Exchange Rate Math Calculator
Calculate currency conversions, fees, and cross rates instantly.
Understanding the Maths Behind Exchange Rates
Exchange rates determine the relative value between two different currencies. Whether you are a traveler planning a trip, an investor dealing in Forex, or a business handling international invoices, understanding the underlying mathematics is crucial for ensuring you get a fair deal. This guide breaks down the formulas used in our Exchange Rate Math Calculator.
The Core Formula
At its simplest level, converting currency involves multiplication. If you hold Currency A (Source) and wish to buy Currency B (Target), the formula is:
For example, if you have 1,000 Units of Currency A and the exchange rate is 1.25 (meaning 1 Unit of A = 1.25 Units of B), the math is: 1,000 × 1.25 = 1,250 Units of Currency B.
Calculating Fees and Commissions
In the real world, banks and exchange bureaus rarely trade at the "mid-market" rate without a markup. They usually apply a commission fee, which alters the math. Fees are typically calculated as a percentage of the source amount before conversion.
The mathematics for the fee calculation is:
Net Source Amount = Source Amount – Fee Amount
Using our previous example with a 2% fee: 1,000 × 0.02 = 20. Your Net Source Amount becomes 980. The conversion is then applied to this net amount: 980 × 1.25 = 1,225 Units.
Calculating the Inverse Rate
Often, you might see a rate quoted as A/B, but you need B/A. This is known as the inverse rate. Mathematically, this is the reciprocal of the original rate.
If 1 USD = 0.85 EUR, then 1 EUR = 1 / 0.85 USD, which equals approximately 1.176 USD.
What is the "Spread"?
The spread is the difference between the Buy (Bid) price and the Sell (Ask) price. The math behind the spread represents the profit margin for the broker. If a broker buys currency at 1.20 and sells it at 1.25, the spread is 0.05 (or 500 "pips" in forex terminology).