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.
Last updated: May 2026
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.