Most beginners start with pairs that include the US dollar, such as EUR/USD or USD/JPY. Sooner or later you meet the crosses: EUR/GBP, GBP/JPY, AUD/NZD, EUR/CHF and many others. A cross is simply a pair that does not contain the US dollar. This article shows how crosses are priced, how to calculate one yourself, and why understanding them reveals exposure you might not know you have. All numbers below are illustrative.
The idea: the dollar sits in the middle
Historically, most currency trading flowed through the dollar. To swap Swiss francs for Japanese yen, a dealer would sell francs for dollars and then sell dollars for yen. Today direct crosses trade actively, but the logic of the dollar as a common denominator still holds: the price of a cross must be consistent with the two dollar pairs behind it. If it were not, traders and algorithms could lock in a risk-free profit, and such gaps vanish within moments.
The arithmetic
There are three cases, depending on how the dollar pairs are quoted.
1. Dollar is the quote currency in both. For EUR/GBP, take EUR/USD and divide by GBP/USD.
Illustrative: EUR/USD = 1.1200 and GBP/USD = 1.3200. Then EUR/GBP = 1.1200 / 1.3200 = 0.8485.
2. Dollar is the base in one and the quote in the other. For GBP/JPY, multiply GBP/USD by USD/JPY.
Illustrative: GBP/USD = 1.3200 and USD/JPY = 157.00. Then GBP/JPY = 1.3200 x 157.00 = 207.24.
3. Dollar is the base in both. For CHF/JPY, divide USD/JPY by USD/CHF.
Illustrative: USD/JPY = 157.00 and USD/CHF = 0.8900. Then CHF/JPY = 157.00 / 0.8900 = 176.40.
A simple memory aid: write the target pair as a fraction and make the dollar cancel. EUR/GBP is (EUR/USD) divided by (GBP/USD) because the USD terms cancel. The same approach works for any cross.
Worked example: reading a move
Say GBP/JPY rises from 207.24 to 209.30 in a day. Is that a pound story, a yen story or a dollar story? Decompose it. If GBP/USD was unchanged at 1.3200 and USD/JPY rose from 157.00 to 158.56, the whole move came from yen weakness against the dollar, and the pound did nothing. If instead USD/JPY was flat and GBP/USD rose to 1.3330, it was a sterling move. Often both contribute. This decomposition is useful because it points you to the right news: a Bank of Japan headline or a UK data release.
Hidden dollar exposure
A cross has no dollar in its name, but a position in it is economically a combination of two dollar positions. Buying GBP/JPY is like buying GBP/USD and buying USD/JPY at the same time: you are long the pound and short the yen, with the dollar legs cancelling out. In practice, the dollar's own moves still influence crosses through liquidity and through how each currency reacts to dollar swings. When you hold several positions, check whether they stack the same idea. Being long GBP/JPY and long AUD/JPY, for instance, is a double bet on yen weakness. Our guide to currency correlation shows how to measure the overlap.
Why crosses can behave differently
- Wider spreads. Many crosses are less liquid than the majors, so spreads are often wider, particularly in off-hours. The true cost matters; see spreads and slippage.
- Different volatility. GBP/JPY has a reputation for large swings because it combines two currencies that can each move sharply. EUR/CHF, by contrast, has historically been a lower-volatility pair, though it can gap on central bank surprises. Check the actual range with an ATR reading before choosing a stop distance.
- Cleaner relative-value views. If you want to express a view on the Bank of England versus the ECB without taking a dollar view, EUR/GBP is the direct instrument. It strips out much of the dollar noise.
- Session timing. Crosses are most active when both currencies' home markets are open. EUR/GBP is liveliest in the London morning, AUD/NZD in the Asia-Pacific session. Compare with forex trading sessions.
Position sizing for crosses
The pip value of a cross is quoted in the second currency, so it must be converted to your account currency. For GBP/JPY, a pip is denominated in yen. If your account is in Canadian dollars you need the JPY to CAD rate to know what a pip is worth. Brokers' calculators do this, but understand the logic, because it means your risk on a cross shifts slightly as the conversion rate changes. Review pip value and position sizing before trading an unfamiliar cross.
Arbitrage and why you cannot profit from the formula
Some newcomers wonder whether they can exploit tiny mismatches between a cross and its implied price. Professionals and algorithms do this at speeds and costs retail traders cannot match. The formula is for understanding and for sanity-checking prices, not for beating the market.
Checklist before trading a cross
- Decompose the cross into its two dollar legs and know which news drives each.
- Check whether your other open positions share either leg.
- Compare the spread with a major to see the real cost.
- Confirm pip value in your account currency.
- Verify typical daily range so your stop is not inside normal noise.
Bottom line
A cross is a dollar-free label on a dollar-linked price. Knowing the arithmetic lets you check quotes, split a move into its sources, and see the exposure you actually carry. It is a few lines of multiplication or division, and it makes you a more informed trader.
This article is educational and is not investment advice. All prices are illustrative.