Cross Exchange Rate Calculator
From two currencies' rates against a common quote currency, derive the cross rate between them — in both directions.
輸入資料
計算結果
重點速覽：Cross rate = indirect rate between two currencies via a common intermediary B (usually USD). A-to-C = (A-to-B) / (C-to-B); C-to-A is its reciprocal (product = 1). Used when no direct quote exists. Example: USD/HKD 7.8, EUR/HKD 8.5 → USD/EUR = 7.8/8.5 ≈ 0.9176. WARNING: Pure mid-rate math; real FX adds bid-ask spreads and fees, rates move; reference only, not advice.
計算公式
A 兌 C 匯率 = (A 兌 B 匯率) ÷ (C 兌 B 匯率)。
C 兌 A 匯率 = (C 兌 B 匯率) ÷ (A 兌 B 匯率)。
兩個匯率互為倒數:crossAC × crossCA = 1。
$$A 兌 C 匯率：$Cross_{A/C}=\dfrac{Rate_{A/B}}{Rate_{C/B}}$$$$$C 兌 A 匯率：$Cross_{C/A}=\dfrac{Rate_{C/B}}{Rate_{A/B}}$$$$$互為倒數：$Cross_{A/C}\times Cross_{C/A}=1$$$使用說明
- Enter A's rate against common B.
- Enter C's rate against the same B.
- View the A-to-C and C-to-A cross rates.
以共同貨幣 B 推算 A 兌 C 與 C 兌 A 的交叉匯率
| A 兌 B | C 兌 B | A 兌 C | C 兌 A | 兩者乘積 |
|---|---|---|---|---|
| 7.8 | 8.5 | 0.9176 | 1.0897 | 1 |
| 7.8 | 6.5 | 1.2000 | 0.8333 | 1 |
| 1.08 | 1.27 | 0.8504 | 1.1759 | 1 |
理財情境案例
案例一：用共同貨幣推算交叉匯率
假設 A 兌 B 匯率為 7.8 (即 1 單位 A = 7.8 單位 B),C 兌 B 匯率為 8.5 (即 1 單位 C = 8.5 單位 B)。想知道 A 兌 C 的匯率。
A 兌 C = (A 兌 B) ÷ (C 兌 B) = 7.8 ÷ 8.5 ≈ 0.9176；C 兌 A = (C 兌 B) ÷ (A 兌 B) = 8.5 ÷ 7.8 ≈ 1.0897。驗證：0.9176 × 1.0897 ≈ 1。
解讀：透過共同貨幣 B，我們算出 1 單位 A ≈ 0.9176 單位 C，反過來 1 單位 C ≈ 1.0897 單位 A。兩個方向的匯率互為倒數，相乘等於 1——這是交叉匯率必然成立的關係，可用來檢查計算是否正確。
案例二：兩種主要貨幣的交叉匯率
外匯報價中，歐元與英鎊常以美元報價：EUR/USD = 1.08 (1 歐元 = 1.08 美元)、GBP/USD = 1.27 (1 英鎊 = 1.27 美元)。想知道歐元兌英鎊 (EUR/GBP)。
以美元為共同貨幣 B：EUR 兌 GBP = 1.08 ÷ 1.27 ≈ 0.8504；GBP 兌 EUR = 1.27 ÷ 1.08 ≈ 1.1759。
解讀：1 歐元約可兌換 0.8504 英鎊，1 英鎊約可兌換 1.1759 歐元。這正是外匯市場推算『非美元貨幣對』的標準做法——先各自取得對美元的匯率，再相除。⚠️ 這是理論中間價 (mid rate);實際兌換時銀行或找換店會加上買賣差價 (spread) 與手續費，成交價會與此不同。本計算器算的是理論交叉匯率，供比較與估算參考。
常見問題
What is a cross rate and why do we need it?
A cross rate is the rate between two currencies derived via a common intermediary, rather than directly quoted. Most FX volume is against the USD; for non-USD pairs (EUR/JPY, GBP/AUD) there is often no active direct quote, so you derive it from each versus USD. In daily life, if you track foreign currencies only against HKD, you can still compare USD vs EUR via USD/HKD and EUR/HKD.
How is the cross rate computed?
Use the same quote currency as the bridge and divide. With rateAB = 1 A in B and rateCB = 1 C in B, A-to-C = rateAB / rateCB and C-to-A = rateCB / rateAB. Intuition: convert 1 A to rateAB of B, then B back to C at rateCB per B. The two results are reciprocals. Ensure both inputs are quoted against the same B (take reciprocals to align directions first).
Why does my result differ from the bank / money changer?
This is the theoretical mid-rate. Real exchange applies a bid-ask spread (they buy low, sell high), fees, and possibly two rounds of spread for a true cross trade, plus constant rate movement and cash-vs-wire price gaps. Use it to estimate and compare, not as your executable rate.
What is triangular arbitrage and its link to cross rates?
Triangular arbitrage profits from a brief inconsistency among three currencies by cycling A→B→C→A. The cross rate is exactly the consistency relationship that should hold; when the direct A/C quote diverges from the cross, arbitrageurs close the gap almost instantly. So cross rates hold in liquid markets, and this calculator shows the theoretical rate — not a trade recommendation.
Why does my cross rate differ from the bank's?
Because this computes the theoretical mid-rate (pure division), while banks/changers quote a bid-ask spread and may charge fees; cross trades effectively take two spreads. Rates also move between quote and execution, and cash rates differ from wire. Use the result as a sanity baseline to judge whether a quote is reasonable, not as the rate you will get.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。