Math for the Workplace 12
Plumbing Information Sheet
Number Sense
Plumbers work with integers, decimals, fractions, ratios, proportions, and percentages. As well,
they work with monetary values. When working with elevations, plumbers work with feet and
decimal feet. Dimensions could be given in feet, inches and fractions.
Plumbers usually round to two numbers after the decimal point.
Operation Sense
Calculations performed by plumbers include, but are not limited to, calculating the amount of
materials being used, such as, pipe, connectors, and fixtures. They must also calculate the cost
price and in turn the retail price charged to the consumer to obtain a profit. The business
calculation of Profit = Retail Price – Cost Price is critical to the viability of a plumber’s business.
A well developed sense of estimation is also important. Estimating the materials for a job or the
length of time to complete a job are both important to being a successful plumber.
They must be very comfortable using technology such as calculators. Plumbers also need well
developed problem solving skills. Problem solving through obstacles such as design changes or
availability of resources all require problem solving skills.
Measurement
Measurement for reading blueprints and using scales requires proportional thinking. Plumbers
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such as 1:50 or 1:100. Plumbers must measure lengths of pipes. They must also be able to
measure the angles. It is essential that all of these measurements be done with both precision and
accuracy.
Plumbers must also be very comfortable doing conversions. Common conversions for plumbers
include:
 BTU = KW
 1” = 25 mm
 1 psi = 7 kPa
 1 imp gal = 4.5 l
Geometry
Understanding angles and geometric properties cannot be understated. Degrees are important for
calculating offsets. Plumbers also use right angle properties and Pythagorean Theorem for
calculating the hypotenuse.
Math For The Workplace 12: Plumbing Information Sheet
August 2008
Examples of Math in Plumbing
 Conversions: fractions to decimals, inches to feet, feet and decimal feet
 Fixture spread for single bathroom group: equal spacing between fixtures
 Angle parts: squares, rectangles, circles, triangles
 Circle parts
 Measurements: centre, face, back, end and throat
 Fitting allowances
 Offsets 45 degrees: 1.414, .707
 Metric and Imperial systems of measurement
o Areas: squares, rectangles, circles and triangles
o Volumes: gallons, weight of water, 6.25 gallons per cubic foot
o Length
o Mass: weight of liter
o Pressure
o Temperature
 Conversions in back of plumbing code
 Grading with a level: 1/4“ per ft., 2% and 1:50
 Fixture spread, battery of fixtures
 Drop, rise and run (Grading)
 Elevations (Horizontal drains)
 Head pressures: 0.434 psi / 0.0361 psi, 27.7” / 2.31’ 1 kPa = 1 dm
 1 gal = 277” cu., 6.25 gal./1ft.cu., 1 gal. = 10 lb.
 1 dm cu. =1 litre=1 kg.
 US to Imperial gal. 5/6 or 6/5
 1 IMP Gal. = 4.54 litres
 1 US Gal. = 3.78 litres
 Parallel offsets using 45 ( 1 and 2 X factors )
 Offset factors from IPT book
 D² over d²
 Linear expansion (coefficients)
 Rolling offsets with 45
 Elevations (Horizontal and vertical) - Transits
 Absolute pressure and temperature
 Water columns
 Psi to ounces
 PPM, mg/l, grains /gal
 Head pressure
 Head of Hg
 Jumper Offsets using 2 - 45 and 1 – 90
 Jumper Offsets using 4 – 45
Math For The Workplace 12: Plumbing Information Sheet
August 2008
Math For The Workplace 12: Plumbing Information Sheet
August 2008
Plumbing Worksheet #1
IMPERIAL CYLINDER TANK CAPACITIES
Where “D” is the diameter in inches, where “r” is the radius, or half the diameter in inches and where
“L” is the length or height in inches:
Volume in Gallons = π r ² H = cubic inches divided by 277 = IMP. Gallons
**** Note: 1 gallon contains 277 cu. inches ****
If “D”, “r” and “L” are measured in feet:
Volume in Gallons = π r ² H = cubic feet multiply by 6.25 = IMP. Gallons
****Note: 1 cu. ft. contains 6.25 gallons:****
SAMPLE PROBLEM
SAMPLE PROBLEM
D equal 24”
D equal 2 ft.
r equal 12”
r equal 1 ft
L equal 48”
L equal 4 ft.
Cubic inches ________________
Cubic feet
_______________
Gallons
Gallons
_______________
________________
****NOTE : 1 Imperial Gallon = 10 pounds****
Math For The Workplace 12: Plumbing Information Sheet
August 2008
Plumbing Worksheet #2
Math For The Workplace 12: Plumbing Information Sheet
August 2008
Plumbing Worksheet #3
ROLLING OFFSET # 3
Calculate the following:
A ___________
B ___________
C ___________
72
D ___________
A=
cm
?
9 .5
cm
C=
?
14cm
B=
D
=?
60
?
cm
Math For The Workplace 12: Plumbing Information Sheet
August 2008
Plumbing Worksheet #4
JUMPER OFFSET
2 - 45 and 1 - 90
1.
K = Half the diameter plus the space times two
K = 7” + 2” = 9” X 2 = 18”
Note:
The 45 degree elbow is above the centre of the cylinder.
K = 18” – (2” X 1.414)
K = 18” – 2.83” = 15.17”
k = 15.17”
2.
L = Half the diameter plus the space times two
L = 7” + 2” = 9” X 2 = 18”
Note:
The 45 degree elbow is below the centre of the cylinder.
L = 18” + (2” X 1.414)
L = 18” + 2.83” = 20.83”
L = 20.83”
Math For The Workplace 12: Plumbing Information Sheet
August 2008
3.
J = the overall measurement minus Half the diameter, plus the space, times two, times .707
minus the distance above the centre line.
J = 21” – (7 + 2) X 2 X .707 – 2”
J = 21” – (9 X 2) X .707 – 2”
J = 21” – (18 X .707) – 2”
J = 21” – (12.73 – 2”)
J = 21” – 10.73 = 10.27”
J = 10.27”
4.
M = the overall measurement minus Half the diameter, plus the space, times two, times .707 plus
the distance below centre line.
M = 26” – (7 + 2) X 2 X .707 + 2”
M = 26” – (9 X 2) X .707 +2”
M = 26” – (18 X .707) + 2”
M = 26” – (12.73 +2”)
M = 26” – 14.73”
M = 11.27”
Math For The Workplace 12: Plumbing Information Sheet
August 2008