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Scalars and vectors
Beginner
Scalars have magnitude only; vectors have magnitude and direction.
A scalar has magnitude only (mass, time, temperature, energy). A vector has magnitude and direction and obeys vector addition (displacement, velocity, force). Direction matters, so equal magnitudes do not make two vectors equal.
Walking 3 km east then 3 km west gives distance 6 km but displacement 0.
Speed is a scalar, velocity is a vector. Average speed and the magnitude of average velocity can differ.
In more detail
A scalar has only magnitude, such as mass, temperature or speed. A vector has both magnitude and direction, such as displacement, velocity or force.
Real-world uses
- Wind speed is a scalar, but wind velocity tells pilots the direction as well.
- Forces on a bridge are vectors, because direction determines whether a cable is in tension or compression.
- A weather forecast gives temperature as a scalar but wind as a vector, because a wind speed without a direction is not enough to plan a flight.
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Frequently asked questions
Is distance a scalar or vector?
Distance is a scalar. Displacement is a vector because it includes direction.
Can a vector have zero magnitude?
Yes, the zero vector has no magnitude and no particular direction.
Can a scalar be negative?
Yes. A temperature below zero or an energy change can be negative. A scalar has a magnitude that may carry a sign, but no direction.
Related topics in Measurement & Math Tools
Dimensionless numbers · Order-of-magnitude estimates · Unit conversion · Vector representation · Vector addition · Parallelogram law