Triangular Arbitrage Calculator
Enter three currency pairs that form a cycle (e.g. EUR/USD, USD/GBP, GBP/EUR) and their rates. We compute (Rate1 × Rate2 × Rate3) − 1, multiplied by 100, as a hypothetical gross percentage change. Rates must use quote units per base unit; no execution is simulated.
Three currency pairs (cycle)
Hypothetical example rates; not current market quotes.
EUR → USD → GBP → EUR
Start with 1 EUR → EUR/USD (×1.08) → USD/GBP (×0.79) → GBP/EUR (×1.18) → 1.006776 EUR. The entered reference-rate product exceeds one; executable profit is not established.
What is triangular arbitrage?
Triangular arbitrage is a strategy that exploits price differences across three currency pairs that form a closed loop (e.g. EUR/USD, USD/GBP, GBP/EUR). You start in one currency, convert through the other two, and return to the first. If the product of the three directed exchange rates is greater than 1, the arithmetic returns more starting currency before costs. The displayed provider prices are not verified executable conversions.
How to use this calculator
- 1
Choose three pairs that form a cycle
For example EUR/USD, USD/GBP, GBP/EUR. The quote of pair 1 should be the base of pair 2, and so on, until the last quote equals the first base.
- 2
Enter rates or fetch reference rates
Type the exchange rate for each pair (units of quote currency per 1 unit of base), or click “Fetch reference rates” to fill from our forex data (FMP).
- 3
Read the result
Gross change % = 100 × ((Rate1 × Rate2 × Rate3) − 1). A positive reference-rate discrepancy is not an executable opportunity: spread, costs, timestamps, venue, and size matter.
Why use a triangular arbitrage calculator?
This calculator helps you quickly check whether a set of three forex rates is internally consistent around a cycle. It is useful for education, back-of-the-envelope checks, and understanding how cross rates relate. Real execution requires accounting for spreads, commissions, and slippage.
Reference: FMP batch forex quotes and OANDA currency and spread definitions. Provider price fields are not broker execution quotes.
Frequently asked questions
What does the calculation represent?
It multiplies three directed conversion rates around a closed loop and subtracts one. The output is a hypothetical gross change in starting currency, before bid-ask spreads, commissions, slippage, funding, or execution delays. It is not evidence that a trade can be executed profitably.
How must the pairs connect?
Use three distinct currency codes in AAA/BBB or AAABBB form. Pair 1 quote must equal pair 2 base, pair 2 quote must equal pair 3 base, and pair 3 quote must equal pair 1 base. For EUR/USD → USD/GBP → GBP/EUR, each rate is quote units received per one base unit.
Can I use a single market price as an executable conversion rate?
Not reliably. Selling the base currency uses an available bid; converting in the opposite direction uses the reciprocal of the available ask. Three reference prices can have different timestamps, venues, or sizes. This calculator does not inspect executable bid-ask quotes, liquidity, or order fills.
What does Fetch reference rates do?
It requests FMP batch forex reference prices through Pineify, whose response is cached for 30 seconds. Provider delay can add to that. All three exact symbols must return positive finite prices before any rate is replaced. Missing symbols leave your inputs unchanged. No inverse quote is synthesized and synchronized execution is not established.
Does a negative result rule out every arbitrage route?
No. It describes only the entered direction and rates. A different direction needs its own executable conversions and costs. This tool neither searches all currency routes nor places trades.
Define and Test Your Forex Rules
Pineify App coding tools require an eligible plan. Describe and inspect a strategy using available TradingView data. This page neither converts a discrepancy into executable orders nor connects three venues for simultaneous trading.