Currency Rate Converter
Our free currency & finance converter handles currency rate conversions. See tables, ratios, and examples for quick reference.
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.
What is triangular arbitrage and how do cross rates make it possible?
Triangular arbitrage exploits a mismatch between a directly quoted cross rate and the synthetic cross rate implied by two dollar pairs. If EUR/JPY trades above EUR/USD multiplied by USD/JPY, a trader can buy euros with dollars, sell those euros for yen, and sell the yen back for dollars to finish with more dollars than they started with. Such gaps are tiny and short lived because algorithmic desks close them within milliseconds, but they are the mechanism that keeps quoted cross rates consistent with their dollar legs.
Why do JPY currency pairs measure pips at the second decimal place?
Pip size is chosen so that one pip represents a similarly small fraction of the quoted price, and because one yen is worth far less than one dollar or euro, a USD/JPY quote carries only two decimals rather than four. One pip is therefore 0.01 yen instead of 0.0001. Pairs quoted to three or five decimals add a fractional pip, often called a pipette, worth one tenth of a pip, which brokers use to advertise tighter spreads.
How is pip value calculated when the quote currency is not your account currency?
Pip value in the quote currency is the pip size multiplied by the position size, so a standard 100,000 unit lot of USD/JPY moves 0.01 times 100,000, or 1,000 yen, per pip. To express that in dollars you divide by the current USD/JPY rate, giving roughly 6.69 dollars at a rate of 149.50. For a pair with no dollar leg, convert the quote currency figure through the relevant cross rate before comparing risk across open positions.
Why does a cross rate conversion usually cost more than a direct one?
When a bank builds a cross rate from two dollar legs it crosses two bid-ask spreads instead of one, and each leg is marked away from the mid price in the bank's favour. A pair with deep interbank liquidity may cross for a fraction of a basis point, while an illiquid emerging market cross can carry a spread of many basis points. Comparing the all-in rate you are quoted against the synthetic mid rate is the quickest way to reveal the true markup.
What is the difference between a spot rate and a forward rate?
The spot rate settles almost immediately, conventionally two business days after the trade, while a forward rate fixes today the rate for settlement on a future date. A forward is not a forecast: it is the spot rate adjusted by the interest rate differential between the two currencies, an adjustment quoted as forward points. The currency with the higher interest rate trades at a forward discount, a relationship known as covered interest parity that arbitrage keeps in place.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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