---
title: "Scalars and Vectors: The Difference Is Direction"
url: https://www.learningloftinstitute.com/glossary/scalar-and-vector-quantities
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Glossary › Scalars and Vectors: The Difference Is Direction"
---
# Scalars and Vectors: The Difference Is Direction
> **Answer.** A scalar is a quantity with size only; a vector has both a size and a direction. Mass, time, speed, distance, energy and temperature are scalars. Displacement, velocity, force, acceleration, momentum and weight are vectors. The test is whether the quantity would be incomplete if the direction were left out.
## Key facts
| | |
| --- | --- |
| Definition | A scalar is a quantity with magnitude only; a vector is a quantity that has both a magnitude and a direction, such as force or velocity. |
| Where students meet it | Grade 8 science, and again in the first lesson of every GCSE and IGCSE physics course, because the whole forces and motion unit is built on it. |
## Twelve quantities, sorted
Learning the definition is easy and applying it is not, so it is worth sorting a list once, carefully, and keeping it. The rule to apply each time: would the quantity still be fully specified if nobody told you which way?
One pair on this list catches almost everyone. Mass is a scalar — 60 kg, and there is nothing more to say. Weight is a vector, because it is a force, and it points downwards, towards the centre of the Earth.
- Scalars: distance, speed, mass, time, energy, temperature
- Vectors: displacement, velocity, force, acceleration, momentum, weight
- The pairs to keep straight: distance and displacement, speed and velocity, mass and weight
## One journey, four correct answers
Walk 3 km east, then 4 km north, taking one hour in total. The distance travelled is 7 km, because distance simply adds up whichever way you turn. The displacement is the straight line from start to finish, which by Pythagoras' theorem is 5 km, on a bearing of about 037°.
Divide each by the hour and the two speeds follow: an average speed of 7 km/h, and an average velocity of 5 km/h on that bearing. Four numbers, one walk, and no contradiction between them — which is why an exam question that says velocity and gets answered with a speed cannot be given the mark.
## Vectors can cancel; scalars cannot
Two forces of 5 N can add to 10 N, or to 0 N, or to anything in between, depending on the directions they act in. Two energies of 5 J always make 10 J. That difference is the whole reason resultant force calculations exist as a topic, and the reason a tug of war can be perfectly balanced while both teams pull as hard as they can.
It is also why direction has to be tracked rather than assumed. Once a direction is chosen as positive, everything the other way carries a minus sign, and the arithmetic then handles cancellation on its own. A single sign, chosen once at the start of a question and then used consistently, does more work than any amount of reasoning about which way things are pointing.
## Questions
### Is weight a scalar or a vector?
A vector. Weight is the force of gravity acting on a mass, measured in newtons, and it acts downwards. Mass is the scalar: it is a measure of how much matter there is, measured in kilograms, and it is the same on the Moon as on Earth while the weight is not.
### Is speed the same as velocity?
No. Speed is how fast, velocity is how fast and in which direction. A car doing 30 m/s round a bend has a constant speed and a changing velocity. In everyday conversation the words are interchangeable; in a physics answer they are not, and swapping one for the other loses marks.
### Can a vector be negative?
In one dimension the minus sign is how direction is written. If right is taken as positive, then −5 m/s means 5 m/s to the left; the size is still 5. In two or three dimensions direction is given by an angle or a bearing instead, and the size on its own is never negative.
### Is temperature a vector, since it goes up and down?
No. Up and down here describe an increase or a decrease in a number, not a direction in space. A vector needs a direction you could point at. Temperature has a size and a sign, which is not the same thing — −5 °C is a temperature, not a temperature pointing somewhere.
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