Currency & Forex
Intermediate

Cross Rate

Derive the exchange rate between two currencies via a common third currency.

Formula

RateA/C=RateA/B×RateB/CRate_{A/C} = Rate_{A/B} \times Rate_{B/C}

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Variables

Rate_{A/C}Cross rate
Rate_{A/B}A per B
Rate_{B/C}B per C

Example

EUR/GBP = EUR/USD ÷ GBP/USD

How it works

A cross rate lets you work out the value of one currency relative to another when you already know each of them relative to a shared third currency. The idea is that the shared currency acts like a bridge: multiplying by one rate and dividing by the other cancels out the common unit, leaving the direct A-to-C exchange rate. This is especially useful in forex markets because not every currency pair is quoted directly all the time.

When to use it

Use this when you need the exchange rate between two currencies that are not directly quoted, but both are quoted against a common base currency such as USD. It is also useful for checking whether a quoted cross rate is consistent with the underlying market rates.

Worked example, step by step

Suppose 1 GBP = 1.27 USD and 1 CAD = 0.74 USD. We want the cross rate GBP/CAD, meaning how many Canadian dollars equal 1 British pound. First write both rates against USD: GBP/USD = 1.27 and CAD/USD = 0.74. To get GBP/CAD, divide the GBP/USD rate by the CAD/USD rate: GBP/CAD = 1.27 ÷ 0.74. GBP/CAD = 1.7162. So, 1 GBP ≈ 1.72 CAD.

Common mistakes to avoid

  • Using the wrong direction for the division and reversing the quote
  • Mixing up which currency is the base and which is the quote
  • Forgetting to keep the units consistent when converting through the common currency

Did You Know?

Before the euro, most European cross rates were computed through the US dollar as the pivot currency.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026