Currency Rate Converter
Our free currency & finance converter handles currency rate conversions. See tables, ratios, and examples for quick reference.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Currency Rate Converter
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Formula: Cross Rate = Rate A x Rate B | Inverse = 1 / Rate
Worked example — EUR/JPY = 162.2075 (1 EUR = 162.21 JPY)
Formula
Cross Rate = Rate A x Rate B | Inverse = 1 / Rate
The cross rate between two currencies is found by multiplying their respective rates against a common third currency (usually USD). For example, EUR/JPY = EUR/USD * USD/JPY. The inverse rate is simply 1 divided by the original rate, which gives the conversion factor in the opposite direction.
Worked Examples
Example 1: Calculating EUR/JPY Cross Rate
Problem:EUR/USD is 1.0850 and USD/JPY is 149.50. What is the EUR/JPY cross rate?
Solution:Cross rate = EUR/USD * USD/JPY = 1.0850 * 149.50 = 162.2075 Inverse = 1 / 162.2075 = 0.006165
Result:EUR/JPY = 162.2075 (1 EUR = 162.21 JPY)
Example 2: Converting Amount via Cross Rate
Problem:Convert 5,000 EUR to JPY using the cross rate above.
Solution:JPY = EUR * Cross Rate = 5,000 * 162.2075 = 811,037.50 JPY
Result:5,000 EUR = 811,037.50 JPY at cross rate 162.2075
Frequently Asked Questions
What is a currency cross rate?
A cross rate is the exchange rate between two currencies calculated through a third common currency, typically the US dollar. For example, if you know the EUR/USD rate and the USD/JPY rate, you can calculate the EUR/JPY cross rate by multiplying them. Cross rates are essential in forex trading because not all currency pairs are directly quoted on exchanges. The interbank market primarily quotes major pairs against the USD, and cross rates are derived mathematically from these direct quotes.
What is the difference between direct and indirect currency quotes?
A direct quote expresses the domestic currency price of one unit of foreign currency, such as 1 EUR = 1.085 USD from a US perspective. An indirect quote is the inverse, expressing the foreign currency price of one unit of domestic currency, such as 1 USD = 0.9217 EUR. The convention varies by country and currency pair. EUR, GBP, AUD, and NZD are typically quoted as the base currency against USD, while USD is the base against JPY, CHF, and CAD. Understanding quote conventions prevents costly miscalculations in forex trading.
What are pips and basis points in currency trading?
A pip (percentage in point) is the smallest standard price movement in a currency pair, typically the fourth decimal place (0.0001) for most pairs or the second decimal place (0.01) for JPY pairs. A basis point is one hundredth of a percentage point (0.01%). In forex, one pip in EUR/USD equals roughly $10 per standard lot (100,000 units). Basis points are more commonly used when discussing interest rate changes. A 25 basis point rate hike means a 0.25% increase, which can significantly impact exchange rates.
How do I calculate the inverse of an exchange rate?
To calculate the inverse exchange rate, simply divide 1 by the original rate. If EUR/USD is 1.0850, the inverse USD/EUR rate is 1 / 1.0850 = 0.9217. This means each US dollar buys 0.9217 euros. The inverse is useful when you need to convert in the opposite direction. Be careful with precision when inverting rates, as small rounding errors in the original rate can become amplified in the inverse. Always use at least 4-6 decimal places for accurate forex calculations.
Why are cross rates important in international business?
Cross rates are crucial for businesses operating in multiple countries because they enable direct conversion between non-USD currencies without physically routing through the dollar. A European company paying a Japanese supplier needs the EUR/JPY rate, which is calculated from EUR/USD and USD/JPY. Banks often charge an additional spread on cross rate conversions since two separate trades are effectively being made. Understanding cross rates helps businesses compare quotes from different banks and identify the most cost-effective conversion paths.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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