What Is a Cross Rate in Currency Markets?
In short
A cross rate is the exchange rate between two currencies that is calculated from the rate of each against a third currency, usually the US dollar.
Most foreign exchange trading is quoted against the US dollar, which is why the dollar is called a vehicle currency. When two currencies are not quoted directly against each other, or when the direct market is thin, their rate can be derived from the two dollar rates. That derived rate is the cross rate. For example, EUR/TRY can be obtained from EUR/USD and USD/TRY.
The calculation depends on how each leg is quoted. If the dollar is the quote currency in one pair and the base currency in the other, the two rates are multiplied; if the dollar is on the same side in both, one rate is divided by the other. The formulas below show both cases; an inverted rate swaps the direction of the multiplication or division.
A cross rate is only as current as its legs. If the two source rates are observed at different times, the derived rate mixes two moments, and it can differ from a rate quoted directly by a dealer, which includes the dealer's own spread. Careful presentations therefore give the time of each input, and a derived rate should not be treated as a price at which a transaction is available. When direct quotes of all three pairs exist, dealers' arbitrage keeps the cross rate close to the direct quote, and the remaining differences usually reflect spreads and timing.
Formula
EUR/TRY = EUR/USD * USD/TRY
EUR/GBP = EUR/USD / GBP/USDThe formula is shown as code; N stands for the number of bars or periods.
How Lzzo.com shows it
Some pairs on Lzzo.com are derived this way, for example lira pairs built from a dollar rate and USD/TRY. Where a pair is derived, its time is the time of the older of the two inputs, and no cross rate is shown when one input is missing. The currency converter also derives the rate between any two supported currencies in this way and states the source.
Related guides
Sources
- Bank for International Settlements, Triennial Central Bank Survey of foreign exchange and OTC derivatives markets 2025
- Federal Reserve Board, Foreign Exchange Rates (H.10)
- European Central Bank, Euro foreign exchange reference rates
Primary and official sources, named as plain text.