Dimensional Analysis Tool

Dimensional analysis is a technique for converting quantities from one unit system to another by multiplying by conversion factors — fractions whose numerator and denominator represent the same physical quantity in different units (so the fraction equals 1). It is useful because it provides a systematic way to track units through multi-step calculations, catch errors, and ensure the final answer has the correct unit.

Enter a starting value (number) and starting unit in the top inputs. Then browse the available conversion buttons grouped by category (Length, Mass, Volume, etc.) and click the one you want to apply first. The chain shows the result. Click more conversion buttons to add further steps. Each step multiplies the running value by the conversion factor. Click Remove to delete any step, or Clear Chain to start over.

Yes. Start with your value in mph, apply the mph → m/s conversion directly (factor 0.44704). Alternatively, you can chain mph → km/h (×1.60934) and then km/h → m/s (÷3.6, i.e., m/s → km/h reversed) to show the intermediate steps. Dimensional analysis is especially powerful for multi-step unit conversions like this.

The tool includes 28 conversions: Length — m↔ft, mi↔km, in↔cm, yd↔m; Mass — kg↔lb, oz↔g; Volume — L↔gal, mL↔fl oz; Time — hr↔min, min↔s, hr↔s, day↔hr; Speed — m/s↔km/h, km/h↔mph, mph↔m/s; Pressure — Pa↔psi, atm↔Pa, bar↔Pa; Energy — J↔cal, kWh↔J, BTU↔J.

Each conversion factor is a ratio equal to exactly 1 (e.g., 1 km / 1000 m = 1). Multiplying any quantity by 1 does not change its physical value, only its expressed units. By chaining multiple factors-of-1 together, all unwanted units cancel in the numerator and denominator, leaving only the desired target unit. This is why the method is also called the "factor-label method."

Start with your value in BTU. Apply BTU → J (factor 1055.06) to get joules. Then you can mentally note that 1 kWh = 3,600,000 J (the kWh → J factor is 3,600,000), so divide your joule value by 3,600,000. In the tool, you can chain BTU → J, and since J → kWh is 1/3,600,000, you can use the inverse. This is exactly the kind of multi-step conversion dimensional analysis is designed for.

Yes. This tool is designed for exactly that use case. Students can practice the factor-label method interactively, seeing each conversion factor explicitly displayed. It covers the physical quantity categories most commonly encountered in introductory physics, chemistry, and engineering courses.

Yes, completely free. No sign-up, no download, and no server connection is required. All 28 conversion factors are embedded in the tool and processing happens entirely in your browser. You can use it offline after the initial page load.