Whether we realize it or not, we all use measurements in our day-to-day lives. If you move, look at a clock, or feel cold sometimes, measurement has played some part in your day. But what are these measurements, and what makes some of them scalar measurements? Let's find out.

## Scalar Definition

If you have heard of scalars, you have likely heard of vectors. Scalars and vectors are very similar but, at the same time completely different.

A **Scalar **is a unit of measurement that strictly only has a magnitude.

This means scalars only have a numerical value, not accompanied by anything else. This differs from vectors, which have a magnitude and a direction. For example, a force is a vector because it has a numerical value but you also have to specify which direction the force is being applied.

Because you don't have to worry about direction, scalar units tend to be a lot easier to deal with in calculations. However, remember that a scalar unit can be a negative number in some cases.

The term scalar was first used in the mathematical sense in 1846 by an Irish Mathematician called William R. Hamilton.

A number line shows the range of a scalar, only able to have magnitude and not direction. source: Wikimedia Commons, public domain.

## Scalar Units

So we know what a scalar is, but what are scalar units? Scalar units are of course, the units of measurement used alongside scalar values. These scalar units aren't altered by changed to the vector space that they occupy, remaining the same. Examples of units for scalar quantities are centimeters, kilograms, joules, and more.

## What are some Examples of a Scalar Measurement?

Many types of scalars will already be familiar to you, and some are only common in physics or other sciences. We explain these units in order of most used to least used.

### Time

Time is used by everyone, everywhere, constantly. Time is the kind of scalar discussed that cannot possibly have a negative value, as negative time does not exist and cannot exist. Time has many different units to describe it as it can range from a minuscule amount to an enormous, unending value. These include centuries, years, weeks, hours, and seconds, as well as many more for both large and small values.

Time is one of the most common scalar units in everyday life. Atif Arshad Wikimedia Commons CC BY 3.0

### Temperature

Temperature is the first scalar unit we'll be going over that is capable of going negative, however, this has nothing to do with temperature moving forwards and backward. The \(0\) point of temperature, where it begins to turn negative, completely changes depending on what unit is being used, and in one case it is not even possible to go below$0$. The units of temperature are Fahrenheit, \(\mathrm{F}\), Celsius, \(\mathrm{C}\), which has its \(0\) point at the freezing point of water, and Kelvin, \(\mathrm{K}\), which cannot go negative as \(0\) Kelvin is known as absolute zero, which means nothing can be colder than it.

Thermometers measure the scalar value of temperature. HitomeAkane, Wikimedia Commons CC BY-SA 4.0

### Speed

Speed actually has a counterpart to it that is a vector. Speed is the distance something or someone travels in a specific amount of time, and since it is scalar the distance traveled has no direction. The vector counterpart for speed is velocity, which can be described as identical to speed, but with a direction being utilized as well. Some units for speed include miles per hour, \(\mathrm{MPH}\), and meters per second, \(\mathrm{m}/\mathrm{s}\).

### Mass

Mass is a scalar that we're all used to using. It describes how much matter there is in an object or person. This unit actually also has a vector counterpart in weight, which people often think is the same thing as mass. Weight is the same, but it also takes into account the gravitational pull acting on that mass, and also the direction that gravitational pull is acting on it. A few examples of units of mass are pounds, \(\mathrm{lbs}\), tons, \(\mathrm{T}\), and kilograms, \(\mathrm{kg}\).

### Distance

Distance is simple and used by many every day. It is the value of space between a point in space, and another point in space, meaning it is also not capable of being negative. Displacement is the vector equivalent of this scalar unit, which describes an object's entire change of position, including direction. Some general units of distance are feet, \(\mathrm{ft}\), inches, \(\mathrm{in}\), yards, \(\mathrm{yds}\), and meters, \(\mathrm{m}\).

### Area

It is good to think of an area as a sort of step up from distance. The area can be described as how much two-dimensional space something takes up, For example when you place a box on the ground, how much floor space does it take up? It is a step up from distance due to the fact that it is still measured by distance, but now it is distance in two dimensions. Therefore, the measurements of area are the same as distance, only squared, since you multiply these distances together. For example, feet become feet squared \(\mathrm{ft}^2\), and meters become meters squared \(\mathrm{m}^2\).

### Volume

If the area is a step up from distance, the volume can be described as a step up from the area. Think of it as the same thing, except add a third dimension. This can also be thought of as how much space something takes up, only in three dimensions this time instead of two. Once again, the units of volume are the same as the area, except it needs to be cubed instead of squared. For example, feet squared becomes feet cubed, \(\mathrm{ft}^3\), and meters squared becomes meters cubed, \(\mathrm{m}^3\).

### Energy

Energy is a scalar unit that is perhaps not as commonly used as other scalar units we have covered so far. Energy can be quantified as the amount of force that has been moved in a specific direction. You may notice that both force and movement with direction are vectors, however, the product of them both is not. This is because when you use these two together to calculate energy, the direction cancels out and forces energy to become scalar. The only commonly used unit of energy is the Joule, \(\mathrm{J}\).

