Implied cross-rate
Implied Rate (A/C) = Rate (A/B) × Rate (B/C)
- Rate (A/B)
- Units of the second currency received for one unit of the first.
- Rate (B/C)
- Units of the third currency received for one unit of the second.
Financial Calculation Summary • Investing
Triangular Arbitrage Calculator
Spot triangular arbitrage opportunities across three currency or crypto pairs. Calculate implied cross-rates, net arbitrage spread, and profit after trading fees.
Prepared on
For informational & planning purposes
InvestingIntermediate5 min
Triangular Arbitrage Calculator
Spot triangular arbitrage opportunities across three currency or crypto pairs. Calculate implied cross-rates, net arbitrage spread, and profit after trading fees.
- triangular arbitrage
- forex
- cross rate
- crypto
- trading fees
- FX
Triangular arbitrage
Three-leg FX or crypto loop.
Default is 0%. The fee is charged on each of the three swaps. 10 basis points is 0.10%, not 10%.
Net profit after fees
+482.40
+0.482% after 0 % × 3 legs
Gross profit
+482.40
+0.482% before fees
Rate product
1.004824
Edge survives three fees
Start versus end (USD)
Gross ending amount before fees, and net amount after three leg fees.
Key Takeaway: USD increases from $100,000 (Start) to $100,482 (Net end), a net change of +$482 (+0.5%).
Note: Estimates are based on user-supplied inputs and standard financial formulas. Verify figures with a qualified financial advisor or accountant before making financial decisions.Page 1 of 1
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Methodology
Formula & methodology
Triangular arbitrage compares a quoted cross with the cross implied by two other pairs. If the product of the three rates you can actually trade is above 1 after fees, the loop returns more of the starting currency than it began with.
Arbitrage condition
Arbitrage exists if Rate(A→B) × Rate(B→C) × Rate(C→A) > 1 + Total Transaction Fees
- Total Transaction Fees
- For a small percent fee f on each leg, drag is about 3f. The calculator applies (1 − f) on each of the three notionals.
Worked example: $100,000 USD → EUR → GBP → USD
- Convert $100,000 USD to EUR at 0.9200. You receive €92,000.
- Convert €92,000 to GBP at 0.8600. You receive £79,120.
- Convert £79,120 back to USD at 1.2700. You receive $100,482.40.
- The product of the rates is 0.9200 × 0.8600 × 1.2700 = 1.004824, which is above 1.
The loop yields +$482.40, or +0.482%, before fees. A 10 bps (0.10%) fee on each leg leaves about $181.25. The gross edge has to clear roughly 30 bps before a 10 bps-per-leg loop pays.
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Guide
How to read this calculator
Helpful tips
- 1Save your calculations by bookmarking this page with your inputs in the URL.
- 2Try different scenarios to understand how changes affect your results.
- 3Share this calculator with friends or family who might find it useful.
- 4Use the results as a starting point for conversations with financial advisors.
- 5Bookmark this page and revisit quarterly to track your progress toward goals.
How to Use the Triangular Arbitrage Calculator
Implied Rate (A/C) = Rate (A/B) × Rate (B/C). An arbitrage opportunity exists when Rate(A→B) × Rate(B→C) × Rate(C→A) > 1 + total transaction fees. Three trades means the fee is paid three times.
Step-by-Step Instructions
1
Choose the Forex preset (USD → EUR → GBP) or the Crypto preset (USDT → BTC → ETH), or type your own ticker labels.
2
Enter the three leg rates: the first currency into the second, the second into the third, and the third back into the first.
The Forex preset loads 0.9200, 0.8600, and 1.2700.
3
Enter the starting amount in the first currency.
4
Enter a trading fee per leg in percent or basis points. The default is 0%. The result shows gross profit and profit after three fee charges.
A 10 bps fee on each leg is about 30 bps of drag.
When to Use This Calculator
Use when analyzing forex markets for arbitrage opportunities or understanding currency pair relationships.
triangular arbitrageforexcross ratecryptotrading fees
Who Benefits Most
- •Forex Traders
- •Currency Analysts
- •Quantitative Traders
- •Finance Students
5 min
IntermediateUnderstanding Your Results
Gross profit ignores fees. Net profit subtracts the fee on each of the three legs.
What Each Result Means
Rate product
The three tradable rates multiplied together.
Interpretation: A product of 1.0000 is a consistent cross. Above 1, the loop gains the starting currency before costs.
Gross profit
Ending amount minus starting amount with a zero fee.
Interpretation: This is the price discrepancy only. It is not a profit you can withdraw.
Net profit after fees
Ending amount after each leg is multiplied by (1 − fee).
Interpretation: If this is zero or negative, the quoted edge does not survive the three trades.
What to Do With Your Results
If Gross profit is positive and net profit is negative:
The cross is mispriced by less than the fee drag. Do not treat it as a trade.
Important Limitations:
- • The rates are the rates you type. A live book has a bid and an ask, and the side you trade is the one that works against the loop.
- • The estimate fills all three legs at the quoted rate and at the same moment. Latency, partial fills, and transfer delays are not modeled.
- • A 0.482% gross edge can disappear inside the bid-ask spread. This is an arithmetic check, not an execution signal.
Real-World Example: $100,000 FX loop, +$482.40 before fees
Scenario
A desk converts $100,000 at USD/EUR 0.9200, EUR/GBP 0.8600, and GBP/USD 1.2700, then repeats the loop with a 10 bps fee on every leg.
Outcome
Gross proceeds are $100,482.40, a gain of $482.40 (0.482%). After three 10 bps fees the gain is about $181.25. The quoted cross has to beat the implied cross by more than the three spreads.
Frequently Asked Questions
Common questions about the Triangular Arbitrage Calculator
Understanding Results(1 questions)
Best Practices(1 questions)
Advanced(1 questions)
Still have questions? Check our financial glossary for definitions or explore our learning resources.
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