System of Measurement
The whole world revolves around measuring things! Everything is measured: the milk you buy, the gas you fill for the vehicle, the steps you walk. Even our productivity is measured in terms of productivity indexes on how productively we work. System of measurement is very important and define and express the different quantities of length, area, volume, weight, in our days to day communications. The system of measurement is based on two important foundation pillars of defining the basic unit of measurement, and the measure of conversion from this basic unit to other related units.
Further, the other related units of measurement can be in the same systems of measurement or a different system of measurement. Let us learn about mathematical theories of measurement on this page. Also, check out the interesting practice questions at the end of the page.
What is Measurement?
The word “measurement” is derived from the Greek word "metron," which means a limited proportion. This word also finds its roots in the words "moon" and "month", possibly because astronomical objects were among the first methods to measure time.
System of Measurement
Measurement systems are a collection of units of measurement and rules relating them to each other. In the old days, we used body parts for informal measurement systems like foot length, cubit, handspan, etc. which were not so accurate and vary from person to person.
So, there was a need to regularize the measurements. A system of measurement like the International System of Units called the SI units ( the modern form of the metric system), Imperial system, and US customary units were standardized across the world.
Introduction to Metric System of Measurement
A metric system is a system of measurement based on the meter for length, kilogram for mass, and liter for volume. It was introduced in France in the 1790s and is now being used officially by many countries around the world. The metric system is based on the international decimal system. The base units used in the metric system are used to derive higher and lower units of measurement. Often the required unit is either larger or much small than the defined units. Let us now look at the below described, different systems of measurement.
Metric System: The units of the metric system, originally taken from observable features of nature (basically what we normally measure like the time, length, mass, etc. are defined by seven physical constants with numerical values in terms of the units. Metrics system evolved and overtime is universally accepted as the International System of Units called the SI System. Many countries follow this system.
US Standard Units: United States, Liberia, and Myanmar have not adopted the metric system as their official system of weights and measures. U.S. customary units are used across the states to measure.
Metric System of Measurement
The Metric system has 3 main units namely, meter to measure the length, kilogram to measure the mass, and seconds to measure time.
Meter: Length is measured in meter. The unit is denoted by the alphabet (m). Look at the chart below. The base unit is "m" and we add "Deca," "Hecto," and "Kilo" to measure large units by successive multiplying by 10 and "deci," "centi," and "millie" successively divide by 10, to measure smaller length. We can use a simple ruler and measure length. For example, a pencil measured on a ruler would be 10 cm long.
Kilogram: Mass is measured in kilograms. Unit is denoted by (kg). It tells us how heavy or how to light an object is. We can multiply and divide the base units to measure smaller and bigger units. In general, for our convenience, we use gram, kilogram, and milligram. Other units are hardly used. We use a weighing scale to measure how heavy things are. A weighing scale is used in supermarkets to weigh groceries. A doctor also used a weighing scale to find the weight of a person.
Second: Time is measured in seconds. The representation of second is (s). Time is the ongoing sequence of events taking place. It is used to quantify the duration of the events. It also helps us set the start time or the end time of events. The base unit for time is seconds. Some of the conversion units of time are. 1 minute = 60 seconds, 1 hour = 60 minutes, 1 day = 24 hours, 1 week = 7 days, 1 year = 12 months, or 1 year = 365 days. We use a clock or watch to tell the current time. A stopwatch can be used to measure the time in seconds.
Other Metric System of Measurements
Though we are aware of the basic defined metric systems for length, mass, volume, but there are numerous other quantities in the physical world, for which we need to define the base unit. Quantities like, force, power, area, magnetic intensity, have their own individual units, which have been derived from the basic 7 quantities of the metric system of measurement. The basic system quantities are sometimes not sufficient to overcome the challenges of studying and measuring other higher quantities existing in physics. Here we shall look at some of the other important physical quantities and their units.
Area: The area is the space occupied by a twodimensional shape or figure. The area is measured in square units like sq. cm or cm^{2}, sq. m or m^{2}, sq km or km^{2} , etc. Let us look at the below example. If the area of each square is 1 cm^{2}. The area of shape A = 1cm^{2}. Area of shape B = (1+1) = 2 cm^{2}. Area of shape C = (1+1+1) = 3 cm^{2}. Area of shape D = (0.5 +1 +0.5 ) = 2 cm^{2}. Now that you know what an Area is, let's learn how to find the Area of a Triangle, Area of a Quadrilateral, Area of a Circle.
Volume: Volume is the space enclosed or occupied by any threedimensional object or solid shape. It has length, width, and height. It is measured in cubic units like cm^{3}, m^{3}, etc. and liquid volume is measured in litres.Let us look at a simple example. The initial volume of water in the container is 20 units. The volume of water when the object is placed inside the container 30 is units. Therefore, the Volume of the object is the difference between the two volumes. 3020 = 10 units. Finding the Volume of an object can help us determine the amount required to fill that object. For example, the amount of water in a bottle. We will now learn how to find the Volume of a Cuboid, Volume of a Cylinder, Volume of a Cone, Volume of a Sphere.
Time: Time is the ongoing sequence of events taking place. It is used to quantify the duration of the events. It also helps us set the start time or the end time of events. One of the very first experiences we have with mathematics is learning how to measure time. You may already know that the measurement of time is done using a watch and a calendar. Now, let's learn how to read and represent time along with how to read a calendar.
