Modern Physics

Scalar magnitude: what it consists of, characteristics and examples

A scalar magnitude is a numerical quantity whose determination requires only knowledge of its value in relation to a given unit of measure of the same kind. Some examples of scalar magnitudes are distance, time, mass, energy, and electrical charge.

Scalar quantities are usually represented with a letter or the absolute value symbol, for example A or ǀ A ǀ. The magnitude of a vector is a scalar magnitude and can be obtained mathematically by algebraic methods.

Likewise, scalar quantities are plotted with a straight line of a certain length, with no specific direction, related to a scale factor.

What is a scalar magnitude?

In Physics, a scalar quantity is a physical quantity represented by a fixed numerical value and a standard unit of measure, which is independent of the frame of reference. Physical quantities are mathematical values ​​related to measurable physical properties of a physical object or system.

For example,

if you want to get the speed of a vehicle, in Km/h, just divide the distance traveled by the elapsed time. Both quantities are numerical values ​​accompanied by a unit; therefore, velocity is a scalar physical quantity. A scalar physical magnitude is the numerical value of a measurable physical property without a specific orientation or direction.

Not all physical quantities are scalar quantities, some are expressed through a vector that has numerical value, direction, and meaning. For example, if you want to obtain vehicle speed, you must determine the movements performed during the elapsed time.

These offsets are characterized by having a numerical value, an address and a specific direction. Consequently, vehicle speed is a physical magnitude of the vector as well as displacement.

Scalar magnitude characteristics

-It is described with a numeric value.

-Operations with scalar magnitudes are governed by basic algebra methods such as addition, subtraction, multiplication, and division.

-The variation of a scalar magnitude depends only on the change in its numerical value.

-It is graphically represented with a segment that has a specific value associated with a measurement scale.

-The scalar field allows you to determine the numerical value of a physical scalar quantity at each point in physical space.

dot product

The dot product is the product of two vector quantities multiplied by the cosine of the angle θ that are formed. When the dot product of two vectors is calculated, the result obtained is a scalar magnitude.

The product of two vector quantities a and b is :

ab = ǀaǀǀbǀ . cosθ = ab.cos θ

a = is the absolute value of the vector a

b = absolute value of vector b

scalar field

A scalar field is defined by associating at each point in space or region of a scalar magnitude. In other words, the scalar field is a function that shows a position for each scalar magnitude within space.

Some examples of the scalar field are: the temperature at each point on the Earth’s surface at an instant of time, the topographic map, the pressure field of a gas, the charge density and the electrical potential. When the scalar field does not depend on time, it is called a stationary field.

By plotting the set of field points that have the same scalar magnitude, equipotential surfaces are formed. For example, the equipotential surfaces of point electrical charges are concentric spherical surfaces centered on the charge. When an electrical charge moves across the surface, the electrical potential is constant at every point on the surface.

Examples of scalar magnitudes

Here are some examples of scalar magnitudes that are physical properties of nature.


It is the average kinetic energy of an object’s particles. It is measured with a thermometer and the values ​​obtained in the measurement are scalar quantities associated with the temperature or cold of an object.


To obtain the mass of a body or object, it is necessary to count how many particles, atoms, molecules, or measure the amount of material that the object integrates. A mass value can be obtained by weighing the object with a scale and it is not necessary to establish the body’s orientation to measure its mass.


Scalar quantities are mainly related to time. For example, the measurement of years, months, weeks, days, hours, minutes, seconds, milliseconds, and microseconds. Time has no direction or sense of direction.


It is associated with the three-dimensional space occupied by a body or substance. It can be measured in liters, milliliters, cubic centimeters, cubic decimeters among other units and is a scalar quantity.


Measuring an object’s speed in kilometers per hour is a scalar magnitude; it is only necessary to establish the numerical value of the object’s trip based on the elapsed time.

electric charge

The protons and neutrons of subatomic particles have an electrical charge that is manifested by the electrical force of attraction and repulsion. Atoms in their neutral state have zero electrical charge, that is, they have the same numerical value of protons as neutrons.


Energy is a measure that characterizes a body’s ability to do a job. By the first principle of Thermodynamics, it is established that energy in the universe remains constant, is not created or destroyed, just transforms into other forms of energy.

Electric potential

The electrical potential at any point in space is the electrical potential energy per unit of charge, represented by equipotential surfaces. Potential energy and electrical charge are scalar quantities; therefore, the electric potential is a scalar quantity and depends on the value of the charge and the electric field.


It is a measure of the amount of mass of a body, particles or substances in a given space and is expressed in mass units per volume units. The numerical value of the density is obtained, mathematically, by dividing the mass by the volume.

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