Table of Contents
1.  Introduction 
2.  Metric System 
3.  Unit Conversion for Length 
4.  Unit Conversion for Area 
5.  Unit Conversion for Volume 
6.  Summary 
7.  About Cuemath 
8.  FAQs 
9.  External References 
07 October 2020
Reading time: 5 minutes
Introduction
In olden days, unscientific methods were used for measurement by keeping objects next to each other for comparing their length and pouring liquids and weighing in the hand to know which is heavier. In 1799, the French government introduced the decimal system of measurement and later the International system of measurement was introduced in 1939.
Measurements are used in data and statics calculations and in geometry where the different types of geometrical figures can be classified
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How to convert units of Length, Area and Volume? 
Metric System
It is a system of measurement derived from a decimal system of measurement. The basic units in this system are meter grams and litre for measuring length ,volume and Capacity respectively.
Difference between Metric system and Imperial system of measurement
Metric system 
Imperial system 
In metric system the basic unit of measurements are meter,grams and litre 
In metric system the basic unit of measurements are feet,pounds and inches 
It is a simple system where conversion from smaller and bigger units are easy 
Conversion of smaller and bigger units are complex 
It is used in all Europe countries and India 
It is used by british countries 
Length, Area, and Volume
They are the one, two and threedimensional measurements of geometrical figures. The prefixes used are kilo, hecto, deka, deci, centi and milli. The base unit remains same for length, Area and Volume which is "meters "
Length
Length Unit Converter
It is a one dimensional scalar quantity used to measure a line segment. The basic unit of measuring length in the International system of units is "METER". Further, according to the length of the specimen units like millimeter, centimeter, decimeter, dekameter, hecto meter and kilometer are respectively used.
Bigger units 
BASE UNIT 
Smaller units 


Kilo(k) 
Hecto (H) 
Deka(D) 
METER(m) 
Deci(d) 
Centi(c) 
Milli (m) 
1000 
100 
10 
1 
1/10 
1/100 
1/1000 
Multiply by 10 \(\Rightarrow\) 
\(\Leftarrow\) Divide by 10 
The above table gives the information about the basic unit 'METER' and its prefixes and how they are converted to smaller and larger units depending on the measurement of specimen to be measured
The rule of conversion is " multiplication is done for converting higher units to smaller units ,similarly when converting smaller units to higher units division is carried out "
Conversion Table For Measurement Of Length
m to dm 1 meter = 10 dm 
Dm to m 1 deci meter = 0.1 meters 
m to cm 1 meter = 100 centimeter 
cm to m 1 centimeter = 0.01meter 
m to mm 1 meter = 1000 millimeter 
mm to m 1 millimeter = 0.001 meter 
m to da m 1 meter = 0.1 da meter 
da m to m 1 decameter = 10 meter 
m to hm 1 meter = 0.01 hecta meter 
hm to m 1 hecta meter = 100 meter 
m to km 1 meter = 0.001 kilometers 
Km to m 1 kilometer = 1000 meter 
Example 
Convert the following:
5 meter = _____deci meter 1 meter = 10 deci meter 5 meter = 5 × 10 = 50 decimeter 
45 deci meter = ___ m 1 deci meter = 0.1 m 45 deci meter = 45 × 0.1 = 4.5 m 
10 m= _____cm 1 meter = 100 centimeter 10 meter = 10 × 100 = 1000 cm 
500 cm = ______ m 1 centimeter = 0.01 meter 500 cm = 500 × 0.01 = 5 m 
16 m= _____mm 1 meter = 1000 milli meter 16 meter = 16 × 1000 = 16000 mm 
68 millimeter = _____m 1 millimeter = 0.001 meter 68 millimeter = 68 × 0.001 = 0.068 m 
20 m= _____decka meter 1 meter = 0.1 decka meter 20 meter = 20 × 0.1 = 2 decameter 
35 decameter = ___ meter 1 decameter = 10 meter 35 deca meter = 35 × 10 = 350 m 
35 m= _____hecta meter 1 meter = 0.01 hecta meter 35 meter = 35 × 0.01 = 0.35 hecta meter 
70 hecta meter = ___ meter 1 hecta meter = 100 meter 70 hecta meter = 70 × 100 = 7000 m 
50 m= _____kilo meter 1 meter = 0.001 kilo meter 50 meter = 50 × 0.001 = 0.05 kilometer 
500 kilometer = ____m 1 kilometer = 1000 m 500 kilometer = 500 × 1000 = 5, 00, 000 m 
Km to mile
1 km = 0.621 mile
mile to Km
1 mile = 1.609 km
Kilometer 
Miles 

