Calculate exchange rates: formula, direction and examples
Convert euros and foreign currencies, calculate reciprocals and avoid common mistakes in rate direction and rounding.
The units determine the calculation
An exchange rate expresses the price of one currency in another. EUR/USD lists the base currency, the euro, first and the quote currency, the US dollar, second. A value of 1.10 means one euro equals USD 1.10 in the calculation. The number alone is therefore insufficient. Only the direction tells you whether to multiply or divide. All figures on this page are hypothetical examples, not current rates.
Convert euros into a foreign currency
The formula is: source amount × target currency rate per unit of source currency = target amount. At a hypothetical rate of USD 1.10 per EUR, EUR 250 gives USD 275. Checking the units helps: euros multiplied by dollars per euro gives dollars. Our converter performs this step and also displays the rate used and its date.
Use the reciprocal for the reverse direction
To convert USD 275 back into euros, divide by 1.10 to obtain EUR 250. Equivalently, multiply by the reciprocal 1 ÷ 1.10. Avoid rounding it before calculating: 0.91 instead of 0.909090… already changes the result slightly. In a real exchange, reversing the transaction need not recover the same amount, because buy and sell rates and fees may differ.
Compare two foreign currencies through the euro
If USD and CHF are each quoted per euro, a cross rate can be calculated. Suppose one euro equals USD 1.10 and CHF 0.95. One dollar then equals 0.95 ÷ 1.10 = CHF 0.863636… For USD 200, that is approximately CHF 172.73. Historical comparisons require both source rates to be from the same observation day; otherwise, you would mix different points in time.
Avoid these input mistakes
Enter amounts using the English format: 1,000.50 means one thousand and fifty cents. A comma separates thousands; a full stop is the decimal separator. Select the source and target currencies, then check the “1 … = …” line. The result is guidance without fees. An executed payment is governed by your provider's statement.
Understand the calculation
The numerical examples are hypothetical. How the converter works explains the calculation and its limits.