Formulas
Quote the rate as units of currency A per 1 unit of currency B (for example, 1.10 USD per EUR). If it moves from S₀ to S₁, B's change against A is (S₁ ÷ S₀ − 1) × 100. A's value in B is the reciprocal 1 ÷ S, so A's change is (S₀ ÷ S₁ − 1) × 100.
The two changes satisfy (1 + a)(1 + b) = 1, so they are not equal and opposite. A 25% rise in one currency is only a 20% fall in the other.
Worked example
The euro goes from 1.10 to 1.25 dollars. The euro appreciated (1.25 ÷ 1.10 − 1) = 13.64% against the dollar. The dollar went from 0.9091 to 0.8000 euros, a depreciation of (1.10 ÷ 1.25 − 1) = −12%.