Cross Rates Explained: How to Calculate Exchange Rates Between Any Two Currencies
Have you ever tried to exchange British pounds for Japanese yen and noticed the rate seems different from what you’d expect? That’s because most exchange rate quotes go through the US dollar first. When you want to convert between two currencies that aren’t the US dollar, you’re dealing with something called a cross rate.
Understanding cross rates is essential whether you’re an international traveler, a forex trader, or someone sending money abroad. In this guide, we’ll break down exactly what cross rates are, how to calculate them step by step, and why they matter for your wallet.
What Is a Cross Rate?
A cross rate is the exchange rate between two currencies when neither is the US dollar. For example, if you want to convert euros (EUR) to British pounds (GBP), that’s a cross rate because USD isn’t directly involved in the quote.
Most currencies around the world are quoted against the US dollar. This makes sense—the dollar is the world’s primary reserve currency and the most traded currency globally. But what happens when you need to convert euros to yen, or pounds to Australian dollars, without going through USD?
That’s where cross rates come in. A cross rate is calculated using the two currencies’ individual rates against a common third currency—usually the US dollar—to determine the direct exchange rate between them.
Cross Rate vs Direct Quote
A direct quote tells you how much of your domestic currency equals one unit of a foreign currency. A cross rate bypasses the dollar entirely to show the relationship between two non-USD currencies. The key difference: cross rates are derived, not directly quoted on the market.
How to Calculate a Cross Rate: Step by Step
Calculating a cross rate involves a simple process called triangulation. You use each currency’s exchange rate against the US dollar to find the rate between them. Here’s the step-by-step method:
Step 1: Find Both Currency Rates Against USD
Look up the current exchange rates for both currencies against the US dollar. You’ll need the rate for Currency A to USD and Currency B to USD.
For example, let’s say:
- EUR/USD = 1.0850 (1 euro = 1.0850 dollars)
- GBP/USD = 1.2720 (1 pound = 1.2720 dollars)
Step 2: Divide to Find the Cross Rate
To find the EUR/GBP cross rate, divide the EUR/USD rate by the GBP/USD rate:
EUR/GBP = EUR/USD ÷ GBP/USD
EUR/GBP = 1.0850 ÷ 1.2720 = 0.8530
This means 1 euro equals 0.8530 British pounds. That’s your cross rate.
Step 3: Verify With a Reverse Calculation
Always double-check by calculating the reverse: GBP/EUR should equal 1 ÷ 0.8530 = 1.1723. If 1 pound = 1.2720 dollars and 1 euro = 1.0850 dollars, then 1 pound should buy 1.2720 ÷ 1.0850 = 1.1723 euros. The math checks out.
Cross Rate Calculation Examples
Example 1: EUR to JPY (Euro to Japanese Yen)
Let’s say:
- EUR/USD = 1.0850
- USD/JPY = 149.50
To find EUR/JPY, multiply (not divide, because JPY is quoted as USD/JPY):
EUR/JPY = EUR/USD × USD/JPY = 1.0850 × 149.50 = 162.21
So 1 euro equals 162.21 Japanese yen.
Example 2: GBP to AUD (British Pound to Australian Dollar)
Given:
- GBP/USD = 1.2720
- AUD/USD = 0.6650
GBP/AUD = GBP/USD ÷ AUD/USD = 1.2720 ÷ 0.6650 = 1.9128
1 British pound equals 1.9128 Australian dollars.
Example 3: CAD to CHF (Canadian Dollar to Swiss Franc)
Given:
- USD/CAD = 1.3620
- USD/CHF = 0.8850
First, find CAD/USD = 1 ÷ 1.3620 = 0.7342
CAD/CHF = CAD/USD × USD/CHF = 0.7342 × 0.8850 = 0.6498
1 Canadian dollar equals 0.6498 Swiss francs.
Why Cross Rates Matter
1. Better Exchange Rate Transparency
When you understand cross rates, you can check whether a bank or exchange service is giving you a fair deal. If a bank quotes you EUR/GBP at 0.8400 when the true cross rate is 0.8530, you know they’re building in a hidden margin. This knowledge helps you avoid unfavorable rates.
2. Lower Costs on International Transfers
If you’re sending money from Europe to Japan, some services route the transfer through USD, effectively charging you two conversion fees instead of one. Knowing the cross rate lets you find services that convert directly, saving you money on every transfer.
3. Forex Trading Opportunities
Currency traders use cross rates to identify pricing discrepancies between brokers. If one broker’s EUR/JPY rate differs from the calculated cross rate, a trader can exploit that gap. This is called triangular arbitrage, and it’s a strategy used by professional forex traders.
