Cross Exchange Rate Calculator
Calculate direct exchange rates between two currencies using their rates against a common third currency (typically USD).
Currency Exchange Rates
Understanding Cross Exchange Rates
Core Formula
Cross Rate (A/B) = Rate A/Base ÷ Rate B/Base
Key Concepts
- Base Currency: Common reference currency (usually USD)
- Quote Currency: The currency being priced
- Reciprocal Rates: Inverse relationship between currency pairs
Real-World Examples
Example 1: EUR/GBP Calculation
Given: EUR/USD = 1.20, GBP/USD = 1.35
Formula: EUR/GBP = 1.20 ÷ 1.35
Calculation: 1.20 / 1.35 = 0.8889
Result: 1 EUR = 0.8889 GBP
Example 2: JPY/AUD Calculation
Given: USD/JPY = 110.50, AUD/USD = 0.7500
Formula: JPY/AUD = (1/0.7500) × 110.50
Calculation: 1.3333 × 110.50 = 147.33
Result: 1 JPY = 0.00679 AUD (1/147.33)
Example 3: GBP/CHF with USD Base
Given: GBP/USD = 1.35, USD/CHF = 0.92
Formula: GBP/CHF = 1.35 × 0.92
Calculation: 1.35 × 0.92 = 1.242
Result: 1 GBP = 1.242 CHF
Example 4: CAD/MXN Calculation
Given: USD/CAD = 1.25, USD/MXN = 20.50
Formula: CAD/MXN = 20.50 ÷ 1.25
Calculation: 20.50 / 1.25 = 16.40
Result: 1 CAD = 16.40 MXN
Example 5: Gold (XAU) Cross Rate
Given: XAU/USD = 1800, USD/CNY = 6.50
Formula: XAU/CNY = 1800 × 6.50
Calculation: 1800 × 6.50 = 11,700
Result: 1 gold ounce = 11,700 CNY
Example 6: Triangular Arbitrage Opportunity
Given: EUR/USD = 1.20, USD/GBP = 0.74, EUR/GBP = 0.90
Calculation: Theoretical EUR/GBP = 1.20 × 0.74 = 0.888
Analysis: Market rate (0.90) higher than theoretical (0.888) → Arbitrage possible
Example 7: NOK/SEK Calculation
Given: USD/NOK = 8.50, USD/SEK = 8.00
Formula: NOK/SEK = 8.00 ÷ 8.50
Calculation: 8.00 / 8.50 = 0.9412
Result: 1 NOK = 0.9412 SEK
Example 8: Inverse Rate Calculation
Given: EUR/USD = 1.20 (Direct Rate)
Formula: USD/EUR = 1 ÷ 1.20
Calculation: 1 / 1.20 = 0.8333
Result: 1 USD = 0.8333 EUR
Example 9: Cross Rate with EUR Base
Given: EUR/GBP = 0.88, EUR/CHF = 1.08
Formula: GBP/CHF = 1.08 ÷ 0.88
Calculation: 1.08 / 0.88 = 1.2273
Result: 1 GBP = 1.2273 CHF
Example 10: Cryptocurrency Cross Rate
Given: BTC/USD = 30,000, ETH/USD = 2,000
Formula: BTC/ETH = 30,000 ÷ 2,000
Calculation: 30,000 / 2,000 = 15
Result: 1 BTC = 15 ETH
Frequently Asked Questions
1. What is a cross exchange rate?
A cross rate is an exchange rate between two currencies calculated through their common relationship with a third currency, typically the US Dollar.
2. Why is USD commonly used as the base currency?
The US Dollar is the world's primary reserve currency and most liquid market, making it the natural base for cross rate calculations.
3. How do I calculate inverse rates?
Inverse rate = 1 ÷ Direct rate. Example: If EUR/USD = 1.20, then USD/EUR = 1/1.20 ≈ 0.8333.
4. Can I use non-USD base currencies?
Yes. The formula works with any base: (A/X) ÷ (B/X) = A/B. Choose X as your preferred base currency.
5. How accurate are cross rate calculations?
Mathematically precise, but actual market rates may differ slightly due to bid-ask spreads and transaction costs.
6. What's the difference between direct and indirect quotes?
Direct: Foreign currency per unit of domestic. Indirect: Domestic per unit of foreign. The formula automatically handles both types.
7. How often should I update exchange rates?
For accurate calculations, use real-time rates from reliable sources. Currency markets fluctuate constantly.
8. Can I use this for cryptocurrency pairs?
Yes. The same principles apply to crypto/crypto calculations using a common base (usually USD or BTC).
9. What if both rates use different base currencies?
Convert to common base first. Example: To get EUR/GBP from EUR/USD and GBP/JPY, first convert GBP/JPY to GBP/USD.
10. How is this used in international business?
Cross rates enable companies to:
- Compare prices across countries
- Hedge currency risks
- Execute triangular arbitrage
- Calculate multi-currency invoices
