How to Calculate Triangular Arbitrage Profit

Triangular arbitrage looks simple — convert A to B to C and back to A for more than you started with — but the profit calculation trips up most beginners because fees compound across three legs. Skip the fee math and every loop looks profitable; do it properly and most apparent edges vanish. This guide gives you the exact formula for triangular arbitrage profit, a fully worked example with verified arithmetic, and a spreadsheet layout you can reuse for live evaluation. Pair it with the strategy overview in our triangular arbitrage guide.

The Core Formula

Let f1, f2, and f3 be the taker fee rates on legs one, two, and three, expressed as decimals (for example, 0.001 for 0.1 percent). Each leg multiplies your amount by its price ratio and then by (1 minus the fee). Chaining all three legs gives: final_amount = start x (1 - f1) x (1 - f2) x (1 - f3) x (leg ratios). The leg ratios are the three conversion rates multiplied together — for instance, units of B per A, times units of C per B, times units of A per C. If the product of the ratios exceeds 1 by more than the fees consume, the loop profits.

From the final amount, the net result is straightforward: net_profit_pct = (final / start - 1) x 100. A positive value means the loop earns money after all three fees; a negative value means it loses. Note that the formula uses taker fees deliberately — triangular arbitrage legs must execute immediately, so modeling maker fees you may not receive is a classic beginner error. Always use the fee tier you actually qualify for, verified on the exchange's live fee page.

Worked Example: 10,000 USDT Start

Suppose you start with 10,000 USDT and each leg charges a 0.1 percent taker fee (f = 0.001). Leg 1 converts USDT to BTC at an illustrative ratio of 0.00001500 BTC per USDT: 10,000 x 0.00001500 = 0.15000000 BTC before fees, minus 0.1 percent gives 0.14985000 BTC. Leg 2 converts BTC to ETH at 15.00 ETH per BTC: 0.14985000 x 15.00 = 2.24775000 ETH before fees, minus 0.1 percent gives 2.24550225 ETH. Leg 3 converts ETH back to USDT at 4,470.00 USDT per ETH: 2.24550225 x 4,470.00 = 10,037.39506 USDT before fees, minus 0.1 percent gives 10,027.35766 USDT.

Now apply the net formula: (10,027.35766 / 10,000 - 1) x 100 = 0.2736 percent, roughly 0.27 percent net profit, or about 27.36 USDT earned on the loop. Notice how the gross edge looked larger before fees: the raw ratio product was 10,000 x 0.00001500 x 15.00 x 4,470.00 = 10,057.50 USDT, a 0.575 percent gross edge, and the three 0.1 percent fees consumed roughly 0.3 percent of it. This is the central lesson of triangular arbitrage math — fees take a fixed bite, and only edges comfortably larger than that bite are worth trading. Check every step of your own calculations the same way before trusting a bot's output.

Building a Spreadsheet Calculator

A spreadsheet is the best learning tool because it forces you to see every leg's math. Set up columns as follows: leg number, pair, execution price, fee rate, amount in, and amount out. Each row's amount-out cell contains the formula: = amount_in x price x (1 - fee_rate). The next row's amount in references the previous row's amount out, chaining the three legs exactly like the formula above. Add a final cell computing (final / start - 1) x 100 for the net percentage, and you have a reusable calculator for any triplet.

• Column A (Leg): 1, 2, 3 — identifies each conversion step.
• Column B (Pair): e.g. USDT/BTC — the market traded on that leg.
• Column C (Price): the execution price, i.e. units received per unit sent.
• Column D (Fee): your actual taker fee as a decimal, e.g. 0.001.
• Column E (Amount in): references the previous leg's amount out; leg 1 is your starting capital.
• Column F (Amount out): = E x C x (1 - D) — paste this formula down all three rows.

Break-Even Check and Fee Tiers

The break-even check is the single most useful cell in your spreadsheet: it tells you the minimum gross edge a loop needs before it is worth considering. Approximately, break-even gross edge = f1 + f2 + f3 (for small fees, the sum is a fine approximation of the compounded drag). With 0.1 percent per leg, you need roughly 0.3 percent gross just to break even — and a sensible trader demands a margin above that for slippage. Build this as a highlighted cell so you never evaluate a loop without seeing its hurdle rate first.

The table above is illustrative — your real numbers come from your actual fee tier — but the pattern is what matters: lower fee tiers dramatically lower the hurdle, which is why high-volume traders see opportunities that are invisible to retail accounts. This is also why fee assumptions are the most dangerous input in the whole calculation. For broader context on how this strategy compares with alternatives, see our cross-exchange arbitrage guide and our scanner comparison for tools that surface live edges.