VOLUMETRIC MEASUREMENT AND YARDAGE
Now that you understand square footage, volumetric measurements should seem easy. Volume is a
measurement of the space found within three-dimensional objects. Volume is expressed in cubic units,
i.e. cubic feet, cubic inches, and cubic yards. As contractors you will use volumetric measurements to
determine quantities of soil, gravel, concrete, water, air and lumber.
1 unit
= One cubic unit
1 unit
1 unit
The cubic unit could be a cubic foot, cubic inch, or a cubic yard.
With a few exceptions, volume may be determined by calculating the square footage of the face of a threedimensional object and then multiplying the square footage by the thickness. Look at the example below
showing a 10-foot by 10-foot concrete slab with a thickness of 1 foot.
10
The concrete slab pictured in fig. 7-1 would represent 100 square feet
s2 = Area or 102 = 100 SF
10
concrete slab
The oblique view of the slab shown in fig. 7-2 shows a slab thickness
or (H)eight of 1 foot.
Volume = S2  H
V = 10  10  1 = 100 ft3
Note: Many texts express cubic footage as ft3 or CF
Figure 7-1
10
10
1
Oblique View
Figure 7-2
In the example above the cubic footage is the same as the square footage because the thickness was one
foot, but what if the slab was 6 thick? First you must be careful not to multiply feet by inches. Six inches
must be converted to feet (612 = .5). Having done this you can now calculate the cubic footage of this
new slab.
V = 10  10  .5
V = 50 ft3
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Try these:
You will find volume formulas on page 36
1.
Calculate the volume of a concrete slab measuring 15 6 14 3  4.
Express answer in ft3
Answer __________
2. Calculate the cubic footage of the concrete slab illustrated below.
4 0
15 0
6-0
5 0
9 3
13 6
Concrete Slab 8 Thick
9 3
Answer _____________
3.
You are building four rectangular columns measuring 18  24 120. What is the total volume
of the four columns expressed in cubic feet?
Answer ___________
4.
You have completed the formwork for 6 cylindrical columns with diameters of 30 and height of 9
feet. What is the combined volume of the six columns expressed in cubic feet?
Diameter = 30
9 0
Answer _____________
5. Calculate the cubic footage contained within the trapezoidal prism below.
9 0
14 0
23 4
Answer ______________
13 6
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CUBIC YARDS
Quantities such as concrete, soil and gravel are bought and sold by the cubic yard.
3
= 1 Cubic Yard = 3  3  3 = 27 cubic feet
3
3
As you can see there are 27 cubic feet in one yard. So to convert cubic feet to cubic yards simply divide the
number of cubic feet by 27.
Example 8-A: You have set the forms for a concrete slab that will be 25 feet by 37 feet and 4 inches thick.
How many cubic yards of concrete must be ordered?
Volume = 25  37  .33 = 308.03 cu. ft.
Step 1: Calculate the volume in cubic feet.
308.03  27 = 11.41Yards
Step 2: Convert to cubic yards
Convert your answers to problems 1 through 4 into yards.
6.
ft3 in problem 1 ____________
7.
ft3 in problem 2 ____________
8.
ft3 in problem 3 ____________
9.
ft3 in problem 4 ____________
10. Calculate the number of yards of concrete needed to build the 8 thick sidewalk illustrated below.
large radius = 8 0
4 0
40 0
8 0
30 0
Cubic footage ________
Cubic Yards
________
4 0
11. You are to build a house on a flat lot. The house measures 78 0 by 42 0. The house is to have a
basement requiring you to dig down 8 6. How many 50 yard dump trucks will it take to
remove the soil?
Total # yd 3_______________
Number of dump trucks________________
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CLOSED FOUNDATION WALLS AND FOOTINGS
Most foundation walls and footings close on themselves as in figure 7-3.
What is the volume of the foundation wall in figure 7-3?
First lets look at the formula for volume:
L  W  H = Volume
40  .5  3 = 60 cu. ft.
Is that an accurate calculation?
