Cross Exchange Rate Calculator

Understanding Cross Exchange Rates

A cross exchange rate (or cross rate) is the foreign exchange rate between two currencies that are not officially quoted against each other, derived by comparing both currencies against a common benchmark base currency (most frequently the US Dollar, Euro, or Japanese Yen).

How Cross Exchange Rates Are Calculated

If Currency A and Currency B are both quoted against Base Currency C, the implied cross rate of Currency A in terms of Currency B is calculated using the ratio of their individual base exchange rates:

$$\text{Cross Rate } (A/B) = \frac{\text{Rate } (A/C)}{\text{Rate } (B/C)}$$

Triangular Arbitrage

In global foreign exchange markets, when the direct market price of a currency pair deviates from its calculated implied cross rate, traders can execute a triangular arbitrage strategy. By simultaneously buying and selling across three currency pairs (A/C, B/C, and A/B), arbitrageurs capture risk-free profits, which rapidly forces market prices back into equilibrium.