Scalar

Also called Scalar quantity

A scalar is a quantity fully described by a magnitude and a unit, with no direction attached. Mass, time, distance, speed, energy, temperature and electric charge are scalars, and a minus sign on one of them is not a direction.

A number and a unit, and that is the whole quantity. AP Physics 1 EK 1.1.A.1 puts it as scalars being described by magnitude only, while vectors take both a magnitude and a direction.

The scalars an AP course actually uses: mass, time, distance, speed, energy, work, power, temperature, electric charge, density and pressure. EK 1.1.A.3 names distance and speed as its examples, set against position, displacement, velocity and acceleration on the vector side.

Scalars add arithmetically. Two masses of 3 kg and 4 kg always make 7 kg. Two forces of 3 N and 4 N make anything between 1 N and 7 N depending on how they point, which is the reason the two categories exist at all.

A minus sign on a scalar is not a direction. A temperature of 5-5 degrees Celsius, a charge of 2-2 C and a potential energy of 40-40 J are all scalars whose sign records a type or a position below a chosen reference, not a way of pointing. A signed number only counts as a one-dimensional vector when it is a component measured along an axis you have declared.

The check that catches people: speed is a scalar and velocity is a vector, even though they share a unit and a symbol. Topic 1.1 Scalars and Vectors in One Dimension is where the AP course sets this up.

Back to the physics glossary