Vectors and scalars

Scalar quantities

A physical quantity is something that can be measured. Scalar quantities only have a magnitude or size.

Examples of scalar quantities

Some examples of scalar quantities include:

  • temperature, eg 10 degrees Celsius (°C)
  • mass, eg 5 kilograms (kg)
  • energy, eg 2,000 joules (J)
  • distance, eg 19 metres (m)
  • speed, eg 8 metres per second (m/s)
  • density, eg 1,500 kilograms per metre cubed (kg/m³)

Vector quantities

Vector quantities have both magnitude and an associated direction. This makes them different from scalar quantities, which just have magnitude.

Examples of vector quantities

Some examples of vector quantities include:

  • force, eg 20 newtons (N) to the left
  • displacement, eg 50 kilometres (km) east
  • velocity, eg 11 metres per second (m/s) upwards
  • acceleration, eg 10 metres per second squared (m/s²) downwards
  • momentum, eg 250 kilogram metres per second (kg m/s) south west

The velocity of an object is its speed in a particular direction. Velocity is a vector quantity because it has both a magnitude and an associated direction. To calculate velocity, displacement is used in calculations, rather than distance.

Unlike distance, which is a scalar quantity, displacement is a vector quantity. It includes:

  • the distance travelled, measured in a straight line from start to finish
  • the direction of the straight line