Currency Arbitrage Calculator
Fetching live exchange rates…
If a Loop Doesn't Close at 1.0, Something Is Mispriced
Convert A into B, B into C, then C back into A. If the three rates are internally consistent, you end up with exactly what you started with — the product of the three rates is 1.0 and the loop closes. If the product comes out above 1.0, the rates disagree with each other, and cycling the loop returns more than you put in. That is triangular arbitrage, and this calculator tests for it with one multiplication.
The Formula
Profit % = (Product − 1) × 100
The product is rounded to eight decimals and the profit percentage to four — precision that matters here more than almost anywhere else on this site, because genuine triangular discrepancies live in the fourth decimal place and vanish under careless rounding. All three rates must be positive.
Reading the Product
| A→B | B→C | C→A | Profit % | Interpretation |
|---|---|---|---|---|
| 1.00 | 1.00 | 1.00 | +0.0000% | Perfectly balanced — no opportunity |
| 0.90 | 0.85 | 1.3072 | +0.0008% | Effectively balanced; noise, not opportunity |
| 0.90 | 0.85 | 1.32 | +0.9800% | Loop returns more than it consumed |
| 0.90 | 0.85 | 1.29 | −1.3150% | Loop loses; the reverse direction is the one to test |
Illustrative rate triplets, not market quotes, computed by running the calculator. A negative result is not useless — it suggests testing the same three currencies traversed in the opposite order.
Why Real Opportunities Are Smaller Than They Look
A product of 1.0098 implies a 0.98% profit, which on a large notional sounds substantial. In practice, three obstacles stand between that number and any money:
- The spread, three times over — you trade at the bid or the offer, never the mid. Each of the three legs gives up half a spread or more, and on major pairs the round trip frequently exceeds the discrepancy.
- Speed — genuine triangular mispricings in liquid markets survive for milliseconds. They are closed by automated systems co-located with the venue, not by anyone typing numbers into a form.
- Execution risk — the loop is only profitable if all three legs fill at the rates you tested. Fill two and miss the third and you are holding an unintended position.
Which is what makes this calculator most useful as a consistency check rather than a trading signal. Feed it three rates from a data source and a large product is far more likely to indicate a stale quote, a rate quoted in the wrong direction, or a data error than a genuine profit.
Where the Test Earns Its Keep
- Validating a rate feed — the triangle is a cheap integrity check across three quotes that should agree.
- Catching an inverted quote — a rate entered upside down usually produces a wildly wrong product rather than a subtle one.
- Teaching market efficiency — the fact that real-world triangles close to within a rounding error is the most tangible demonstration of efficiency available.
- Comparing a provider's three quotes — a consistently negative loop across a provider's own rates is a way of seeing the margin they build in.
How to Use This Calculator
- Enter Rate A -> B — units of B per one unit of A.
- Enter Rate B -> C — units of C per one unit of B.
- Enter Rate C -> A — units of A per one unit of C, closing the loop back to where you began.
- Submit. A result near zero means the rates are consistent; a clearly positive one means they are not.
Related Calculations
- Cross Currency Converter — the two-leg version, for building a synthetic rate rather than testing a loop.
- Currency Exchange Calculator — obtain the reciprocal of a rate quoted the wrong way for your chain.