How to Calculate Currency Appreciation
Currency appreciation equals (new exchange rate − old exchange rate) ÷ old exchange rate × 100, with the rate quoted per one unit of that currency.
The Currency Appreciation formula
Calculator
Get the appreciation percent from two rates, plus the different percentage the other currency moved.
Foreign currency per 1 unit of the currency you are tracking, before the move.
The same quote after the move, written the same way round.
Each unit now buys 1 of the other currency instead of 0.8, a change of 25%.
- Change in the other currency
- −20%
- Old rate, quoted the other way
- 1.25
- New rate, quoted the other way
- 1
- Gap between the two percentages
- 5 points
- Reading
- Appreciation
The other currency moved −20%, not the mirror of 25%, because each percentage divides by its own starting rate.
One unit of the other currency used to cost this much of the currency you are tracking.
The same quote after the move, which is the denominator the other side's percentage never uses.
The two figures differ by 5 percentage points, which is why copying one across as the other loses marks.
Positive means the tracked currency appreciated, so each unit buys more foreign currency than before.
How to calculate Currency Appreciation, step by step
- 1Pick the currency you are tracking. Decide whose appreciation you want, because the answer changes depending on which currency sits in the denominator.
- 2Quote both rates the same way. Write the old and new rates as units of the other currency per one unit of the currency you are tracking, flipping either quote if needed.
- 3Subtract and divide. Take (new rate − old rate) and divide by the old rate.
- 4Convert to a percent. Multiply by 100. A positive number means the currency appreciated, so each unit now buys more foreign currency.
- 5Do not mirror the percentage. The other currency's percentage change is a different number, so recompute it with that currency in the denominator.
Worked example: Currency Appreciation
Suppose an illustrative rate moves from 1 dollar = 0.80 euros to 1 dollar = 1.00 euros. The dollar appreciated by (1.00 − 0.80) ÷ 0.80 × 100 = 25%. Now flip the quote to see the euro: it started at 1 euro = 1 ÷ 0.80 = $1.25 and ended at 1 euro = 1 ÷ 1.00 = $1.00, so the euro changed by (1.00 − 1.25) ÷ 1.25 × 100 = −20%. The euro depreciated 20% while the dollar appreciated 25%, and that gap is the classic trap: the two percentages never match because each divides by its own starting value.
Currency Appreciation questions
What is the formula for currency appreciation?
Appreciation % = (new rate − old rate) ÷ old rate × 100, where the rate is quoted as foreign currency per one unit of the currency you are tracking.
If the dollar appreciates 25%, does the euro depreciate 25%?
No, the euro depreciates 20%. The percentage is calculated on the euro's own starting value of $1.25 per euro, not on the dollar's starting value.
What causes a currency to appreciate?
Anything that raises demand for the currency does it: stronger export sales, higher real interest rates that pull in financial inflows, more foreign investment, or expectations that the currency will rise.
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