Cross Rate Calculator

Derive a cross rate from two quotes against a common currency, handling every combination of base and quote.

A cross rate is the exchange rate between two currencies worked out from what each of them is worth against a third, and a cross rate calculator exists because that number is so rarely quoted directly. If you have a quote for sterling against the dollar and a quote for the euro against the dollar, the sterling–euro rate is already implied by those two numbers; it just has not been written down yet. This Cross Rate Calculator will derive the exchange rate from that pair of quotes, which takes exactly one division or one multiplication — the entire difficulty is knowing which, and in which order.

Formula: cross = rate A / rate B when both share a quote currency, or A x B when they chain

Your figures

How your two quotes are arranged

A is the currency the cross is quoted for, B the currency it is quoted in, and C the currency both of your existing quotes have in common. Every quote reads as units of the second currency for one unit of the first.

First rate

The first quote in the arrangement chosen above — A/C, or C/A when the shared currency is the base of both.

Second rate

The second quote in the arrangement chosen above — B/C, C/B or C/B respectively.

Spread on the first leg

Your dealing spread on that quote, as a percentage of it. Leave blank to derive the cross from mid rates alone.

Spread on the second leg

The same for the second quote. Two legs mean two spreads, which is the substantive cost of assembling a cross rather than dealing it.

Results

Cross rate A/B

1.17593

A/C ÷ B/C — units of B for one unit of A

A/C as entered: 1.27000
B/C as entered: 1.08000
Arithmetic usedA/C is the number of C per A, and B/C is the number of C per B. Dividing the first by the second cancels the C and leaves B per A, which is the quote A/B. Dividing them the other way round would give A/B inverted.: A/C ÷ B/C
B/A — the cross invertedOne divided by the cross: the same rate quoted for the other currency.: 0.850394
A/B after both spreadsEach leg dealt on the side that costs you: the numerator lower, the denominator higher.: 1.17475
B/A after both spreads: 0.851245
Cost of crossingMid cross less the dealt cross, per unit of A, and the same figure as a percentage of the mid.: 0.00118 · 0.100%
Spreads enteredFirst leg, then second. Both are charged, because both legs are dealt.: 0.050% · 0.050%

What this means

A/C is the number of C per A, and B/C is the number of C per B. Dividing the first by the second cancels the C and leaves B per A, which is the quote A/B. Dividing them the other way round would give A/B inverted. On the rates entered that gives A/B = 1.17593, which inverts to 0.850394. Dealing each leg on the side that costs you turns the cross into 1.17475 — 0.00118 per unit of A, or 0.100% of the mid. That is the arithmetic of paying two spreads instead of one.

A/C = 1.27
B/C = 1.08
A/B = 1.27 ÷ 1.08 = 1.175926
B/A = 1 ÷ 1.175926 = 0.850394
After 0.05% on the first leg and 0.05% on the second, A/B = 1.174751
Every rate, spread and mark-up above is yours to enter. No rate is fetched and no bank's or broker's figure is preset — where a field opens with a number it is a round illustration to overwrite, because the rate that applies to a transaction is the one that account is actually dealt at.
A cross derived wrongly reads exactly like one derived correctly, which is why the cancellation is written out above. The check that settles every case is to read each quote as a ratio of units and see which currency cancels.
Take both quotes at the same moment. Two rates from different times build the gap between those timestamps into the cross.
A cross a provider quotes directly may be cheaper than assembling it from two trades, because the spread above is charged twice. Comparing the two is the reason to calculate this figure.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Cross Rate calculation

That is why this calculator asks first how your two quotes are arranged rather than asking for currency codes. Every FX cross calculation falls into one of three arrangements: the shared currency sits on the bottom of both quotes, on the top of both quotes, or on the bottom of one and the top of the other. Each arrangement has its own arithmetic, and the panel names the one it used and writes out why the shared currency cancels, because a cross rate derived the wrong way round looks exactly like one derived correctly.