5 
5 × 0.621 = 3.105 
10 
10 × 0.621 = 3.210 
40 
40 × 0.621 = 24.84 
200 
200 × 0.621 = 124.2 
500 
500 × 0.621 = 310.5 
Area
Area Unit Converter
It is a scalar quantity, which is used to measure the quantity of two dimensional geometric plane figures where length and breadth is taken into consideration.Since area is the twodimensional plane, the basic unit used to measure is \(" mm^2" (Length \times Length)\). Depending on the size of the plane surface the measurement can as follows,
Bigger units 
BASE UNIT 
Smaller units 


kilo 
hecta 
deca 
meter 
deci 
centi 
milli 

km^{2}  ham^{2}  dam^{2}  m^{2}  dm^{2}  cm^{2}  mm^{2}  
1000 
100 
10 
1 
1/10 
1/100 
1/1000 

Multiply by 10 \(\Rightarrow\) 
\(\Leftarrow\) Divide by 10 
Conversion Table For Measurement Of Area
m^{2 }to dm^{2} 1 meter = 10 decimeter 1 m^{2}= 10 × 10 = 100 dm^{2} 
m^{2 }to cm^{2} 1 meter = 10 centimeter 1 m^{2}= 100 × 100 = 10000 cm^{2} 
m^{2 }to mm^{2} 1 meter = 10 mm 1 m^{2}= 1000 × 1000 = 1000000 mm^{2} 
m^{2} to da m^{2} 1 meter = 0.1 decameter 1 m^{2}= 0.1 × 0.1 = 0.01 da m^{2} 
m^{2 }to hm^{2} 1 meter = 0.01 hectameter 1 m^{2}= 0.01 × 0.01 = 0.0001 hm^{2} 
m^{2 }to km^{2} 1 meter = 0.01 kilometer 1 m^{2}= 0.001 × 0.001 = 1 × 10 ^{6}kilo m^{2} After multiplying the decimal, after point we get 6 numbers, so to convert it into simple form above answer can be written 
dm^{2 } to m^{2} 1 dm= 0.1 m 1 dm^{2}= 0.1 × 0.1 = 0.01 m^{2} 
cm^{2 } to m^{2 } 1 cm= 0.01 m 1 cm^{2}= 0.01 × 0.01 = 0.0001 m^{2} 
mm^{2} to m^{2} 1 cm= 0.001 mm 1 mm^{2}= 0.001 × 0.001 = 1 × 10 ^{6}m^{2} 
da m^{2 } to m^{2} 1 da m= 10 m 1 da m^{2}= 10 × 10 = 100 m^{2} 
hm^{2 } to m^{2} 1 hm= 100 m 1 hm^{2}= 100 × 100 = 10000 m^{2} 
km^{2 }to m^{2 } 1 km= 100 m 1 km^{2}= 1000 × 1000 = 1000000 m^{2} 
Example 
Convert the following:
Acre is an imperial system of measuring a land whereas feet is a metric system of measurement.
Acre to square feet
1 acre = 43560 square feet.
Square feet to acre
1 square feet = 2.296 × 10^{5 }acre
Square feet 
Acres 
5000 
5000 ÷ 43560 = 0.1147 
10,000 
10,000 ÷ 43560 = 0.2295 
Acres 
Square feet 
10 
10 × 43560 = 435600 
50 
50 × 43560 = 2178000 
Volume
Volume is a three dimensional measurement where length ,breadth and height of the geometrical solid figure are taken for the consideration .The unit used is " mm^{3 }(length breadth height)”.The below table gives the conversion of smaller and bigger units.
Volume Unit Converter
Bigger units 
BASE UNIT 
Smaller units 

