# Cross Rate

The cross rate is the exchange rate between currency A and currency C derived from actual exchange rate between currency A and currency B and between currency B and currency C.

Sometimes cross rate is referred to an exchange rate between two currencies not involving the US dollar.

Currency vendor provides quotes for only the most liquid currencies such as the US dollar, Euro, Pound Sterling, Swiss Franc, etc. Exchange rates between other currencies is normally calculated as the cross rates using the quotes for major currencies.

## Formula

 A = A × B C B C

Where,

A/C = units of currency A per unit of currency C
A/B = units of currency A per unit of currency B
B/C = units of currency B per unit of currency C

## Example

As at 27 December 2012, the exchange rate between Euro and US dollar is 0.75 € per US$. Exchange rate between US$ and Swiss Franc is 1.09 US$per Swiss Franc. Find the exchange rate between € and Swiss Franc in € per Swiss Franc. € per Swiss Franc = 0.75 € per US$ × 1.09 US\$ per Swiss Franc = 0.8175 € per Swiss Franc

Finding the same exchange rate in Swiss Franc per € would involve taking a reciprocal of the exchange rate calculated above. Swiss Franc per € exchange rate would be 1.223 Swiss Francs per € (1 ÷ (0.8175 € per Swiss Franc)).

Written by Obaidullah Jan