Speed: Speed is the change in position of the object with respect to time. It is the ratio of distance traveled by the object to the time taken to travel that distance. SI unit of speed is m/s. It is also expressed in km/hr or miles/hr. In vehicles, we have a speedometer that records the speed at which the vehicle is traveling.
Acceleration: Acceleration is the rate of change of velocity with respect to time. It is a vector quantity. It has magnitude and direction. It is measured in meters per second^{2} (m\s^{2 }), and the dimension is LT^{2}.
Force: Force is a push or a pull. When two objects interact with each other, the object changes its position based on the force acting on it. You apply force to move an object from its place and you also apply force to stop a moving object. SI unit of force is Newton named after the scientist. It is basically kgm/s^{2 }(kilogram  meter per second^{2}), and the dimension is LMT^{2}.
SI Units: The international system of units called the SI units is derived from the metrics system. The basic 7 measurable quantities are standardized, and they use the units listed below in the table. There are the basic 7 units of measurement, and the rest other units are derived from here like the area, volume, force, acceleration, etc we just discussed above. Please find below the seven different quantities and their units of measurements.
Quantity  SI Units 
Length  meter 
Time  seconds 
Temperature  Kelvin 
Electric Current  ampere 
Luminous intensity  candela 
Mass  kilogram 
US Standard System of Measurements
Just like the metrics system, the US follows the imperial system of units, also called the U.S customary units. Here things are measured in feet, inches, pounds, ounces, etc. Let us see them in detail in the following sections.
Length: The four most commonly used measures of length are inch, feet, yards, miles. Let us look at the conversions from one unit to another. 1 inch = 2.54 cms. 1 foot = 12 inches. 1 yard = 3ft or 36 inches. 1 mile = 1760 yards(5280 ft), (1 metrics 1.609344 km.)
Area: An area is a twodimensional unit it is measured in terms of length X length. It is the amount of space occupied by the object. We use Inch, Feet, Yards, Miles to measure length. The area is measured in square units such as square Inch, square Foot, square Yard, square Mile, acre. A small area is measured in a square inch and larger surfaces are measured in square yards. Land area is usually measured in acres. Let us look at a few examples of areas. A chessboard is 100sq inches, a garage is 200 sq ft, a part is 100 sq yards, a botanical garden is 500 sq miles, a football ground is exactly 1 acre (1 acre = 43,560 feet.)
Volume: Volume is a threedimensional quantity. It is the amount of capacity/space a substance contains, or the space it can hold. The most common measures of volume in the US customary units are Fluid Ounces (fl. oz), Cups, Pints, Quarts, and Gallons. Note that an ounce is the measure of mass and a fluid ounce is a measure of volume. A fluid ounce is the size of a medicine cup. Other units like peck (1 peck = 2 gals), barrel (31.5 gals) are hardly used. Let us look at the conversion from one unit to another. 1 cup = 8 fl oz. 1 pint = 2 cups. 1 quart = 2 pints, 1 gallon = 4 quarts.
Mass: The most common measurements of mass in the US customary units are Ounces (oz), Pounds (lb), and Tons (ton). Other very small units like dram (weight of grain) are hardly used. Let us look at the conversions from one Unit to another. 1 Ounce = 16 dr, 1 pound = 16 oz, and 1 ton = 2000 lb. There are two variants for the ton. A short ton is 2,000 pounds, and a long ton is 2,240 pounds. In general, when we say a ton, it means a short ton.
Time and Date: Time is measured in seconds. We use a clock (digital or analog) to tell the current time. There are 12hr clock and 24hour clock formats as well. Further, let us learn more about measuring time reading and representing time and how to read a calendar. In the US, the format for writing the date is "month–day–year". For example 7/4/2000 means the 7th month  July, 4  Date, and the year 2000 It is the Millenium year Independence Day, July 4th!
Temperature: Temperature is the measure of how hot or cold substances are. We use a thermometer to measure the temperature. The temperature is measured in degrees Celsius (°C) or Fahrenheit (°F). 0 degrees celsius is equal to 32 degrees Fahrenheit. To convert Celsius to Fahrenheit, you can use the formula Fahrenheit = 9/5 × Celcius + 32
Speed: Speed is the total distance covered by an object in a given time. It is the ratio of distance covered to the time traveled. In British and US customary units, speed is measured in miles per hour (mph). The speedometer is an instrument that gives the current speed at which the vehicle is traveling. You might have seen it in your car.
Direction: The four cardinal directions are North, South, East, and West. A magnetic compass tells the direction. The diagonal directions include the NorthEast, NorthWest, SouthEast and SouthWest. A compass is generally used for navigation and is used in seas, deserts, where it is difficult to find the direction.
Conversions from One System of Measurement to Another
The conversion of length, mass, area, volume from one system of measurement to another system of measurement is very helpful to identify the units. In the below set of tables, we have listed the different units of length, area, volume, mass from US standard measurement to the metric measurement system. Please find below the different units of conversion of length from US standard measurement to the metric measurement system.
Length Conversions  
US standard meaurement  Metric Measurement 
1 inch  2.54 cm 
1 ft  0.3048 m 
1 yard  0.914 m 
1 mile  1.609 km 
Please find below the different units of conversion of mass from US standard measurement to the metric measurement system.
Mass Conversions  
US Standard Measurement  Metric Measurement 
1 ounce  28.34g 
1 pound  0.453 kg 
1 ton  907.184 kg 
The following table shows the different units of conversion of the volume from US standard measurement to the metric measurement system.
Volume(capacity) Conversions  
US standard measurement  Metric measurement 
1 fluid ounce  29.573 ml 
1 fluid pint  0.473 l 
1 fluid quart  0.946 l 
1 gallon  3.785 l 
Please find below the different units of conversion of the area from US standard measurement to the metric measurement system.
Area Conversions  
US standard measurement  Metrics measurement 
1 sq.in  6.45 sq cm 
1 sq ft  0.929 sq.m 
1 sq yd  0.836 sq m 
1 acre  4046.86 sq m 
System of Measurement Solved Examples

