Calculate cross exchange rates by entering any two of A:B, A:C, and B:C to find the missing pair and see calculation steps clearly.
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Cross Exchange Rate Formula
A cross exchange rate uses two exchange rates that share a common currency to calculate the exchange rate between the other two currencies. In this calculator, currencies are labeled A, B, and C.
- A:B = the exchange rate between currency A and currency B
- A:C = the exchange rate between currency A and currency C
- B:C = the exchange rate between currency B and currency C
The calculator works by taking any two known exchange rates and solving for the missing one:
- If A:C and B:C are known, it calculates A:B by dividing A:C by B:C.
- If A:B and B:C are known, it calculates A:C by multiplying A:B by B:C.
- If A:C and A:B are known, it calculates B:C by dividing A:C by A:B.
Common Cross Rate Setups
The same formulas apply to any currencies as long as the rates are quoted in the same direction.
| Known rates | Missing rate | Formula to use |
|---|---|---|
| A:C and B:C | A:B | A:B = A:C ÷ B:C |
| A:B and B:C | A:C | A:C = A:B × B:C |
| A:C and A:B | B:C | B:C = A:C ÷ A:B |
Interpreting the Rate Direction
| Rate format | Meaning | Example |
|---|---|---|
| A:B = 1.2500 | 1 unit of A equals 1.2500 units of B | 1 A = 1.2500 B |
| A:C = 0.9000 | 1 unit of A equals 0.9000 units of C | 1 A = 0.9000 C |
| B:C = 0.7200 | 1 unit of B equals 0.7200 units of C | 1 B = 0.7200 C |
Example
Example 1: Calculate A:B
Suppose A:C = 1.0800 and B:C = 0.9000.
So, A:B = 1.2000.
Example 2: Calculate B:C
Suppose A:C = 1.3500 and A:B = 1.5000.
So, B:C = 0.9000.
FAQ
What is a cross exchange rate?
A cross exchange rate is the exchange rate between two currencies calculated through a third currency. For example, if you know A:C and B:C, you can calculate A:B because both rates share currency C.
Why does the direction of the exchange rate matter?
The direction matters because A:B is not the same as B:A. If A:B = 1.2500, then 1 A equals 1.2500 B. The reverse rate is B:A = 1 ÷ 1.2500 = 0.8000. Enter each rate in the same direction shown by the calculator labels.
Can a cross exchange rate include fees or spreads?
The formula gives the mathematical cross rate from the exchange rates you enter. If a bank, broker, or exchange service applies a spread or fee, the actual rate offered may be different from the calculated cross rate.
