The units inch, foot, yard and mile are called Imperial or US Customary units of measure of length and the cube of them are called Imperial or US Customary units of measure of volume.
Conversion between Imperial Units of Measure of Volume
Volume Measure
The following are some common conversions for volume.
1 cubic foot = 1728 cubic inches
1 cubic yard = 27 cubic feet
1 US gallon = 231 cubic inches
1 Imperial gallon ≈ 277.42 cubic inches
1 cubic foot ≈ 7.48 US gallons
1 cubic foot ≈ 6.23 US gallons
Note: Not all of the above conversion rates are exact figures. The figures show after the ≈ sign have further infinite decimal digits.
1. To convert from cubic feet to cubic inches, cubic yards to cubic feet, and cubic miles to cubic yards, we use multiplication.
Example:
2 cubic feet = 1728 x 2 = 3456 cubic inches since 1 cubic foot = 123 cubic inches.
2. To convert from cubic yards to cubic miles, cubic feet to cubic yards, and cubic inches to cubic feet, we use division.
Example:
54 cubic feet = 54 ÷ 27 = 2 cubic yards because 27 cubic feet = 1 cubic yard
Metric Units of Measure of Volume
There is another system for measurement which is called metric system. The units of measuring Volume are derived from units of measure of length, which are millimeter, centimeter, meter and kilometer. Volume units are cubic millimeter, cubic centimeter, cubic meter, cubic kilometer. One can change any unit in the metric system to the others very easily.
Conversion
Metric Volume Units
1 cubic centimeter (cm^{3}) = 1000 cubic millimeters (mm^{3})
1 cubic decimeter (dm^{3}) = 1000 cubic centimeter (cm^{3})
1 cubic meter (m^{3}) = 1000 cubic decimeter (dm^{3})
1. To convert from cubic meters to cubic decimeter, cubic decimeters to cubic centimeters, and cubic centimeters to cubic millimeters, we use multiplication.
Example:
2 cubic meters = 2 x 1000 = 2000 cubic decimeters since 1 cubic meter = 1000 cubic decimeter. (1 dm^{3} is also known as a Liter)
2. To convert from cubic decimeter to cubic meters, cubic centimeters to cubic decimeters, and cubic millimeters to cubic centimeters, we use division.
Example:
4000 cubic centimeter = 4000 ÷ 1000 = 4 cubic decimeters because 1000 cubic centimeter = 1 cubic decimeter.
A Short Review
You need to know 2 things:
 the conversion factor, and
 the magnitude of units to be converted. (i.e. which is bigger)
For example that m^{3} is bigger than dm^{3} and not the other way around.
If converting a bigger unit to a smaller, multiply by the conversion factor.
5 ft^{3} = 5 x 1728 = 8640 in^{3}
5 m^{3} = 5 x 1000 = 5000 dm^{3}
If converting from a smaller to a bigger, divide by the conversion factor.
5 in^{3} = 5 ÷ 1728 = 0.0028 in^{3}
5 dm^{3} = 5 ÷ 1000 = 0.005 m^{3}
Worksheet: Level 1
The operations used are clearly specified. Only one type of mathematical operation is used in a task.
Worksheet: Level 1 Sample Questions
Example:
 Since 3 feet make a yard, what is the conversion factor between ft³ and yd³
Further examples:
What is the conversion factor between:
 feet and inches?
 cubic feet and cubic inches?
 cm and m?
 cm^{3} and m^{3}?
Worksheet: Level 1 Answer Key
Download Worksheet: Level 1
Worksheet: Level 2
Tasks involve one or two types of mathematical operation. Few steps of calculation are required.
Worksheet: Level 2 Sample Questions
Example:
Convert the following amount:
(Remember, conversion factor is 1728 between in³ and ft³)

3 ft³ = ___ in³ ?
Further examples:
Convert the following:
 31.4 m^{3} = _____ cm^{3}
 62,503 in^{3} = _____ ft^{3}
Worksheet: Level 2 Sample Answer Key
Answer:
Convert the following amount:

