How to Calculate Currency Cross Rates

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This calculator helps you determine the exchange rate between two currencies when their direct rate is not readily available. Instead, we use a common third currency as an intermediary. For example, if you want to find the EUR/AUD rate but only have EUR/USD and AUD/USD rates, you can use USD as the intermediary.

How to Calculate Currency Cross Rates

The principle behind cross rate calculation is straightforward. If you have the exchange rates for Currency A against Currency C (A/C) and Currency B against Currency C (B/C), you can derive the exchange rate for Currency A against Currency B (A/B).

Scenario 1: Both given rates are quoted against the same base currency (e.g., USD).

  • You have A/USD and B/USD.
  • To find A/B, you can use the formula: A/B = (A/USD) / (B/USD)
  • Alternatively, if you have USD/A and USD/B, you can find A/B by: A/B = (USD/A) * (B/USD)

Scenario 2: One given rate involves the target base currency (e.g., A/C) and the other involves the target quote currency as the base (e.g., B/C).

  • You have A/C and B/C.
  • To find A/B, you can use the formula: A/B = (A/C) * (C/B). Note that if you only have B/C, you'll need to invert it to C/B.

Let's use the first scenario for this calculator, where we use a common intermediary currency.







function calculateCrossRate() { var currency1Amount = parseFloat(document.getElementById("currency1_amount").value); var currency1ToBaseRate = parseFloat(document.getElementById("currency1_to_base_rate").value); var currency2ToBaseRate = parseFloat(document.getElementById("currency2_to_base_rate").value); var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous results if (isNaN(currency1Amount) || isNaN(currency1ToBaseRate) || isNaN(currency2ToBaseRate)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (currency1ToBaseRate === 0 || currency2ToBaseRate === 0) { resultDiv.innerHTML = "Exchange rates cannot be zero."; return; } // Calculate the amount of the base currency equivalent to currency1Amount var baseCurrencyEquivalent = currency1Amount * currency1ToBaseRate; // Calculate the cross rate of Currency 1 to Currency 2 // Cross Rate (C1/C2) = (C1/Base) / (C2/Base) var crossRateC1toC2 = currency1ToBaseRate / currency2ToBaseRate; // Calculate the amount of Currency 2 equivalent to currency1Amount var currency2Amount = baseCurrencyEquivalent / currency2ToBaseRate; resultDiv.innerHTML = "

Results:

" + "Amount of Currency 1: " + currency1Amount.toFixed(2) + "" + "Exchange Rate (C1 to Base): " + currency1ToBaseRate.toFixed(4) + "" + "Exchange Rate (C2 to Base): " + currency2ToBaseRate.toFixed(4) + "" + "
" + "Calculated Cross Rate (Currency 1 per Currency 2): " + crossRateC1toC2.toFixed(6) + "" + "This means " + currency1Amount.toFixed(2) + " of Currency 1 is equivalent to approximately " + currency2Amount.toFixed(2) + " of Currency 2."; }

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