Last updated: November 18, 2025
Dimensional analysis explained
Dimensional analysis (the factor-label method) rewrites any unit as a fraction equal to 1, then multiplies those fractions until unwanted units cancel. Our calculator lets you plug in one or two ratios, shows the combined factor, and outputs the converted value without juggling long strings of numbers.
How the conversion works
Start with a value, then multiply by ratios that equal 1 (same quantity expressed in two units). Because when and are the same quantity, multiplying by these ratios changes the unit without changing the underlying measurement:
The calculator also reports the combined multiplier so you can reuse it later.
Units and conversions
| Field | Meaning |
|---|---|
| Starting value | The quantity you want to convert |
| Factor numerator | New unit equivalent (goes on top) |
| Factor denominator | Old unit equivalent (goes on bottom) |
| Total factor | Product of all ratios |
| Result | Final value with desired units |
Worked examples
- Miles per hour → meters per second
Convert 30 mph to m/s using two factors.
- Pressure unit swap
Convert 25 lb/ft² to kg/m².
Tips and pitfalls
- Always write the units with each factor; if a unit doesn’t cancel, you flipped a ratio.
- Stack more than two factors by multiplying once, recording the total factor, and reusing it for future calculations.
- Keep significant figures from your least precise measurement; conversion factors defined by standards (like 2.54 cm/in) are exact.
- When converting compound units (e.g., lb·ft), remember to apply ratios to each dimension separately.