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Derived units
Beginner
Units built from base units, such as newton = kg·m/s².
N = kg·m·s⁻²Derived units are products and quotients of base units. Many have their own names to save writing: newton for force, joule for energy, watt for power, pascal for pressure. Knowing the base-unit form lets you check any equation.
Pressure is force over area, so 1 Pa = 1 N/m² = 1 kg·m⁻¹·s⁻². Energy 1 J = 1 N·m = 1 kg·m²·s⁻².
Mixing a derived unit with the wrong prefix, such as using kN as N, gives answers off by a thousand. Convert first.
In more detail
Derived units are combinations of base units. For example, speed is metres per second, and the newton is kilogram metre per second squared, the unit of force.
Real-world uses
- Engineers check force calculations by confirming the answer comes out in newtons.
- Energy in joules and power in watts are derived units used in every electricity bill and appliance label.
- Engineers use the watt, which is a derived unit (kg·m²/s³), to rate motors, lamps and power plants in a way that every country understands.
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Frequently asked questions
Why is the newton a derived unit?
It is defined through Newton's second law, so one newton is the force that gives one kilogram an acceleration of one metre per second squared.
What is a derived unit with a special name?
The joule (energy), watt (power), pascal (pressure) and coulomb (charge) are common examples.
How do I check a derived unit?
Substitute the base units of each defining quantity. For example, a joule is a newton times a metre, which is kg·m²/s².
Related topics in Measurement & Math Tools
What is physics? · Physical quantity · SI base units · Prefixes (milli, kilo, mega) · Scientific notation · Length measurement