Foundations, Units & Measurement

a physical quantity

A physical quantity is anything about the world that you can measure and put a number to, like how long a table is, how hot the water is, or how fast a car moves. It answers the question 'how much?' of some property. The key idea is that in physics we do not just say something is 'big' or 'hot'; we pin it down with a number and a unit.

Precisely, a physical quantity is written as a number times a unit: quantity = numerical value times unit. The length '3 metres' means 3 of the standard unit called the metre. The number alone is meaningless (3 of what?), so the unit is part of the quantity. Some quantities, like temperature or mass, need only a number and unit (scalars); others, like velocity, also need a direction (vectors).

This is the raw material of the whole subject: every law of physics is a relationship between physical quantities. Whenever you write an equation, both sides must be the same kind of quantity with matching units, which is exactly what makes dimensional analysis possible.

A car's speedometer reads 90 km/h. That single reading is a physical quantity: the number 90 paired with the unit kilometre-per-hour. Drop the unit and '90' tells you nothing.

A quantity is always a number and a unit together.

A bare number is not a physical quantity. Always carry the unit; most beginner mistakes in physics are really lost or mismatched units.

Also called
quantity物理量