The currencies are labelled A, B and C rather than picked from a list. A is the currency the cross is quoted for, B the currency it is quoted in, and C the currency your two existing quotes have in common. Letters make the cancellation visible in a way currency codes obscure, and they keep the calculator usable for pairs no dropdown would ever have included.

Both dealing spreads are optional inputs, and entering them is what turns a textbook mid rate into a number you could act on. Assembling a cross from two trades means crossing two spreads, not one, so the calculator applies each leg on the side that costs you and reports the gap between the mid cross and the dealt cross.

Cross Rate formula

both quotes share C as their quote currency   A/B = A/C ÷ B/C
both quotes share C as their base currency    A/B = C/B ÷ C/A
the two quotes chain end to end              A/B = A/C × C/B

inverse                                      B/A = 1 ÷ A/B

dealt cross (division)  = first × (1 − s₁ ÷ 100) ÷ (second × (1 + s₂ ÷ 100))
dealt cross (chain)     = first × (1 − s₁ ÷ 100) × second × (1 − s₂ ÷ 100)
cost of crossing        = mid cross − dealt cross

A: The currency the derived cross is quoted for — the one you are pricing. It ends up on the left of the answer, so the cross reads as units of B per unit of A.
B: The currency the derived cross is quoted in. The answer is denominated in this currency, and the inverse quote turns it into the base instead.
C: The currency your two existing quotes have in common — usually the US dollar, since most currencies are quoted against it. It cancels out of the arithmetic entirely and never appears in the answer.
X/Y notation: Units of Y for one unit of X. A/C at 1.2680 means one unit of A buys 1.2680 units of C. Every quote in the calculator is read this way, which is what makes the cancellation work.
s₁, s₂: The dealing spread on each leg, as a percentage of that leg's rate. A leg in the numerator is dealt lower and a leg in the denominator higher, because both moves are in the direction that costs you.

The currency cross rate formula is short enough to memorise, and the reliable way to settle its direction is to stop reading quotes as prices and start reading them as ratios of units. A/C means "units of C per unit of A", and B/C means "units of C per unit of B". Divide the first by the second and the C cancels top and bottom, leaving units of B per unit of A — which is precisely the quote A/B. Nothing about that argument requires knowing which currencies are involved or which is stronger; it is pure unit algebra, and it gives the same answer every time.

The same check disposes of the other two arrangements without any new ideas. When C is the base of both quotes you have units of A per C and units of B per C, so the C is underneath both and the division has to run the other way — the second rate over the first — to leave B on top and A underneath. When one quote has C on the bottom and the other has it on the top, the two chain end to end and the operation is a multiplication. That third case is the only one of the three that is not a division, which is exactly why it is the one people reach for a division on.

Spreads are applied per leg rather than as a single figure on the result, because that is what actually happens: assembling a cross means executing two trades, and each is dealt at the side of its own spread that suits the person quoting it. The consequence is worth internalising — the cost of crossing is very nearly the sum of the two spreads, so a broker who quotes the cross directly with one spread may well be cheaper than building it yourself, even at an apparently worse headline number. Comparing those two figures is the practical reason to derive a cross at all.

Cross Rate: a worked example

Deriving a sterling–euro cross from two dollar quotes: A/C at 1.2680 (sterling against the dollar) and B/C at 1.0850 (the euro against the dollar), so the shared currency C is the dollar and sits on the quote side of both, with dealing spreads of 0.10% on the first leg and 0.05% on the second.

ArrangementA/C and B/C — both quoted in the shared currency, so A/B = A/C ÷ B/C
Mid cross A/B1.2680 ÷ 1.0850 = 1.16866
Inverse B/A1 ÷ 1.16866 = 0.855678
First leg dealt down1.2680 × (1 − 0.10 ÷ 100) = 1.266732
Second leg dealt up1.0850 × (1 + 0.05 ÷ 100) = 1.0855425
Dealt cross A/B1.266732 ÷ 1.0855425 = 1.16691
Cost of crossing1.16866 − 1.16691 = 0.00175, or 0.150% of the mid

One unit of A is worth 1.16866 units of B on the mid, and 1.16691 once both legs are dealt. The 0.150% cost is almost exactly the 0.10% and 0.05% spreads added together, which is the point: crossing pays both, and a directly quoted cross only has to beat 0.150% to be the cheaper route.

