How to Calculate an Exchange Rate

Exchange Rates: An Overview

An exchange rate defines how much it costs to exchange one currency for another. Exchange rates fluctuate constantly throughout the week as currencies are actively traded. This trading pushes the price up and down, similar to the way that prices of other assets such as gold or stocks move up and down.

The official exchange rate of a currency on the foreign exchange market (forex) is also known as the market price (the current price at which a currency can be bought or sold). That exchange rate or price (e.g., for how many U.S. dollars it takes to buy a Canadian dollar) is different from the exchange rate you may receive from your bank when you exchange currency. It is often a key element of financial trilemmas.

Here’s how exchange rates work, and how to figure out if you are getting a good deal.

Understanding Exchange Rates

Traders and institutions buy and sell currencies 24 hours a day during the week. For a trade to occur, one currency must be exchanged for another. For example, to buy British pounds (GBP), a different currency must be used for the transaction.

The two currencies used will create a currency pair. If U.S. dollars (USD) are used to buy GBP, the exchange rate is for the GBP/USD pair.

Access to these forex markets can be found through any of the major forex brokers.

How to Read a Currency Pair

It’s important to understand how to read a currency pair. In the ordering of a currency pair, the currency listed on the left is the currency being purchased. It always represents one unit of the currency. The currency on the right is the currency used to make the purchase.

Take the USD/CAD currency pair. USD is the currency being bought, CAD (Canadian dollars) is the currency used to make the purchase. The exchange rate represents how much of the second currency, CAD, is needed to purchase one unit of the first (USD).

How to Calculate an Exchange Rate

If the USD/CAD currency pair is 1.33, that means it costs 1.33 Canadian dollars to obtain 1 U.S. dollar.

Conversely, to find out how much it costs to buy one Canadian dollar using U.S. dollars, use the following formula:

1 / exchange rate

1 / 1.33 = 0.7518

It costs 0.7518 U.S. dollars to buy one Canadian dollar. This price would be reflected by the CAD/USD pair. Note that the position of the currencies has switched: Canadian dollars are being bought with U.S. dollars.

Some of the most popular currencies that trade against the U.S. dollar are the euro (EUR/USD), the Japanese yen (USD/JPY), the British pound (GBP/USD), the Chinese yuan (USD/CNY), the Swiss franc (USD/CHF), the Australian dollar (USD/AUD), and the Canadian dollar (USD/CAD).

Conversion Spreads

When you go to the bank to convert your money to another currency, you most likely won’t get the market price that traders get on the forex. The bank or currency exchange house will markup the price so they make a profit. Credit cards and payment service providers such as PayPal also do this when converting currencies.

If the USD/CAD price is 1.33, the market is saying it costs 1.33 Canadian dollars to buy 1 U.S. dollar. At the bank, though, it may cost 1.37 Canadian dollars. The difference between the market exchange rate and the exchange rate it charges is the bank’s profit. It is compensating itself for providing the immediate currency exchange service.

To calculate how much more a bank might charge you vs. the market exchange rate, take the difference between the two exchange rates, and divide it by the market exchange rate (then multiply by 100 to convert the decimal to a percentage):

((1.37 - 1.33)/1.33) × 100 = 3% markup

A markup will also be present if converting U.S. dollars to Canadian dollars. If the CAD/USD exchange rate is 0.75 (see above), then the bank may charge 0.7725. They are charging you more U.S. dollars than the market rate:

((0.7725 - 0.75)/0.75) × 100 = 3% markup

The bank gives you cash, whereas traders in the market do not deal in cash. Wire fees and processing or withdrawal fees would be applied to a forex account if an investor needed the money in physical form.

In most cases, someone converting currencies wants to get the cash instantly and with as few fees as possible. Paying a markup to a bank or credit card company is a worthwhile compromise.

However, if you are converting one currency to another, to save money, shop around for an exchange rate that is closest to the market exchange rate.

Currency Calculation Example

Need a foreign currency? Exchange rates can help you to determine how much foreign currency you can get for a specific amount of your local currency, or how much of your local currency you’ll need to spend for a certain amount of the foreign currency.

For example, if you’re heading to Europe, you’ll need euros (EUR) and will need to check the EUR/USD exchange rate at your bank. The market rate may be 1.113, but a bank might charge you 1.146 or more. That means it may take $1.146 U.S. dollars to buy 1 euro.

What You Get for $1,000

Assume you have $1,000 with which to buy euros. How many will that $1,000 get you? Divide $1,000 by 1.146 (what a bank may charge) and the result is 872.60 euros. That is how many euros you get for your $1,000.

How Much You Pay for 1,500 Euros

Now assume you already know that you want 1,500 euros for your trip. How much will they cost you in U.S. dollars? Multiply 1,500 by 1.146 (the same bank exchange rate) and the result is $1,719. That is how much you need to pay to get your 1,500 euros.

The Bottom Line

Exchange rates are the cost of one currency relative to another. The order in which a currency pair is listed matters. Remember, the currency on the left is always equal to one unit, and the exchange rate is how much of the currency on the right it takes to buy one unit of that first currency.

With the exchange rate, you can calculate both the amount of foreign currency you’d get for a certain amount of dollars and what you’d have to pay for a certain amount of foreign currency.

Banks will markup the exchange rates of currencies to compensate themselves for the service they provide. Shopping around may save you money as some companies will have a smaller markup, relative to the market exchange rate, than others.