In our everyday activities, we measure one thing or the other. If we embark on a journey, for instance, we sometimes want to know:
how far (distance) have we gone on the journey,
how long (time) have we been on the journey,
how fast or slow (speed) has the journey been,
how cheap or expensive (cost) is the mode of transportation on the journey,
and so on. All these will be determined by measurement, and for us to determine these factors above, there must be a standard unit or reference with which they would be compared.
Therefore, measurement is a process or technique in which an unknown quantity is quantitatively compared with a standard unit or reference to assign a numerical value to it. It is a basic activity in science, mathematics, and daily life that allows us to describe, analyse, and interact with the physical and abstract world.
Measurements can basically be carried out in two ways; by direct and indirect measurement.
This involves using a measuring instrument to carry out the measurement.
This involves measuring a quantity through calculation, observation, or inference.
A measurement must include the following:
Quantity to be measured: This is the quantity or property that is to be measured in particular. This could be a length, time, distance, height, speed, temperature, mass, and so on.
Standard or unit: This is a predefined and universally accepted reference used for comparing the value of the quantity. For example, the predefined and universally accepted reference for length is metre, for mass is kilogram, for time is second, etc.
Measuring instrument: This is the tool or system used to perform the measurement. For example, we use the ruler to measure the length, the thermometer to measure the temperature, and so on.
Numerical value: This is the result of the measurement after comparing it with the standard or unit, expressed in terms of the chosen unit.
The basic quantities measured in physics are length, time and mass, which are base quantities, and area and volume, which are derived quantities from length.
Let's discuss these quantities one after the other.
Length is one of the fundamental physical quantities that plays a vital role in understanding the spatial dimensions of objects and phenomena in the physical world.
The SI unit of length is the metre (
) and is the distance travelled by light in a vacuum during a specific time interval. At one time it was the distance between two marks on a certain metal bar. The submultiples of metre are:
A multiple for large distances is
See the theory Unit conversion for more submultiples and multiples of units.
The measuring instruments of length include a ruler (e.g. meter rule), vernier calipers, and a micrometer screw gauge.
Ruler
Many length measurements are made with rulers.
To read a ruler correctly, we must ensure that our eyes are directly over the mark on the scale just as shown in the figure below.
Ruler
The reading in the figure above is 
or 
or 
. Lengths can be measured with a ruler to an accuracy of about 
.
Vernier calipers
The vernier calipers are used for more accurate measurements than what can be achieved by a ruler. The simplest type enables a length to be measured to 
. A vernier caliper with its parts is shown below:
Vernier calipers
The functions of some key parts of a vernier caliper are shown in the table below.
The vernier scale is a small sliding scale which is 
long but divided into 10 equal divisions. Therefore:
The main scale is in centimetres. Let's now see how to read the vernier calipers.
To measure the length of an object with a vernier caliper, one end of the length to be measured is made to coincide with the zero of the main scale and the other end with the zero of the vernier scale.
Micrometer screw gauge
The micrometer screw gauge also gives more accurate measurements than a ruler. In fact, It measures very small objects to 
. A micrometer screw gauge with its parts is shown below:
Micrometer screw gauge
One revolution of the thimble scale (drum) opens the accurately flat, parallel anvil and spindle (jaws) by one division on the main scale of the gauge; this is usually 
or 
. If the thimble scale has a scale of 50 divisions round it, then rotation of the thimble scale by one division opens the anvil and spindle (jaws) by 
.
Let's now see how to read the micrometer screw gauge.
To measure the length of an object with a micrometer screw gauge, the object is placed between the anvil and spindle (jaws) and tightened by rotating the thimble scale. A friction clutch ensures that the jaws exert the same force when the object is gripped.
Other measuring instruments used to measure length include the tape rule.
Time is a fundamental concept used to measure the sequence of events, their duration, and the intervals between them.
The SI unit of time is the second (
) which is defined as the time interval for a certain number of energy changes to occur in the caesium atom. The submultiples of second are:
A multiple for large distances is
Other units of time include the minutes (
), hours (
) and even days.
Therefore:
Instruments used to measure time include clocks, watches, stopwatches, sundials (historically), and for highly accurate measurements, atomic clocks; with the basic unit of time being the second. Basically, the stopwatches are used to measure time in the laboratory. Stopwatches can be analog or digital.
Analog stopwatch
An analog stopwatch is as shown below:
Analog stopwatch
It has two scales:
the inner scale which represents minutes, and
the outer scale which represents seconds.
Let's now see how to read the analog stopwatch.