How to use the Cross Rate calculator

Work out which currency your two quotes have in common — it is C, and it will not appear in the answer. For most pairs of quotes that currency is the US dollar.
Decide which of the other two currencies you want the calculator to derive the exchange rate for. That one is A; the remaining one is B, and the answer will read as units of B per unit of A.
Choose the arrangement that matches how your quotes are written. Both quoted in C means both look like something/C; both quoted from C means both look like C/something; the chain option is for one of each.
Enter the two rates in the order the chosen arrangement names, then read the "arithmetic used" row to confirm the calculator is dividing or multiplying the way you expected before trusting the number.
Take both quotes from the same moment. Rates from two different times build the gap between those timestamps into the cross, which shows up as an error you cannot see.
Enter a spread on each leg if you intend to trade the cross rather than just quote it, then compare the dealt cross against whatever your broker quotes for that pair directly.

Limitations of the Cross Rate calculator

Every calculation makes assumptions. These are the ones that matter here.

The cross is only as current as the two quotes it came from. Stale rates, or rates captured seconds apart in a fast market, produce a cross that never existed at any single instant.
Spreads are modelled as a symmetric percentage of each leg's mid. Real quotes are two-sided and often asymmetric, and they widen at the session roll and around scheduled news.
Commission, financing and any minimum ticket charge are excluded. On a small cross trade those can easily exceed the spread cost calculated here.
A derived cross is a fair value, not an executable price. Whether you can deal at it depends on liquidity in both legs at the size you want, which no rate arithmetic can tell you.
The calculator does not verify that your two quotes genuinely share a currency. Enter unrelated rates and it will produce an arithmetically valid number that means nothing.

Frequently asked questions about Cross Rate

How do I know which arrangement my two quotes are in?

Write both quotes down and look at where the shared currency sits. If it is the second currency in both — such as GBP/USD and EUR/USD — they share a quote currency and the operation is a division. If it is the first in both, such as USD/CHF and USD/JPY, they share a base and the division runs the other way. If it is second in one and first in the other, they chain and you multiply.

Why is my derived cross different from the rate my broker quotes?

Two reasons, and they pull in opposite directions. Timing accounts for small gaps: your two quotes were captured at slightly different moments from the ones the broker used. Spread accounts for larger ones: a directly quoted cross carries one spread while a derived one carries two, so the broker's dealable price can be better than your assembled price even when their mid looks worse.

Do the two spreads add together or compound?

They compound, but so gently that adding them is a good approximation at realistic sizes. Dealing 0.10% down on the numerator and 0.05% up on the denominator costs 1 − 0.999 ÷ 1.0005, which is 0.14993% rather than a flat 0.15%. The gap only becomes visible when the spreads themselves are wide, which is precisely when the cost matters enough to compute exactly.

Can a triangular rate calculator find arbitrage between the derived and the quoted cross?

Almost never in practice. Triangular relationships are among the most heavily watched in any market, and apparent gaps in retail quotes are usually explained by timestamps, by the fact that you are comparing a mid against a dealable price, or by the two spreads you would cross to capture it. The realistic use of this calculation is choosing the cheaper of two execution routes, not finding free money.

Why does the calculator use A, B and C instead of currency codes?

Because a list of currency codes is always a list of the currencies somebody thought to include, and the ones people ask about are frequently the ones missing. Letters make the tool work for any three currencies at all, and they make the cancellation legible: seeing the C disappear from both halves of A/C ÷ B/C explains the direction far better than watching USD vanish from a formula.

Last reviewed 29 August 2026. See our methodology and editorial policy.

More forex calculators