About the Currency Cross Rate Calculator
Most currencies are quoted against the US dollar, so the rate between two non-dollar currencies — a cross rate such as EUR/JPY or GBP/CAD — is derived from their two dollar quotes. This currency cross rate calculator does that derivation for any pair: enter each currency’s quote against a common currency, tell it which way round each quote is written, and it returns the cross rate, its inverse and the converted amount.
It is designed for forex traders checking a broker quote, finance students learning quotation conventions, and businesses that need a rate for a pair their bank does not show. Switch on bid/ask mode to build a realistic two-way cross price, where the spread widens because you cross two spreads, and enter a market quote to see whether a triangular arbitrage gap exists.
The calculator does not fetch live prices; type in current quotes from your broker or a data source. Real dealing prices also include fees and change by the second, so small arbitrage gaps usually disappear once costs are included.
With the default inputs, the cross rate (1 a in b) is 162.967. Change any value above to recalculate instantly.
How to use the currency cross rate calculator
- 1Type the three currency codes: the cross base (A), the cross quote (B) and the common currency.
- 2For each quote, choose how it is written (for example EUR/USD or USD/JPY) and enter the rate.
- 3Turn on bid/ask mode if you want a two-way cross price with a realistic spread.
- 4Enter an amount of currency A to convert, and optionally a dealer’s quote to check for arbitrage.
Formula and method
Each quote is first turned into the value of one unit of that currency in the common currency: an A/C quote is used directly, while a C/A quote is inverted (1 ÷ rate). The cross rate A/B is the value of A in C divided by the value of B in C. For EUR/JPY from EUR/USD 1.0850 and USD/JPY 150.20 that is 1.0850 × 150.20 = 162.967.
With two-way prices, inverting a quote swaps its bid and ask (the inverse bid is 1 ÷ ask). The cross bid assumes you sell A at its bid and buy B at its ask, and the cross ask the reverse, so the cross spread is roughly the sum of both legs’ spreads. The mid cross is the average of the cross bid and ask, and conversions in bid/ask mode use the cross bid.
- A/C
- Units of the common currency per 1 unit of A
- C/B
- Units of B per 1 unit of the common currency
- A/B
- Cross rate: units of B per 1 unit of A
Worked examples
EUR/JPY from EUR/USD and USD/JPY
EUR/USD 1.0850 means €1 buys $1.085, and USD/JPY 150.20 means $1 buys ¥150.20. Multiplying gives €1 = ¥162.967, so €1,000 converts to ¥162,967. The inverse is 1 ÷ 162.967 ≈ 0.0061362 euros per yen.
GBP/CAD with a market-quote check
GBP/USD 1.27 × USD/CAD 1.36 = 1.7272, so £5,000 is about C$8,636. A dealer quoting 1.7300 is 0.16% above the implied cross — a gap that could only be traded if it exceeds the spreads on all three legs.
AUD/EUR with bid/ask spreads (both quoted against USD)
Both quotes give US dollars per unit of the currency (A/C and B/C form), so AUD/EUR = AUD/USD ÷ EUR/USD. The bid divides the AUD bid by the EUR ask (0.6598 ÷ 1.0852 = 0.60800) and the ask divides the AUD ask by the EUR bid (0.6602 ÷ 1.0848 = 0.60859).
Frequently asked questions
What is a cross rate in forex?+
A cross rate is an exchange rate between two currencies that is calculated from each currency’s rate against a third, usually the US dollar. EUR/JPY, GBP/CHF and AUD/NZD are common examples traded as cross pairs.
How do I calculate a cross rate when both quotes have USD as the base?+
If both are written USD/X, such as USD/CAD and USD/JPY, divide them: CAD/JPY = USD/JPY ÷ USD/CAD. Select the C/A form for quote 1 and C/B for quote 2 and the calculator handles the inversion for you.
Why is the spread on a cross pair wider?+
A cross price is built from two separate dollar legs, so you effectively pay both spreads. Inverting a quote also swaps its bid and ask, which is why the derived bid uses the opposite side of the second leg.
What is triangular arbitrage?+
Triangular arbitrage is converting through three currencies (for example USD to EUR to JPY and back to USD) to profit when a quoted cross differs from the implied cross. In liquid markets such gaps are tiny and close in milliseconds, and spreads and fees usually exceed them.
Does this calculator use live exchange rates?+
No. It is a pure calculator that works with whatever quotes you type in, so you can use your broker’s live prices, a central bank reference rate, or historical rates for back-testing.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.