About

A cross exchange rate is the rate between two currencies, neither of which is the official currency of the country where the quote is given. In practice, most currency pairs do not trade directly against each other. Instead, they are quoted through an intermediary - typically USD. If you know the rate of A per USD and B per USD, the cross rate A/B is derived by division. Getting this wrong in a multi-leg FX transaction compounds rounding errors and can result in measurable P&L slippage on large notional amounts. This calculator performs triangulated cross rate derivation, computes bid/ask spreads from configurable basis points, and displays the full intermediary path so you can audit the arithmetic.

The tool fetches live spot rates from a public API and falls back to a built-in reference matrix when offline. Note: rates shown are mid-market indicative rates. Your actual execution rate will differ due to dealer spread, liquidity, and settlement timing. For exotic pairs with thin liquidity, the effective spread can be 50 - 200 basis points wider than majors.

Formulas

The cross exchange rate between two currencies A and B is derived through a common intermediary currency I (typically USD):

Cross Rate_A/B = Rate_A/IRate_B/I

The bid and ask prices incorporate a spread measured in basis points (bps). One basis point equals 0.0001 of the quote currency. The half-spread h is applied symmetrically:

h = spread_bps20000

Bid = Mid × (1 − h)

Ask = Mid × (1 + h)

For the converted amount:

Result = Amount × Cross Rate_A/B

Where Rate_A/I = units of currency A per 1 unit of intermediary I. spread_bps = total bid-ask spread in basis points. Mid = the mid-market cross rate before spread adjustment.

Reference Data

Currency	Code	Region	Typical Spread (bps)	Daily Volume (USD bn)	Category
US Dollar	USD	United States	0 - 1	6,600	Reserve
Euro	EUR	Eurozone	1 - 3	2,300	Major
Japanese Yen	JPY	Japan	1 - 3	1,200	Major
British Pound	GBP	United Kingdom	1 - 4	970	Major
Australian Dollar	AUD	Australia	2 - 5	470	Major
Canadian Dollar	CAD	Canada	2 - 5	430	Major
Swiss Franc	CHF	Switzerland	2 - 4	390	Major
Chinese Yuan	CNY	China	3 - 8	340	Restricted
Swedish Krona	SEK	Sweden	3 - 8	130	Minor
New Zealand Dollar	NZD	New Zealand	3 - 7	120	Minor
Mexican Peso	MXN	Mexico	5 - 15	110	EM
Singapore Dollar	SGD	Singapore	2 - 6	100	Minor
Hong Kong Dollar	HKD	Hong Kong	1 - 3	95	Pegged
Norwegian Krone	NOK	Norway	3 - 8	90	Minor
South Korean Won	KRW	South Korea	5 - 12	80	EM
Turkish Lira	TRY	Turkey	10 - 30	70	EM
Indian Rupee	INR	India	5 - 15	65	Restricted
Russian Ruble	RUB	Russia	10 - 50	45	EM
Brazilian Real	BRL	Brazil	8 - 20	55	EM
South African Rand	ZAR	South Africa	5 - 15	50	EM
Danish Krone	DKK	Denmark	2 - 5	48	Minor
Polish Zloty	PLN	Poland	5 - 12	40	EM
Thai Baht	THB	Thailand	5 - 15	35	EM
Israeli Shekel	ILS	Israel	4 - 10	25	Minor
Czech Koruna	CZK	Czech Republic	5 - 12	22	EM
Philippine Peso	PHP	Philippines	8 - 20	15	EM
UAE Dirham	AED	UAE	1 - 3	18	Pegged
Saudi Riyal	SAR	Saudi Arabia	1 - 3	16	Pegged
Hungarian Forint	HUF	Hungary	6 - 15	12	EM
Colombian Peso	COP	Colombia	10 - 25	8	Exotic

Frequently Asked Questions

You can, but only if both quotes share the same base currency. If EUR/USD = 1.08 and GBP/USD = 1.27, dividing gives EUR/GBP = 1.08/1.27 ≈ 0.8504 because both are quoted per 1 USD. If the base currencies differ (e.g., USD/JPY and EUR/USD), you must invert one rate first. This calculator handles that normalization automatically using the selected intermediary.

Each basis point equals 0.01% of the notional amount. On a 1,000,000 EUR cross trade with a 10 bps spread, the cost is approximately 1,000,000 × 0.001 = 1,000 EUR round-trip. For exotic pairs where spreads reach 50-200 bps, this cost scales to 5,000-20,000 EUR per million. The calculator shows both bid and ask so you can see the full round-trip cost.

Triangulation through a volatile intermediary introduces basis risk. If you compute EUR/JPY through USD, and USD moves 0.5% between the two leg executions, your effective cross rate shifts by roughly that amount. For large institutional trades, this is mitigated by executing both legs simultaneously. This tool computes a snapshot rate; real execution requires time-stamped quotes from your dealer.

No. These are mid-market indicative rates sourced from a public aggregator (Open Exchange Rates API). For accounting, you should use your central bank's official fixing rate or the rate stipulated in your contract. Many jurisdictions (e.g., IAS 21) require the rate at the transaction date, not an average. Use this tool for estimation and triangulation logic verification only.

Both KRW and JPY are low-denomination currencies. 1 USD ≈ 1,300 KRW and ≈ 150 JPY, so 1 KRW ≈ 0.115 JPY and 1 JPY ≈ 8.67 KRW. The cross rate reflects the genuine economic ratio. If the number seems unwieldy, switch the pair direction using the swap button, or convert a specific amount rather than reading the unit rate.

Yes. The calculator lets you select any currency as the intermediary. EUR is a common alternative for European cross pairs (e.g., SEK/NOK through EUR). The mathematical result should be identical regardless of intermediary, assuming consistent rate sources. In practice, minor differences arise from rate staleness and quote timing across different base pairs.