How to Calculate Triangular Arbitrage Profit
Calculating triangular arbitrage profit involves comparing the amount of cryptocurrency you start with against the amount you have after completing three connected trades.
A typical cycle might be:
USDT → BTC → ETH → USDT
The basic calculation is not simply about finding three prices that appear inconsistent. You also need to account for trading fees, bid-ask spreads, slippage, order-book liquidity, and the actual prices at which your orders can execute.
The final result should therefore be based on executable prices and total costs, not just a theoretical price difference.
What Is Triangular Arbitrage Profit?
Triangular arbitrage profit is the difference between your starting amount and the amount you have after completing a three-trade cycle.
For example, if you start with 10,000 USDT and complete the entire cycle with 10,025 USDT, the gross difference is:
10,025 − 10,000 = 25 USDT
However, this only represents a positive difference if all relevant costs have already been included in the calculation.
If trading fees and slippage were excluded, the 25 USDT would only represent a theoretical result.
The Basic Triangular Arbitrage Formula
A simplified calculation can be represented as:
Final Amount = Starting Amount × Rate 1 × Rate 2 × Rate 3
The resulting amount is then compared with the starting amount.
Gross Difference = Final Amount − Starting Amount
To calculate the actual result, costs must be included:
Net Result = Final Amount After Costs − Starting Amount
The exact calculation depends on whether the quoted pair is being bought or sold and whether the exchange quotes the asset in the direction required by the trading cycle.
Step 1: Choose Three Connected Trading Pairs
Start by identifying three pairs that create a complete trading loop.
For example:
- BTC/USDT
- ETH/BTC
- ETH/USDT
A possible cycle is:
USDT → BTC → ETH → USDT
The starting and ending asset are both USDT.
This makes it possible to directly compare the amount you began with against the amount remaining after the cycle.
Step 2: Determine the Executable Prices
The next step is to identify the actual prices available in the order book.
For a market order, the relevant price may be the current best ask when buying or best bid when selling.
The last traded price is not necessarily the price at which your order will execute.
This distinction is important because an arbitrage calculation based on last-traded prices can produce a misleading result.
Step 3: Calculate Each Conversion
Suppose you start with:
10,000 USDT
You first convert USDT into BTC.
Then you convert BTC into ETH.
Finally, you convert ETH back into USDT.
For illustration, assume the executable rates produce these hypothetical results:
10,000 USDT → 0.10 BTC
Then:
0.10 BTC → 1.60 ETH
Then:
1.60 ETH → 10,040 USDT
Before considering additional costs, the theoretical difference is:
10,040 − 10,000 = 40 USDT
This is the gross difference from the hypothetical cycle.
It should not automatically be treated as net profit.
Step 4: Include Trading Fees
Triangular arbitrage normally involves three trades.
If a trading fee applies to each transaction, the calculation needs to account for the fee at each stage.
For example, suppose an illustrative exchange charges a 0.10% fee per trade.
The calculation would apply the fee after each executed trade rather than simply subtracting 0.10% once at the end.
Conceptually:
Amount after Trade 1 = Amount × Rate 1 × (1 − Fee)
Amount after Trade 2 = Amount after Trade 1 × Rate 2 × (1 − Fee)
Amount after Trade 3 = Amount after Trade 2 × Rate 3 × (1 − Fee)
The final amount is then compared with the original starting amount.
Actual exchange fee schedules vary, so the current fee applicable to the account and trading pair should always be verified.
Step 5: Account for Slippage
Slippage occurs when the actual execution price differs from the price used in the initial calculation.
For example, a bot may detect an opportunity using the best available ask.
But if the intended order is larger than the liquidity available at that price, part of the order may execute at less favorable prices.
This can reduce or completely eliminate the apparent arbitrage difference.
Therefore, a realistic calculation should consider the weighted average execution price for the intended order size.
Step 6: Check Order-Book Liquidity
Order-book depth is closely connected to slippage.
Suppose the best available price can execute only 500 USDT worth of your order, while your intended trade is 10,000 USDT.
The remaining amount may need to execute against deeper levels of the order book.
The same analysis should be performed for all three legs.
A triangular arbitrage opportunity is therefore more meaningful when the calculated result survives the actual available liquidity across the complete cycle.