Digital stopwatch
A digital stopwatch is commonly used in sports, laboratory experiments, and other situations where precise timing is needed. It is shown below:
Digital stopwatch
It is an electronic device used to precisely measure elapsed time, displaying the time digitally on a screen, allowing for highly accurate readings usually down to hundredths of a second, and operated with buttons to start, stop, and reset the timer.
A digital stopwatch can be designed to read hours, minutes, and seconds down to hundredths of a second. We need to note the tag on each part of the reading to understand what it represents.
Let's now see how to read the digital stopwatch.
Mass can simply be defined as the measure of the amount of matter in a body. It measures the amount of substance in an object.
The SI unit of mass is Kilogram (
). Other units include grams (
) and pounds (
).
Mass is typically measured in the laboratory using balances. A balance is a device that measures the mass of an object by balancing the object against a known mass. There are different types of balances, including beam balances, spring balances, and electronic balances.
Beam balance
A beam balance is a simple instrument used to measure the mass of an object by comparing it with known standard masses. It is shown below:
Beam balance
It operates on the principle of equilibrium, which means the mass on one side of the balance is equal to the mass on the other side when the beam is level.
The object whose mass is to be measured is placed on one pan and an object with a known mass is placed on the opposite pan. The objects are adjusted until the beam is level, as indicated by the pointer. At equilibrium, the mass of the object is equal to the total mass of the object with a known mass.
Electronic balance
An electronic balance is a modern, digital instrument used to measure the mass of an object with high precision and accuracy. It is shown below:
Electronic balance
Unlike mechanical balances, it uses electronic sensors and components to determine the mass of an object and displays the measurement on a digital screen.
The object is placed on the weighing pan and the mass is displayed digitally on the screen.
Spring balance
A spring balance is basically used to measure the weight of an object (force due to gravity), from which the mass of the object can be inferred if the local gravitational acceleration is known. A spring balance is shown below:
Spring balance
The mass 
of the object can be inferred from the weight 
measured by the spring balance using the formula:
where 
is the local gravitational acceleration which is approximately 
on the Earth surface.
The area of a shape is simply the amount of space enclosed within it. We can only determine the area of two-dimensional figures which include squares, rectangles, triangles, circles, and so on.
Area is always expressed in square units. Some units of area are 
, 
, 
, 
, 
, and so on.
The area of a shape cannot be determined by measuring with an instrument. It is determined by calculation using the appropriate formula. Let's list some shapes and the formula of their area:
Square: The area 
of a square of side length 
is given as:
Rectangle: The area of a rectangle with side length and width 
is given as:
Triangle: The area of a triangle of base 
and height 
is given as:
Circle: The area of a circle of radius 
is given as:
The volume of an object is the amount of substance the object can hold. We can determine the volume of any object, either regularly or irregularly shaped.
Volume is always expressed in cube units. Some units of volume are 
, 
, 
, 
, 
, and so on.
The method used in measuring the volume of an object depends on if the object is regularly shaped or irregularly shaped.
Regularly shaped object
These are objects that have a regular shape. The shape could be a cube, cuboid, cylinder, cone, and so on. The volume of a regularly shaped object is determined using the formula of the volume of the shape of the object.
The volume 
of a regular shape is generally given as the product of the base area and the height of the shape:
Let's list some shapes and the formula of their volume.
Cube: The volume of a cube with length of an edge is given as:
Cuboid: The volume of a cuboid with length , width and height is given as:
Cylinder:The volume of a cylinder with a base radius and height is given as:
Cone: The volume of a cone with a base radius and height is given as:
Irregularly shaped object
The volume of an irregularly shaped object can be determined using a measuring cylinder. A measuring cylinder is shown below:
Measuring cylinder
The volume of a liquid may be obtained by pouring it into a measuring cylinder and the volume is read on the cylinder. When making a reading, the cylinder must be upright and the eye must be level with the bottom of the curved liquid surface, i.e. the meniscus.
For an irregularly shaped solid, we can pour water into a measuring cylinder and record the volume of the liquid which is taken to be the initial volume 
. We then carefully place the irregularly shaped solid into the water and ensure it is fully submerged without touching the sides or bottom of the container. Then, we record the new water level which will be taken as the final volume 
.
The volume of the solid is therefore the difference between the final volume and the initial volume :
All quantities can be measured either directly or indirectly.
The reading of a measurement is not complete without including the appropriate SI unit of the quantity being measured. Therefore, we must ensure the unit of the quantity we are measuring is included in our reading.
