Currency Arbitrage Calculator
Find profit opportunities by trading through three currency pairs in a loop. Use this when you spot a pricing discrepancy between USD, EUR, and GBP exchange rates and want to know if the trade is profitable after transaction costs.
About this calculator
Triangular arbitrage exploits price mismatches between three currency pairs. You convert an initial amount through three sequential trades — USD → EUR → GBP → USD — and check whether you end up with more than you started. The gross return is: finalAmount = initialAmount × rate1 × rate2 × rate3. Because each leg of the trade incurs a transaction cost, the formula applies a cost deduction to each leg: profit = (initialAmount × rate1 × rate2 × rate3) × (1 − transactionCost/100)³ − initialAmount. A positive result means a profitable arbitrage opportunity exists after fees. In practice, these windows close within milliseconds, so the calculator helps you pre-screen whether a detected mispricing is large enough to survive real-world trading costs.
How to use
Suppose you start with $10,000. The USD→EUR rate is 0.92, EUR→GBP is 0.87, and GBP→USD is 1.26. Each trade costs 0.1%. Step 1: gross return = 10,000 × 0.92 × 0.87 × 1.26 = $10,085.04. Step 2: apply three transaction cost deductions: $10,085.04 × (1 − 0.001)³ = $10,085.04 × 0.997 = $10,054.83. Step 3: profit = $10,054.83 − $10,000 = $54.83. You would net approximately $54.83 on a $10,000 round trip.
Frequently asked questions
What is triangular currency arbitrage and how does it work?
Triangular arbitrage is a strategy that exploits inconsistencies in the quoted exchange rates between three currencies. A trader converts currency A to B, then B to C, then C back to A. If the combined rates imply a different cross-rate than the market quotes, a risk-free profit exists in theory. In practice, arbitrage windows are extremely short-lived because algorithms close the gap almost instantly.
How do transaction costs affect currency arbitrage profitability?
Transaction costs are compounded across all three legs of the trade, which means even a small fee dramatically erodes profit. With a 0.1% cost per leg, the effective cost is roughly 0.3%, and with 0.5% per leg it rises to about 1.5% — often larger than the mispricing itself. This is why the calculator raises the cost factor to the power of 3. Most retail-level mispricings do not survive realistic transaction costs, making arbitrage practical only for institutional traders with near-zero spreads.
When should I use a triangular arbitrage calculator in real trading?
Use this calculator during the research or screening phase, before placing any trades. Feed in live interbank rates and your broker's all-in transaction cost (spread plus commission) to see whether a detected rate discrepancy is large enough to yield a positive profit. It is also useful for backtesting historical rate data to understand how often true arbitrage opportunities existed in a given currency trio and how large they typically were.