Scalars and Vectors
A scalar has only size, while a vector has both size and direction.
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A scalar has only size, while a vector has both size and direction.
- Speed is a scalar and velocity is a vector
- Force and displacement are vectors
- Vectors are drawn as arrows
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Scalars and Vectors?
Within Physics, which covers forces, energy, waves, electricity, magnetism, light and space explained through motion and experiments, this topic explains Scalars and Vectors. Physics topics explain how things move, push, heat up and carry energy, so each one here pairs a definition with a live model you can change.
Check that you can explain Scalars and Vectors in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Scalars and Vectors explains how the physical world behaves, from sport and transport to electricity and medicine.
Scalars and Vectors in detail
A scalar has size (magnitude) only, such as mass, speed, time, energy and temperature. A vector has both magnitude and direction, such as displacement, velocity, force and acceleration. Vectors are drawn as arrows whose length shows the magnitude.
Vectors cannot simply be added as numbers. Two forces of 3 N and 4 N at right angles give a resultant of 5 N, found by Pythagoras or a scale diagram. Vectors can also be resolved into perpendicular components. Distinguishing scalars from vectors prevents errors such as mixing up speed and velocity.
How the interactive helps you understand Scalars and Vectors
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Scalars and Vectors.
Real-life uses and examples
- Predict what a ball, car or circuit will do with Scalars and Vectors before you do the calculation.
- Explain everyday devices, such as brakes, lifts or chargers, using Scalars and Vectors.
- Use Scalars and Vectors to make sense of a practical and its results.
Common mistakes to avoid
- Mixing up Scalars and Vectors with a related quantity that has different units.
- Forgetting that some quantities, such as force or velocity, also have a direction.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Scalars and Vectors
What is Scalars and Vectors?
A scalar has only size, while a vector has both size and direction.
What are the most important points about Scalars and Vectors?
The main points are: Speed is a scalar and velocity is a vector; Force and displacement are vectors; Vectors are drawn as arrows.
Why is Scalars and Vectors useful?
Understanding Scalars and Vectors explains how the physical world behaves, from sport and transport to electricity and medicine.
How can I practise Scalars and Vectors?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Scalars and Vectors?
Related topics in Physics include Density, Acceleration, Projectile Motion.