Example 1: How many feet are there in 6 miles?
Solution:
From the conversion chart above, we can see that 1 mile = 5280 ft. Thus, in 6 miles there are 6 × 5280 = 31,680 ft. Therefore 6 miles = 31,680 feet.

Example 2: Emy measured 3 inches in her inch scale. How many centimeters will it be approximately equal to?
Solution:
We know that 1 in = 2.54 cm. Thus, 3 in = 3 × 2.54 = 7.62 cm. Therefore 3 inches = 7.62 cm.

Example 3: Which of the following weighs the heaviest? (a) a sack of wheat weighing 12 kg (b) a bag of rice weighing 0.15 ton (c) a box of corn weighing 100 pounds.
Solution:
We know that 1 pound is roughly 1/2 kg. Hence 100 pound is approximately 50 kg. 1 ton is roughly 1000 kg. 0.15 ton is approximately 150 kg. So, a bag of rice weighing 0.15 ton weighs the heaviest. Therefore, a bag of rice of 0.15 ton weighs the heaviest.

Example 4: A football ground exactly measures 1.32 acres in size. How many square feet does it measure?
Solution:
We know that,1 acre = 43560 sq ft. Thus, 1.32 acre = 1.32 × 43560 = 57499.2 sq. ft. Therefore 1.32 acres = 57499.2 sq.ft

Example 5: Water boils at 100 degrees Celsius. What is the temperature in degrees Fahrenheit?
Solution:
We know that Fahrenheit = 9/5 × C +32. Substituting C = 100 We get, F = 9/5 ×100 +32. Simplifying it further, we get, F = 9 × 20 +32 = 180 + 32 = 212. Degree Fahrenheit = 212. Therefore, 100 Celsius is equal to 212 Fahrenheit.
Practice Questions on System of Measurements
FAQs on System of Measurement
Why Measurements are Important?
Measurement is important in our day to day life to get the right amount of the quantity we require. Exact measurement helps in taking correct decisions.
What Measurements are in the Metric System??
The basic units of measures of the metric system are length (measured in meter) mass (measured in kilogram) and time (measured in seconds). Meter, kilogram, and seconds are the base units, kilo, hecto, deka, deci, centi, and milli are prefixed with a base unit to measure larger or smaller quantities.
What are the 7 Basic Units of Measurement?
The basic 7 units of measurement are listed below, the rest of the measures are derived from the base units.
Quantity  SI Units 
Length  meter 
Time  seconds 
Temperature  Kelvin 
Electric Current  ampere 
Luminous intensity  candela 
Mass  kilogram 
What are the 3 System of Measurements?
The three standard systems of measurements are the International System of Units (SI) units, British Imperial System, and the US Customary System. Of these, the International System of Units(SI) units are prominently used.
What is the Main System of Measurement?
The main system of measurement is the international system of units(SI) units, and all other systems of measurement is linked to it. The British Imperial system and the US customary system linked to the SI units of measurement with the units of conversion, and can be conveniently used to convert from one unit to another.
How to Read the Metric System of Measurement?
The metric system of units can be read with the basic units and their conversions. Length, weight, volume, time are the basic dimensions of the measurement of the metric system. The basic unit of length is the meter and all higher units are derived by multiplying the basic unit with an exponent of 10. Similarly the basic unit of weight in grams, for the volume it is liter, and for the time it is seconds.
How does the System of Measurement Work?
The system of measurement works on two basic principles. Firstly the basic units of measurement for the system is to be defined for the various physical quantities. Secondly, the conversion of these units to higher and lower units should be defined, along with its conversion to other systems of measurements. With these two principles, the systems of measurement are completely defined and it works clearly.