Scalar vs. Vector: What's the Difference?
Read the comparison below, or explore it visually. Create a visual lesson comparing scalar and vector using available credits or plan allowance.
A scalar is a physical quantity fully described by its magnitude alone, while a vector needs both a magnitude and a direction. Mass, time and temperature are scalars, so they add like ordinary numbers; displacement, velocity and force are vectors, so they add by the triangle or parallelogram law, and two forces of 5 N can combine to anything from 0 N to 10 N.
At a glance
| Scalar | Vector | |
|---|---|---|
| Described by | Magnitude only | Magnitude and direction |
| How they add | Ordinary arithmetic: 3 kg + 2 kg = 5 kg | Triangle or parallelogram law |
| Representation | A number with a unit | An arrow, or a bold or arrowed symbol |
| Can be negative? | Some can, e.g. temperature in °C | Magnitude is never negative; direction can reverse |
| Examples | Mass, time, speed, distance, energy | Displacement, velocity, acceleration, force |
Which should you use?
Scalars are enough when direction has no meaning, such as the 2 kg mass of a bag of rice, the 40 minutes a train takes, or the 35 °C temperature in a city.
Vectors are needed when direction changes the outcome, such as a plane's velocity in a crosswind or two people pulling a cart with ropes at different angles.