Cross Exchange Rate Calculator
Calculate the exchange rate between two currencies using a common third currency (typically USD) as the bridge.
How to use this tool
- Enter base currency rate vs. usd (e.g., eur/usd), quote currency rate vs. usd (e.g., gbp/usd) and amount to convert (in base currency) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your cross exchange rate (base/quote) and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
Cross Rate: RateA/B = RateA/USD ÷ RateB/USD
Where both rates are expressed as units of the respective currency per 1 USD.
Converted Amount: AmountB = AmountA × RateA/B
How it works
A cross exchange rate is the exchange rate between two currencies derived indirectly through a third common currency — typically the US Dollar. This method is used when a direct market quote between two non-USD currency pairs is not readily available.
Both input rates should be expressed as how many USD one unit of each currency buys (i.e., the direct USD quote). The cross rate is then the simple ratio of the two USD rates. This calculator assumes mid-market rates with no bid-ask spread.
Worked example
Calculate EUR/GBP cross rate
- EUR/USD = 1.10 (1 Euro buys 1.10 US Dollars)
- GBP/USD = 1.25 (1 British Pound buys 1.25 US Dollars)
- EUR/GBP = EUR/USD ÷ GBP/USD = 1.10 ÷ 1.25 = 0.8800
- Converting 1,000 EUR: 1,000 × 0.8800 = 880.00 GBP
The EUR/GBP cross rate is 0.8800, meaning 1 Euro buys 0.88 British Pounds. 1,000 EUR converts to 880.00 GBP.
Common mistakes to avoid
- Dividing in the wrong direction -- if both rates are quoted as units per USD, the cross rate is A/USD divided by B/USD, not multiplied.
- Using bid rates for one currency and ask rates for another, ignoring the bid-ask spread that applies to each leg and underestimating transaction cost.
- Assuming the cross rate is symmetric -- Rate_A/B is not the same as Rate_B/A; one is the reciprocal of the other.
Key terms
- Cross Exchange Rate
- The exchange rate between two currencies calculated indirectly through a third currency, usually the US Dollar.
- Base Currency
- The first currency in a currency pair; the currency being bought or exchanged from.
- Quote Currency
- The second currency in a currency pair; the currency being received in exchange.
- Triangular Arbitrage
- A trading strategy that exploits discrepancies between three currency pairs to generate a risk-free profit.
Frequently asked questions
- Why do banks use USD as the bridge currency?
- The USD is the primary reserve currency and the most liquid market. Almost every currency pair has an active USD market, minimizing the bid-ask spread. Direct cross-currency markets (EUR/JPY) exist for major pairs but are less liquid.
- How does the cross rate differ from the official exchange rate?
- The cross rate calculated from interbank USD quotes is a theoretical mid-market rate. The rate you receive from a bank will differ due to bid-ask spreads and fees.
- Can I use a cross rate to convert between two non-USD currencies?
- Yes. Enter the USD rate for each currency, and the calculator derives the rate between them. For example, to get EUR/JPY, divide USD/JPY by USD/EUR.