How to Calculate the Percent Change

The percent change formula is a basic but useful tool. You can apply it to any variable that’s observed at various points in time. For all variables for which you want to measure the percent change, use the following formula:

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Because the subject here is the exchange rate, suppose that X denotes the exchange rate. Also:

  • %delta is the percent change.

  • Xt is the exchange rate in the current period (t).

  • Xt – i is the exchange rate in the previous period (t – i), where i can be yesterday, last month, last year, or ten years ago.

To find the percent change in the exchange rate, start with the current exchange rate minus the previous exchange rate, divide that answer by the previous exchange rate, and then multiply by 100 to express the change as a percent.

The table shows the monthly dollar–euro exchange rates as of the first of every month between January and August 2012.

The Dollar–Euro Monthly Exchange Rate (2012)
Date Exchange Rate Percent Change Terminology (Refers to the Dollar)
January 1.2910
February 1.3238 +2.54 Depreciation
March 1.3208 –0.23 Appreciation
April 1.3160 –0.36 Appreciation
May 1.2806 –2.69 Appreciation
June 1.2541 –2.07 Appreciation
July 1.2278 –2.10 Appreciation
August 1.2406 +1.04 Depreciation

Notes: FRED, St. Louis Federal Reserve Bank. Available at http://research.stlouisfed.org/fred2/series/EXUSEU/downloaddata?cid=95.

All monthly rates imply the exchange rate on the first of the month.

Even though the table title doesn’t explicitly indicate it, the exchange rates are nominal exchange rates. Remember that all exchange rates provided are the nominal exchange rates unless otherwise noted.

The percent change in the exchange rate is listed in the third column and the associated terminology in the fourth column. Focus on the percent change column for now. You don’t see any entry for January (the first observation) because you lose the first observation in percent change calculations.

Take the percent change for February 1, 2012, which is +2.54 percent. Apply the percent change formula to the exchange rates (E) in January and February:

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Another example is the percent change in the exchange rate in July 2012, which is a 2.1 percent decline:

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All other percent changes in the third column are calculated similarly.

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