3ft³ = 3 × 1728 = 5184 in³
Download Worksheet: Level 2
Worksheet: Level 3
Tasks require a combination of operations. Several steps of calculation are required.
Worksheet: Level 3 Sample Questions
Example:
Convert the following amount:
(Remember, conversion factor is 1760³ between yd³ and mi³)
 7.5 ft³ = ___ mi³
Further examples:
Convert the following:
 42,150,000 mm^{3} = _____ km^{3}
 84.5 in^{3} = _____ mi^{3}
Worksheet: Level 3 Sample Answer Key
Answer:
Convert the following amount:
(Remember, conversion factor is 1760³ between yd³ and mi³)
Answer:
7.5 ft³ = 7.5 ÷ 3³ ÷ 1760³ = 0.00000000005 mi³
Download Worksheet: Level 3
Infosheet: Advanced
Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.
Measurement math connections for trades & technology
Length or Distance is a 1D or 1 dimensional concept. It means it runs in 1 direction or in a single line. For this reason it is called linear. It can be measured directly with rulers, tape measures, reflected laser beams in distance finders.
There are many synonyms or alternative names for Length. Some of these names include radius, caliber, depth, or edge. (See table below) These are all linear concepts. Any 3 of these can combine to indicate Volume. For example Length, Width, and Thickness can combine to express the Volume of wood that makes a maple shelf, or Height, Width and Depth can combine to express the Volume a bookcase takes up fully assembled.
Volume or space is a 3D or 3 dimensional concept. It can relate to hollow or solid objects (3D things). It spreads in 3 linear directions in all 3 surface plains of space. For this reason objects are called volumetric or spatial. Volume or space can not directly be measured since measurement tools are linear. Volumetric “measurements” are always calculated from linear measurements. Some digital instruments say they “measure” Volume/Space, but it cannot be measured directly. These instruments calculate volume or space from reflected laser beam Distance measurements.
Volume or space can be inside or outside, hollow or solid, very irregular or very geometric. Inside or outside volume can be partial or full.
Volume or space can be measured in Metric or Imperial units, many of these are used only in specific industries. For example grain harvest size in bushels is mostly applicable to grain storage and transport. Volume of wood in trees or logs measured in cords or board feet only relates to logging and lumber production. Space inside a combustion chamber of an engine in cubic inches is only used in automotive parts context. Suitcase, bag and garment sizes and suitability for air travel is concern for manufacturing industry.
Many units of measure of Volume/space originate from linear units of measure but are modified to reflect that they are used for expressing size of Volume. In this process linear units of measure become volumetric/spatial. Examples include in → in^{3}, km → km^{3}, yd → yd^{3}.
Sometimes these units can be spelled this way: cu.ft. or cubic feet, cu. kms or cubic kilometers. Regardless of spelling variations they are still volumetric/spatial units of measure for Volume.
Some other units of measure words show no relation to linear units, but they are. Examples include board foot (= a piece of wood, 1 inch thick, 1 foot long & 1 foot wide), Imperial gallon (= the volume of 10 pounds of water at 62 °F (17 °C), 1 pound = weight of a platinum cylinder 1.35 inches high, and 1.15 inches diameter), a US gallon (= 231 in^{3}). For more on the differences between Volume and Capacity, see Episode 28 Advanced.
Some volumetric units of measure are funny or anecdotal, they work unofficially as figures of speech. “A 10gallon hat” relates to volume, so does “a sinkhole the size of 5 Olympic swimming pools”. It could be meaningfully used to indicate Volume during rescue or evacuation.
Conversion Table
Property of matter being measured:

possible synonyms

symbol

Unit of measure

Metric

symbol

Imperial & US

symbol

Distance (1D)
in straight line:
straight lines of circles:
loops (full or part) & :

length, width, height,
depth, thickness, gauge,
side, edge, strain

L or l, w, h,
d, th, ga.
s, e, e (greek epsilon)

meter
and other prefixes (kilo, centi, …)

m

mile, fathom
furlong, yard
feet, inch,
barleycorn
point

mi, fm
fur, yd,
ft, in

pt

diameter, caliber, bore
radius, chord

d or Ø, cal, b or Ø,
r, ch

perimeter, circumference, arc, stroke

p or P, c,
a, s

Volume (3D)
(empty space)

space, inside

V

meter cubed
and other prefixes (kilo, centi, …)

m^{3}

cubic mile
cubic yard
cubic feet
cubic inch
dry ounce

mi^{3}
yd^{3}
ft^{3}
in^{3}
oz
ga
bu

capacity
(liquids)

space, inside

V

liter
and other prefixes (kilo, centi, …)

L

gallon, quart
pint, gill
fluid ounce, table and tea spoon

ga, qt
pt, gl
floz, tbsp., tsp
