Cross Rate Calculation
Multiply or divide, then pick the side the bank deals at in each leg.
A cross rate is an exchange rate between two currencies worked out through a third. Indian banks deal most actively in USD/INR, and the world market quotes most currencies against the US dollar, so a bank quoting EUR/INR to a customer usually builds it from EUR/USD and USD/INR.
The method is mechanical, but two-way quotes punish anyone who multiplies the wrong sides. The whole skill is choosing which side of each quote to use.
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The Method
- 1
Write both quotes with the common currency visible
EUR/USD and USD/INR share USD: one has it as the quote currency, the other as the base.
- 2
Decide: multiply or divide
If the common currency is the quote in one pair and the base in the other (EUR/USD and USD/INR), multiply. If it is the base in both (USD/JPY and USD/INR), divide.
- 3
For a two-way quote, follow the bank
Ask what the bank does in each leg. To buy EUR against INR, the bank buys EUR for USD and then sells those USD for INR. Each leg uses the side at which the market will deal with the bank.
- 4
Sanity-check the spread
A cross rate's spread is always wider than either input's, because it carries both spreads.
Worked Example 1: Multiply (Illustrative Figures)
EUR/USD 1.1600/1.1605 and USD/INR 88.4800/88.5200. Find EUR/INR.
Bid (bank buys EUR)
Calculation
EUR/USD bid × USD/INR bid = 1.1600 × 88.4800
Result
102.6368
Ask (bank sells EUR)
Calculation
EUR/USD ask × USD/INR ask = 1.1605 × 88.5200
Result
102.7275
Two-way cross
Calculation
Result
EUR/INR 102.6368/102.7275
| Side | Calculation | Result |
|---|---|---|
| Bid (bank buys EUR) | EUR/USD bid × USD/INR bid = 1.1600 × 88.4800 | 102.6368 |
| Ask (bank sells EUR) | EUR/USD ask × USD/INR ask = 1.1605 × 88.5200 | 102.7275 |
| Two-way cross | EUR/INR 102.6368/102.7275 |
Worked Example 2: Divide (Illustrative Figures)
USD/JPY 150.00/150.10 and USD/INR 88.4800/88.5200. Find the rupee rate for 100 yen.
Bid (bank buys JPY)
Calculation
USD/INR bid ÷ USD/JPY ask × 100 = 88.48 ÷ 150.10 × 100
Result per 100 JPY
58.9474
Ask (bank sells JPY)
Calculation
USD/INR ask ÷ USD/JPY bid × 100 = 88.52 ÷ 150.00 × 100
Result per 100 JPY
59.0133
Two-way cross
Calculation
Result per 100 JPY
₹58.9474/59.0133 per 100 JPY
| Side | Calculation | Result per 100 JPY |
|---|---|---|
| Bid (bank buys JPY) | USD/INR bid ÷ USD/JPY ask × 100 = 88.48 ÷ 150.10 × 100 | 58.9474 |
| Ask (bank sells JPY) | USD/INR ask ÷ USD/JPY bid × 100 = 88.52 ÷ 150.00 × 100 | 59.0133 |
| Two-way cross | ₹58.9474/59.0133 per 100 JPY |
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Why Division Crosses the Sides
When you divide, the ask of the divisor pairs with the bid of the numerator. A larger divisor gives a smaller result, so the lowest possible JPY/INR comes from the lowest rupees per dollar (USD/INR bid) and the most yen per dollar (USD/JPY ask). That lowest number is the bank's buying rate. The reasoning reverses for the selling rate.
The yen result is stated per 100 units because FEDAI Rule 5.7 lets merchant rates be quoted per 1 or per 100 units of foreign currency, and per 100 keeps small-value currencies readable.
How CCFE Tests This
Questions give two quotes and four answer options that differ only in which sides were combined. The trap options multiply bid by ask, or divide bid by bid. Work out which side the bank uses in each leg before touching the numbers, and check that your bid is below your ask. Single-rate versions (no spread) test only the multiply-or-divide choice.
FAQs
What is a cross rate in forex?expand_more
An exchange rate between two currencies derived from each one's rate against a third currency, usually the US dollar.
How do you calculate EUR/INR from EUR/USD and USD/INR?expand_more
Multiply. For a two-way quote, bid × bid gives the EUR/INR bid and ask × ask gives the EUR/INR ask.
When do you divide to get a cross rate?expand_more
When the common currency is the base in both quotes, such as USD/JPY and USD/INR. Then the bid uses USD/INR bid ÷ USD/JPY ask, and the ask uses USD/INR ask ÷ USD/JPY bid.
Does FEDAI publish cross rates?expand_more
Banks compute their own customer cross rates. The daily reference rates for USD/INR and other major currencies are published by FBIL, which took over that role from RBI in July 2018.
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