A Complete Hypothetical Example
Consider a simplified cycle:
USDT → BTC → ETH → USDT
Starting amount:
10,000 USDT
After the first trade:
10,000 USDT → 0.10 BTC
After the second:
0.10 BTC → 1.60 ETH
After the third:
1.60 ETH → 10,040 USDT
The initial theoretical difference is:
10,040 − 10,000 = 40 USDT
Now assume the three trades collectively incur costs of 25 USDT through applicable trading fees and execution effects.
The simplified net result becomes:
40 − 25 = 15 USDT
The example is purely illustrative. Actual results depend on real-time prices, order-book depth, fees, order size, and execution conditions.
Gross Spread vs Net Profit
This distinction is critical when evaluating crypto arbitrage.
Gross spread represents the apparent difference before all relevant costs.
Net result represents what remains after applicable costs and execution effects.
A large displayed spread does not necessarily produce a large net result.
For example:
Displayed difference: 0.50%
Trading fees: 0.30%
Slippage and spread: 0.15%
The remaining theoretical difference would be approximately:
0.50% − 0.30% − 0.15% = 0.05%
Even this simplified calculation does not guarantee that the trade will finish with a positive result because prices can change while the three orders are executing.
Why Order Direction Matters
One of the easiest mistakes in triangular arbitrage calculations is using the wrong side of a trading pair.
When buying an asset, the relevant executable price is generally the ask.
When selling an asset, the relevant executable price is generally the bid.
Using the wrong price can make an apparent arbitrage opportunity look more attractive than it actually is.
A reliable calculation should therefore follow the exact direction of each trade.
How a Triangular Arbitrage Bot Calculates Profit
An automated arbitrage system can continuously:
- Collect live order-book data.
- Identify connected trading pairs.
- Determine the executable bid and ask prices.
- Calculate the three conversions.
- Apply trading fees.
- Estimate slippage.
- Check available liquidity.
- Compare the final amount with the starting amount.
- Determine whether the calculated difference meets predefined conditions.
This allows potential opportunities to be evaluated much faster than manual calculations.
Common Mistakes When Calculating Arbitrage Profit
Several mistakes can produce misleading results.
Using Last-Traded Prices
The last traded price may not be available for your order size.
Ignoring Trading Fees
Three trades can mean three separate fee calculations.
Ignoring Slippage
Large orders can move through multiple order-book levels.
Ignoring Liquidity
A price may be available for only a small amount.
Assuming the Spread Is Guaranteed
The price relationship can change before all three trades are completed.
Using the Wrong Bid or Ask
The direction of each trade determines which side of the order book is relevant.
Is Triangular Arbitrage Profit Guaranteed?
No.
A calculated opportunity is not a guarantee of profit.
Prices can change during execution, orders can be partially filled, liquidity can disappear, and technical or exchange-related problems can affect the result.
For this reason, triangular arbitrage should be evaluated using realistic execution assumptions rather than theoretical prices alone.
Frequently Asked Questions
How do you calculate triangular arbitrage profit?
Start with an initial asset, apply the three executable exchange rates in sequence, include trading fees and estimated execution costs, and compare the final amount with the starting amount.
What is the triangular arbitrage formula?
A simplified formula is:
Final Amount = Starting Amount × Rate 1 × Rate 2 × Rate 3
For a realistic calculation, applicable fees and execution effects must also be included.
Are triangular arbitrage calculators accurate?
They can be useful for estimating opportunities, but their accuracy depends on the quality and freshness of the market data, fee information, liquidity assumptions, and execution prices they use.
Why can an arbitrage opportunity disappear?
Other traders may act on the same price difference, while normal market activity can change the order books. The opportunity can therefore disappear before all three trades are completed.
Does a higher arbitrage spread always mean higher profit?
No. A larger displayed spread does not necessarily produce a larger net result because liquidity, order size, fees, slippage and execution conditions can materially affect the outcome.
Conclusion
Calculating triangular arbitrage profit requires more than multiplying three cryptocurrency prices together.
A realistic calculation should start with the executable bid and ask prices, follow the correct trading direction, account for trading fees, consider order-book liquidity and slippage, and compare the final amount with the original starting balance.
The most important distinction is between a theoretical arbitrage spread and the actual result after costs and execution.
PokoBit focuses on crypto arbitrage and cryptocurrency market opportunities, making triangular arbitrage calculations an important concept for anyone researching automated and manual arbitrage strategies.
Always verify current exchange prices, fees, liquidity and trading conditions before evaluating a live arbitrage opportunity.