Let’s test it. Look
10 0
at figure 7-4
10 0
6 wall thickness
6
3 0
Figure 7-3 (not to scale)
10 0
12
Centerline
10 0
6
Footing
Figure 7-4
Plan View (not to scale)
As you can see from figure 7-4 the corners overlap. If we use the exterior perimeter measurement for length
in the volume formula, each corner will be added in twice. In reality most contractors don’t worry about the
overlap and use the extra concrete as part of their waste factor, however you may run into situations where
it is necessary to calculate exact volume, and here’s how.
All you need is a perimeter measurement taken at the centerline of the wall. This represents the average
length of the wall. By using the centerline length in the volume formula, the correct volume for both wall
and the footing may be easily obtained. Here is an easy way to calculate the centerline measurement.
Step 1: Add up the exterior perimeter of the foundation wall.
10 + 10 + 10 + 10 = 40
Step 2: Multiply the wall thickness times 4
.5  4 = 2
Step 3: Subtract the answer from step 2 from the total perimeter measurement.
40 – 2 = 38
Step 4: Use this number as the perimeter length or centerline length in the volume formula.
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38  .5  3 = 57cu. ft.
38  1  .5 = 19 cu. ft.
Wall Volume
Footing Volume
Note: It doesn’t matter how many zigs or zags there are in the foundation wall as long as the wall closes
on itself.
Example 7-B: Calculate the total cubic yards of concrete needed for the foundation wall below.
45 6
32 4
Wall Thickness = 8
Wall height = 18
30 0
Footing = 15  8
10 0
Note: The answers below were calculated with calculator set to four decimal places and rounded to two
places.
Step 1: Add up the perimeter measurements
77.8333 + 77.8333 + 40 + 40 = 235.67
Step 2: Multiply 4 times the wall thickness
4  .6667 = 2.67
Step 3: Subtract 2.67 from perimeter measurement
235 67 – 2.67 = 233
Step 4: Solve for wall volume
233  .6667  1.5 = 233 cu. ft.
Step 5: Solve for footing volume
233  1.25  .6667 = 194.17 cu. ft.
Step 6: Add wall and footing volumes
233 + 194.17 = 427.17 cu. ft.
Step 7: Calculate cubic yards
427.17  27 = 15.82 CY or 16 cubic yards
Try these:
10 0
7 0 typ.
5 0
20 0
22 0
35 0
House footprint
13-0
55 0
Answer questions 11 through 13 based upon the illustration above.
12. How many cubic feet are contained within the walls of the structure illustrated above if the wall
thickness is 8 and the wall height is 2 6?
Answer ___________
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13. How many cubic feet are contained within the footing measuring 15 wide by
12 high?
Answer __________
14. How many yards of concrete are necessary for the foundation wall and footing?
Answer ________
AIR VOLUME
Air is most often measured in cubic feet. Typically the reason for measuring air volume is to determine air
exchange. That is, how much air volume is there and how often is it replaced with fresh air.
Code requires a bathroom, without an operable window, to have a fan that will turn the air over once every
twelve minutes. If you know the air volume of the bathroom you can determine how powerful a fan is
needed. Cubic feet per minute (CFM) is the most common measure of air movement. Fans are rated by
CFM.
Example 8-C: You are trying to determine how large a fan will be necessary to turn the air every 12
minutes in a bathroom measuring 8 0  12 0  8 0.
Step 1: Calculate the volume of the room
8  12  8 = 768 cu. ft.
Step 2: Divide the room volume by 12 minutes
768 cu. ft.  12 min. = 64 CFM
Therefore a fan with a capacity of moving at least 64 cfm is necessary.
15.
A bathroom with a vaulted ceiling (illustrated and dimensioned below) has no windows. You must
provide a fan that will turn the air over every 12 minutes. What size fan is needed?
Total cubic feet ____________
Fan size in CFM ______________
8 0
11 3
15 6
8 9
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Square & Rectangular
Cubes:
VOLUME FORMULAS
Volume = length  width  height
or
V = lwh
Triangular Prism:
Volume = 1/2  base  height length
or
V = 1/2bhl
Trapezoidal Prism:
Volume = 1/2* (base1 + base2)  h  l
or
V=
b1 + b2 h  l
2
Circles:
(Cylinders)
Volume =  radius radius length
or
V = r2L
Spheres:
Volume = 4/3    radius3
or
V = 4/3r3
r
r
d
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