Free · Exchange-rate arithmetic

Cross-Currency Rate with Explicit Quote Direction

Calculate a cross rate and reciprocal quotes from two exchange rates that share a reference currency.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

If one unit of A buys 4 units of C and one unit of B buys 2 units of C, then one unit of A buys 2 units of B.

B per A = (C per A) / (C per B); each reverse quote = 1 / forward quote

Worked example

Enter these known values and leave the other values blank.

Units of C per 1 A
4
Units of C per 1 B
2
Units of A per 1 C
0.25
Units of B per 1 C
0.5
Units of B per 1 A
2
Units of A per 1 B
0.5

Assumptions and limitations

  • All entered quotes must be positive and refer to the same market time and a compatible basis.
  • These are arithmetic mid-rate relationships. Bid/ask spreads, transaction fees, settlement timing and executable liquidity are not included.
  • Rates are entered manually; this tool does not fetch live quotes.

Common questions

Which direction is the cross-rate result?

The B-per-A result says how many units of B correspond to one unit of A. The reciprocal field shows A per B.

Can I enter the reciprocal quotes instead?

Yes. Enter A per C and B per C; the model calculates the forward directions and cross rate.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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