### Density

Density is a unit that defines how much matter is present within a certain amount of space. Due to this, mass and volume are heavily related to density. Density is typically measured in \(\mathrm{kg}/\mathrm{m}^3\).

### Work

Work is a very interesting and somewhat complicated scalar unit. It describes the transference of energy into something or someone through the use of force. Since this is a form of energy, it is calculated with the use of force and movement with direction again, making it scalar. This unit however can be negative, as the energy transference can go the other way by being pushed in an opposite direction. Since work is energy, the unit for work is the Joule, \(\mathrm{J}\).

## Scalar Product

A scalar product, also known as the dot product, is the combination of two sequences of numbers of equal length, formed into a singular number. This is done by taking the component of one of two vectors in the direction of the other vector and then multiplying it by the magnitude of this remaining vector. This will give you the scalar product of these two vectors.

## Scalar Product Formula

In order to calculate the scalar product of two vectors, the equation is as follows:

$$ a \cdot b = |a||b|\cos{\theta} $$

Where \(a\) and \(b\) are both vectors and \(\theta\) is the angle between both of them. The vertical bars signify that we are taking the magnitude of \(a\) and \(b\).

## Scalar - Key takeaways

A scalar unit is a unit that has only magnitude, which is a numerical value, as opposed to a vector unit which has both magnitude and direction.

Scalar units can be negative, however not all scalar units are capable of this.

Some good examples of scalar units are time, distance, speed, volume, and many more.

## FAQs

### What are 10 examples of scalar quantity? ›

Other examples of scalar quantities are **mass, speed, distance, time, energy, density, volume, temperature, distance, work** and so on.

**What is scalar quantity and examples? ›**

scalar, **a physical quantity that is completely described by its magnitude**. Examples of scalars are volume, density, speed, energy, mass, and time. Other quantities, such as force and velocity, have both magnitude and direction and are called vectors.

**What are the 10 examples of scalar and vector quantities? ›**

SCALAR QUANTITY : **Mass, Speed, Distance, Time, Area, Volume, Density, Temperature**....etc. VECTOR QUANTITY : Linear momentum, Acceleration, Displacement, Momentum, Angular velocity, Force, Electric field, Polarization....etc.

**What are the 30 examples of scalar quantity? ›**

...

**Examples of Scalar Quantities are as follows:**

- Mass.
- Speed.
- Distance.
- Time.
- Volume.
- Density.
- Temperature.

**What is a real life example of scalar? ›**

For example, **a long road trip covered a distance of 338 miles.** **You drove that distance in 5 hours.** **Therefore, your average speed for the trip was 338 miles divided by 5 hours, or 67.6 mph**. These are all scalar quantities.

**What's an example of a vector quantity? ›**

For example, **displacement, velocity, and acceleration** are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars.

**How many quantities are scalar? ›**

Scalar quantities **have a size or magnitude only and need no other information to specify them**. Thus, 10 cm, 50 sec, 7 litres and 3 kg are all examples of scalar quantities. Vector quantities have both a size or magnitude and a direction, called the line of action of the quantity.

**Is weight a scalar or vector? ›**

Weight is a **scalar quantity**.

**What are the 3 scalar quantities? ›**

Mass and speed are scalar quantities. Distance is a scalar quantity and displacement is a vector quantity.

**What are the different types of scalar? ›**

The five scalar data types are **numeric, character, integer, logical, and complex**.

### What are the five example of vector? ›

Examples of vector quantities include displacement, velocity, position, force, and torque.

**Which list of quantities are vectors? ›**

**There are only six vector quantities:**

- displacement.
- velocity.
- acceleration.
- force.
- weight.
- momentum.

**What are the 5 scalar quantities? ›**

**Scalar quantities**

- temperature – eg 10 degrees Celsius (°C)
- mass – eg 5 kilograms (kg)
- energy – eg 2,000 joules (J)
- distance – eg 19 metres (m)
- speed – eg 8 metres per second (m/s)
- density – eg 1,500 kilograms per metre cubed (kg/m
^{3})

**Is temperature a scalar or vector? ›**

A scalar quantity is the one which has only magnitude, while a vector quantity is a quantity which has magnitude as well as direction. Temperature is a scalar quantity as it is independent of direction at a point.

**Which is not a scalar quantity? ›**

**momentum**. Explanation for correct answer: (D) Momentum: It is having both direction and magnitude which is in vector.

**What is the only scalar quantity? ›**

A scalar quantity is a physical quantity with only magnitudes, such as **mass and electric charge**. On the other hand, a vector quantity is a physical quantity that has both magnitudes and directions like force and weight.

**What are the 12 types of vectors? ›**

**There are 12 types of vectors that are as follows:**

- Zero Vector.
- Unit Vector.
- Position Vector.
- Equal Vector.
- Negative Vector.
- Collinear Vector.
- Co-initial Vector.
- Like and Unlike Vectors.

**What are 4 examples of vectors? ›**

Examples of vectors in nature are **velocity, momentum, force, electromagnetic fields and weight**.

**What is a scalar for dummies? ›**

Scalars are **quantities that are fully described by a magnitude (or numerical value) alone**. Vectors are quantities that are fully described by both a magnitude and a direction.