4. Travel Planning
If you’re traveling from Europe to Australia, knowing the EUR/AUD cross rate helps you budget accurately. You won’t be surprised by the actual cost of goods when you arrive, because you’ve calculated the real exchange rate rather than relying on airport exchange booths.
Common Cross Rate Pairs
The most commonly traded cross rate pairs include:
- EUR/GBP (Euro to British Pound) — one of the most traded crosses
- EUR/JPY (Euro to Japanese Yen) — popular for carry trades
- GBP/JPY (British Pound to Japanese Yen) — known for high volatility
- AUD/JPY (Australian Dollar to Japanese Yen) — another carry trade favorite
- EUR/CHF (Euro to Swiss Franc) — closely watched in European markets
- EUR/AUD (Euro to Australian Dollar) — important for EU-Australia trade
These pairs have enough trading volume that they’re now quoted directly on most forex platforms, but they’re still technically cross rates because they don’t involve the US dollar.
Cross Rates and the Bid-Ask Spread
When you calculate a cross rate yourself, you get the mid-market rate—the theoretical rate at the center of the market. In reality, exchange services apply a bid-ask spread, which is the difference between the price they’ll buy and sell a currency.
This spread gets wider on cross rates because two conversions are happening. If you convert EUR to GBP through USD, you pay the spread twice. That’s why finding a service that offers direct cross-rate conversion can save you significantly.
To learn more about how the mid-market rate works and why it’s the benchmark for fair exchange, check out our guide on the mid-market rate explained.
How to Use Cross Rates in Real Life
For Travelers
Before your trip, calculate the cross rate between your home currency and your destination currency. Compare it to what banks, airports, and card networks offer. If their rate is significantly worse than your calculated cross rate, look for alternatives like multi-currency cards or specialist transfer services.
For Business Owners
If your business deals with suppliers or customers in different countries, cross rates help you understand the true cost of your transactions. A European company buying from Japan should track EUR/JPY directly, not just watch each currency against the dollar.
For Migrant Workers and Expats
Sending remittances home often involves cross-currency conversions. Knowing the cross rate helps you compare money transfer services and choose the one that gives you the most local currency for your money.
Tools for Finding Cross Rates
You don’t have to calculate cross rates manually every time. Here are some tools:
- Currency converter apps — Most show direct rates between any two currencies, already calculated
- Central bank websites — Publish daily reference rates for major pairs
- Forex broker platforms — Display live cross rates with real-time updates
- Google — Simply search “EUR to GBP” for a quick rate
However, understanding the calculation behind these tools gives you the knowledge to verify rates and spot when a service is adding hidden fees.
Frequently Asked Questions
Is a cross rate the same as the real exchange rate?
No. A cross rate is the exchange rate between two non-USD currencies, typically derived through triangulation. The “real” exchange rate (or mid-market rate) is the midpoint between bid and ask prices on the market. A cross rate can be at the mid-market level, but in practice, exchange services add spreads.
Why are most currencies quoted against the US dollar?
The US dollar is the world’s primary reserve currency and the most traded currency in forex markets. Quoting against USD simplifies the global currency system and reduces the number of rates needed—instead of tracking every possible pair, the market quotes each currency against USD.
Can cross rates have higher fees?
Yes. When a bank or exchange service converts two non-USD currencies, they may route the transaction through USD, applying two spreads instead of one. This is why comparing services and understanding the true cross rate is important for getting the best deal.
Do I need to calculate cross rates myself?
Not necessarily. Most currency converter tools calculate cross rates automatically. But knowing how the calculation works helps you verify rates and identify when a service is offering an unfavorable exchange.
What is triangular arbitrage?
Triangular arbitrage is a forex trading strategy that exploits pricing inconsistencies between three currencies. If the cross rate between two currencies doesn’t match the rate derived through a third currency (usually USD), a trader can buy and sell the mismatched pairs to profit from the difference.
Conclusion
Cross rates might sound technical, but they’re simply the exchange rates between two currencies that don’t involve the US dollar. By understanding how triangulation works—finding each currency’s rate against USD and dividing or multiplying them—you can calculate any cross rate yourself.
This knowledge helps you avoid hidden fees, compare money transfer services accurately, and make smarter financial decisions when dealing with multiple currencies. Whether you’re traveling, trading, or sending money internationally, cross rates are a fundamental concept worth knowing.
Ready to convert currencies at the real rate? Use our currency conversion guide to learn more about how exchange rates work, or explore our guide on exchange rate fluctuations to understand what moves currency values.