Capital letters "A", "B", "C" each represent different currencies. A currency pair can be expressed in two forms, but you only need to enter one for each pair.
First currency pair
Exchange rate A/C
or exchange rate C/A
Second currency pair
Exchange rate B/C
or exchange rate C/B
Cross rate
Cross rate A/B
or cross rate B/A

# Cross Exchange Rate Calculator

By Marcin Manias

Our cross exchange rate calculator is a simple tool that lets you calculate foreign exchange cross rates, also referred to as cross exchange rates or simply the cross rate.

In the article below, we explain what is the cross exchange rate, show you the cross currency conversion formula, and, finally, teach you how to do the cross rate calculation yourself!

You may think that phrases such as "cross exchange rate calculation formula" are financial terms that go hand in hand with stock markets, and are therefore only useful for traders. Well, we're here to say that that's not true! When traveling abroad, the cross currency exchange rate is something that becomes as handy as knowing how much should you tip, or calculating the gas cost of your trip.

## What is cross exchange rate? - Exchange rates and currency pairs

To easily understand what is cross exchange rate, let's go back a little bit and start from the beginning.

An exchange rate is the current rate at which one currency can be exchanged for another.

Economic factors determine exchange rates. They change with time, and are used to determine the value of one currency in relation to another. This comparison of relative value is called a currency pair. For example, EUR/USD is a very popular currency pair. `EUR/USD 1.1000` - this entry - or quotation as one would say in the financial world - means that 1 Euro can be exchanged for 1.1 United States dollars.

## Cross currency exchange rates - Foreign exchange cross rates

A cross currency pair is, by definition, a pair of currencies where neither is the official currency of the country in which the rates are checked. Let's take a look at an example to better explain this: the pound sterling (GBP) is the official currency of the United Kingdom, and the EUR/USD could be called a cross-currency pair there. The exchange rate between a cross currency pair is called the foreign exchange cross rate or just the cross rate.

As is often the case, the real-world tends to leave definitions behind. Investors in the foreign exchange market (Forex) call any pair of currencies that doesn't include the US dollar a cross rate, regardless of where they are trading from. In that sense, the EUR/USD pair would not be called a cross rate, but the GBP/EUR pair would be. Nevertheless, we have good news for you - whatever currency pairs you have in mind when thinking about cross exchange rates, the cross-currency conversion formula remains a simple one. Read on to find out more.

## Cross currency conversion formula

The point of calculating the cross rate is to find the exchange rate between two currencies when you only know the individual exchange rates between those two currencies and a third common currency (for example the national currency of the country you are in).

What exchange rate are you looking for?

The one that directly compares the two currencies, omitting the third one.

But why?

Most of the time, the main reason you calculate the cross rate is because your current situation means that it is easier to exchange your money twice than to exchange it directly. It does not matter whether you are on holiday 😎, visiting your local currency exchange, or are trading on Forex 💲, some currency combinations are hard to find and rarely traded directly. In any case, you should probably know what deal you are getting before making any transactions - calculating cross currency exchange rates tells you exactly that.

Now that you know the what and the why, the last important question is how.

The answer here is going to be unsatisfying - it is the common answer in the world of finance: "it depends". It depends on the quotation given - there are two cases:

1. Let's start with the simpler one. You have two foreign exchange quotes where the order of the currencies is the same. It means that in both quotes the common currency is the denominator. For example, you have quotes for EUR/USD (euro/dollar) and GBP/USD (pound/dollar). You want to find out the EUR/GBP cross rate. You can do this by simply diving the first rate by the second:

`EUR/USD ÷ GBP/USD = EUR/GPB`.

Because the denominator, a common currency (in this case the dollar), is the same, you can cross-cancel it.

1. Things are a little bit trickier when you have quotes in which the order of currencies is different. Let's stay with the currencies from the previous example. This time you have quotes for USD/EUR and GBP/USD. You want the common currency - USD - to be the denominator in both quotes. In simple terms, you need to "flip" one of the pairs. In other words, you need to find the reciprocal of a fraction:

`1 ÷ USD/EUR = EUR/USD`.

Once you've done this, line your quotes up and do the same as before, diving the first rate by the second:

`EUR/USD ÷ GBP/USD = EUR/GPB`.

2. Alternatively, you can use our calculator instead. The capital letters "A","B", and "C" each represent different currencies. As you can see the letter "C" is present in both pairs and represents the common currency. For example, "A" could be EUR, "B" - GBP, and "C" - USD. Enter the quotations and we will take of care of calculating the cross rates properly. You don't have to worry about anything!

## Cross exchange rate calculation formula in practice - cross rate calculation

Now that you know the cross currency conversion formula. Let's see how to use it in practice with numbers.

• Let's say you know the euro-dollar rate, and it is 1.1 EUR/USD.
• You also know the dollar-pound rate, and it is 0.8 USD/GBP.
• You want to calculate the EUR/GBP cross rate.

You can do it in a few simple steps:

1. Find your common currency - the currency that occurs in both pairs. In this example, it is USD.

2. Check the order of the currencies. If the common currency is the denominator in both quotes, proceed to the next step. If not, find the reciprocal. Here, one pair has the dollar first, and the other has it second. You need to find the reciprocal for one of them:

`1 ÷ 0.8 USD/GBP = 1.25 GBP/USD`.

3. Divide the first rate by the second to cancel the common currency:

`1.1 EUR/USD ÷ 1.25 GBP/USD = 0.88 EUR/GBP`.

4. That's it. You've successfully calculated the cross exchange rate.

Remember, there is no need to do it by hand, so get back to your hammock, relax, and let our cross exchange rate calculator do the work for you.

Marcin Manias

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