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Unit conversion
Beginner
Multiply by ratios equal to one to change units.
Multiply by conversion factors written as fractions equal to one so the unwanted units cancel. This works for compound units too, but powers need care.
72 km/h = 72 × (1000 m / 1 km) × (1 h / 3600 s) = 20 m/s.
Convert squared or cubed units by squaring or cubing the factor. 1 m³ = 10⁶ cm³, not 100.
In more detail
Unit conversion multiplies a quantity by a fraction equal to one, written as a ratio of equal quantities in different units. Writing the units alongside the numbers ensures the unwanted units cancel.
Real-world uses
- Converting a car's speed from 90 km/h to metres per second for a physics problem.
- Converting pressure from atmospheres to pascals when reading gas data.
- A cyclist converts a speed of 36 km/h into metres per second, which is 10 m/s, before using it in a stopping-distance formula.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How do I convert 90 km/h to m/s?
Multiply by 1000 m per km and divide by 3600 s per hour, giving 25 m/s.
Why use the factor-label method?
Keeping units in the working catches mistakes, because mismatched units will not cancel.
Why does multiplying by a conversion factor not change the physics?
The factor equals one, such as 1000 m / 1 km, so only the units change, not the quantity.
Related topics in Measurement & Math Tools
Limitations of dimensional analysis · Dimensionless numbers · Order-of-magnitude estimates · Scalars and vectors · Vector representation · Vector addition