**How do you know if something is scalar? ›**

**Scalar quantities have only magnitude**; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction. Force, displacement, and acceleration all occur with a designated direction.

### What is always a scalar? ›

True. The magnitude of a vector gives its length, which is always a scalar.

**What are real life examples of vectors? ›**

Vectors have many real-life applications, including situations involving force or velocity. For example, **consider the forces acting on a boat crossing a river**. The boat's motor generates a force in one direction, and the current of the river generates a force in another direction. Both forces are vectors.

**Is speed A vector or a scalar? ›**

Speed is a **scalar quantity** because it has no defined direction and only magnitude. Velocity is a vector quantity having both magnitude and a direction.

**What are vectors give two examples? ›**

A vector is a living organism that transmits an infectious agent from an infected animal to a human or another animal. Vectors are frequently arthropods, such as **mosquitoes, ticks, flies, fleas and lice**.

**Is pressure a vector quantity? ›**

Pressure has an intensity but not a direction. In modern terms, **it is a scalar, not a vector**.

**Is Earth a scalar or vector? ›**

The Earth's population may increase or decrease but there is no direction of its movement and thus it is a **scalar quantity**.

**Is energy a vector quantity? ›**

Mass and energy are **scalar quantities**, while momentum is a vector quantity.

**What are the 4 scalar quantities? ›**

Some common scalar quantities are **distance, speed, mass, and time**. Some common vector quantities are force, velocity, displacement, and acceleration.

**What is scalar and vector quantities with example? ›**

Examples of Scalar and Vector Quantities

**Some common examples of scalar quantities are mass, time, speed, volume, temperature, density, and many more**. Displacement, velocity, acceleration, momentum, force, weight, etc. quantities are represented by vectors.

**Which of the following are all scalars? ›**

Scalar: **Mass, distance, time, volume, density, speed, temperature, energy**.

### Why is it called a scalar? ›

The word scalar **derives from the Latin word scalaris, an adjectival form of scala (Latin for "ladder"), from which the English word scale also comes**.

**How do you know if a quantity is scalar or vector? ›**

A vector quantity has a direction and a magnitude, while a scalar has only a magnitude. You can tell if a quantity is a vector **by whether or not it has a direction associated with it**. Example: Speed is a scalar quantity, but velocity is a vector that specifies both a direction as well as a magnitude.

**What is the best example of vector quantity? ›**

**Some examples of vector quantities include:**

- force, eg 20 newtons (N) to the left.
- displacement, eg 50 kilometres (km) east.
- velocity, eg 11 metres per second (m/s) upwards.
- acceleration, eg 9.8 metres per second squared (m/s²) downwards.
- momentum, eg 250 kilogram metres per second (kg m/s) south west.

**Is Mosquito a vector? ›**

**Mosquitoes are unquestionably the most medically important arthropod vectors of disease**. The maintenance and transmission of the pathogens that cause malaria, lymphatic filariasis, and numerous viral infections are absolutely dependent on the availability of competent mosquito vectors.

**Is bacteria a vector? ›**

**In bactofection-based gene therapy, the bacterium is considered the 'vector'**, which mediates carriage of the plasmid-based gene to the new host cell. Delivery of genetic material is achieved through entry of the entire bacterium into target cells.

**What is not a vector quantity? ›**

**Distance is a scalar quantity with only magnitude and not a vector quantity**. It means that when an object moves, the direction of the object does not consider; only the magnitude of the distance is considered.

**What are all the scalar and vector quantities? ›**

Scalar: **Volume, Mass, Speed, Velocity, Density, Number of Moles, Angular Frequency**. **Vector: Acceleration, Velocity, Displacement, Angular Velocity**.

**What are common scalar quantities? ›**

Some common scalar quantities are **distance, speed, mass, and time**. Some common vector quantities are force, velocity, displacement, and acceleration.

**What is an example of a scalar in real life? ›**

For example, **a long road trip covered a distance of 338 miles.** **You drove that distance in 5 hours.** **Therefore, your average speed for the trip was 338 miles divided by 5 hours, or 67.6 mph**. These are all scalar quantities.

**What is a scalar quantity for kids? ›**

A scalar is **a quantity that is fully described by a magnitude only**. It is described by just a single number. Some examples of scalar quantities include speed, volume, mass, temperature, power, energy, and time.

### What are 5 examples of a vector quantities? ›

Vector Quantities: Vector quantities refer to the physical quantities characterized by the presence of both magnitude as well as direction. For example, displacement, force, torque, momentum, acceleration, velocity, etc.

**What is a scalar quantity in short? ›**

A scalar quantity is **a quantity that can be defined by its magnitude (or numerical value ) alone**. Magnitude has enough information to describe the quantity. For example- distance, speed, time, temperature, etc. A vector quantity is associated with a magnitude as well as direction.

**Is feet a scalar or vector? ›**

The foot per second (plural feet per second) is a unit of both **speed (scalar) and velocity (vector quantity, which includes direction)**. It expresses the distance in feet (ft) traveled or displaced, divided by the time in seconds (s).