kilo 
hecta 
deca 
meter 
deci 
centi 
milli 
km^{3}  ham^{3}  dam^{3}  m^{3}  dm^{2}  cm^{3}  mm^{3} 
1000 
100 
10 
1 
1/10 
1/100 
1/1000 
Multiply by 10 \(\Rightarrow\) 
\(\Leftarrow\) Divide by 10 
Conversion Table For Measurement Of Volume In Terms Of Meter
m^{3} to dm^{3} 1 meter = 10 dmeter 1 m^{3 } =10 × 10 × 10 = 1000 dm^{3} 
m^{3} to cm^{3} 1 meter = 10 cm 1m^{3} = 100 × 100 × 100 = We have 6 zeros after 1, the simplied answer will be 1m^{3} = 1 × 10^{6}cm^{3} 
m^{3} to mm^{3} 1 meter = 100 milli meter 1 m^{3}= 1000 × 1000 × 1000 = 1 × 10^{9} mm^{3} 
m^{3} to da m^{3} 1 meter = 0.1 deca meter 1 m^{3}= 0. 1× 0.1 × 0.1 = 0.001 da m^{3} 
m^{3} to hm^{3} 1 meter = 0.01 hecta meter 1 m^{3}= 0.01 × 0.01 × 0.01 = 1 × 10^{6}hm^{3} After multiplying the decimal, after point we get 6 numbers, so to convert it into simple form above answer can be written 
m^{3} to km^{3} 1 meter = 0.01 kilo meter 1 m^{3}= 0.001 × 0.001 × 0.001 = 1 × 10^{9} km^{3} 
dm^{3 } to m^{3} 1 dm= 0.1 m 1 dm^{3}= 0. 1× 0.1 × 0.1 = 0.001 m^{3} 
cm^{3 } to m^{3} 1 cm= 0.01 m 1 cm^{3}= 0.01 × 0.01 × 0.01 = 1 × 10^{6} m^{3} 
mm^{3 } to m^{3} 1 cm= 0.001 mm 1mm^{3}= 0.001 × 0.001 × 0.001 = 1 × 10^{9} m^{3} After multiplying the decimal, after point we get 9 numbers, so to convert it into simple form above answer can be written 
da m^{3 } to m^{3} 1 da m= 10 m 1 da m^{3}= 10 × 10 × 10 = 1000 m^{3} 
hm^{3 } to m^{3} 1 hm= 100 m 1 hm^{3}= 100 × 100 × 100 = 1 × 10^{6}m^{3} 
km^{3 } to m^{3} 1 km= 100 m 1 km^{3}= 1000 × 1000 × 1000 We have 9 zeros after 1, the simplied answer will be = 1 × 10^{9} m^{3} 
Examples 
Convert the following :
1. litre to m^{3}
Answer : \(1 \rm{m}^3= 1000 \text{ litres}\) \(1 \text{litre} = \frac{1}{1000}\rm{m}^3\)
\(1 \text{ litre} = 0.001 \text{ m}^3\) 
2. m^{3} to cm^{3}
Answer :
\(\begin{align}1 \text{m}^3&= 100 × 100 × 100 \text{ cm}^3\\1 \text{m}^3 &= 10,00,000 \text{ cm}^3\end{align}\)
we have 6 zeros after one so in the simplest form, it can be written as
\(1 \text{m}^3 = 1 \times 106 \text{ cm}^3\) 
3. cubic feet to \(\text{m}^3 \)
Answer :
1 feet \(= 0.305 \text{ m}\)
1 cubic feet \(=0.305 × 0.305 × 0.305 \text{m}^3\)
1 cubic feet\(= 0.0284 \text{m}^3\) 
4. km^{3} to mile^{3}
Answer :
\(1 \text{ km} = 0.621\) mile
\(= 0.621 \times 0.621 \times 0.621\)
1 km^{3}= 0.239 mile^{3} 
mile^{3 } to km^{3}
Answer : 1 mile \(= 1/ 0.621 \text{ km}\)
\(1 \text{ mile}^3 = (\frac{1}{0.621}) \times (\frac{1}{0.621}) \times (\frac{1}{ 0.621}) \text{ km}^3\)
\(1 \text{ mile}^3 = 0.0414 \text{ km}^3\) 
Summary
According to the international system of measurement "METER" is the unit used for measuring length anywhere in the world and it is known as the base unit. Length, Area and Volume uses meter as the base unit, depending on the size of the object to be measured prefixes like kilo, hecta, deka, deci, centi and milli are used.
When converting larger prefixes kilo, hecta and deka to smaller prefixes deci, centi and milli multiplication with 10 is carried respectively and for converting smaller prefix to higher prefix division by 10 are done.
Written by Nethravathi C, Cuemath Teacher
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Frequently Asked Questions (FAQs)
What is the metric system?
It derived from a decimal system of measurement where the basic units like meter, grams and litre are used for measuring length ,volume and capacity
What is the imperial system?
It is a used in British countries, the basic units feet, inches and pounds are used for measuring length ,volume and capacity
What are the metric system prefixes?
Metric system of prefixes are kilo(1000),deca(100),hecta(10),deci(1/10),centi(1/100) and milli(1/1000)
How to convert cm to m?
To convert from centimeters to meters, simply divide the number of centimeters by 100 and change the units to m
External References
To know more about conversions, please visit this blog: