeholder = "145.50"; r2.placeholder = "0.8900"; } else if (method === 'chain') { label1.innerText = "Base Currency vs USD (e.g., EUR/USD)"; label2.innerText = "USD vs Target Currency (e.g., USD/JPY)"; hint.innerText = "Use to bridge two pairs via multiplication. Result is Base/Target (e.g., EUR/JPY)."; r1.placeholder = "1.1000"; r2.placeholder = "135.00"; } } function calculateCrossRate() { var rate1 = parseFloat(document.getElementById('rate1').value); var rate2 = parseFloat(document.getElementById('rate2').value); var method = document.getElementById('crossMethod').value; var resultDisplay = document.getElementById('displayResult'); var inverseDisplay = document.getElementById('displayInverse'); var formulaText = document.getElementById('formulaDisplay'); var resultsArea = document.getElementById('resultsArea'); // Validation if (isNaN(rate1) || isNaN(rate2) || rate1 <= 0 || rate2 50, use 2 decimals, else 5. var decimals = result > 50 ? 2 : 5; resultDisplay.innerText = result.toFixed(decimals); inverseDisplay.innerText = inverse.toFixed(decimals); formulaText.innerText = formulaExplanation; }

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