24 Key Plumbing Math Formulas to Know [With Examples]

Volume Calculation Formulas

If you need to determine how much fluid or air can fit into a container, pipe, or vessel, then you’ll need a volume calculation formula. These formulas are used to estimate water usage and storage capacity.

Gallons from cubic inches

Gallons = Cubic Inches ÷ 231

• Gallons = The total volume of the tank in US gallons

• Cubic Inches = The volume of the tank in inches

• 231 = The number of cubic inches contained within one US gallon

Example: You have a tank with a volume of 462 cubic inches and need to know the volume in gallons. Divide 462 by 231. The result is 2 gallons, meaning the tank holds 2 gallons of liquid.

462 Cubic Inches / 231 = 2 gallons

Gallons from cubic feet

Gallons = cubic feet x 7.48 (can be rounded to 7.5 if needed)

• Gallons = The total volume in US gallons

• Cubic Feet = The volume of the tank in feet

• 7.48 = The number of gallons in one cubic foot

Example: You know a tank holds 10 cubic feet of liquid, but you need to know how many gallons that amounts to. Multiple 10 by 7.48, and you get 74.8 gallons.

10 cubic feet x 7.48 = 74.8 gallons

Finding the volume of a rectangular tank

V = L x W x H

• V = The volume expressed in cubic units (liters, cubic feet, etc.) 

• L = Length of the tank

• W = Width of the tank

• H = Height of the tank

Example: You have a rectangular septic overflow tank that measures 5 feet long, 3 feet wide, and 2 feet high. Multiply 5 x 3 x 2. The volume of the tank is 30 cubic feet.

5 feet x 3 feet x 2 feet = 30 cubic feet

Finding the volume of a cylindrical tank

V = π x R^2 x H

• V = Volume in cubic units

• R = Radius, or a straight line from the center of a circle to the edge (half the diameter) of the tank’s base

• H = Height of the tank

• π = A constant that represents the ratio of a circle's circumference to its diameter and is approximately equal to 3.14

Example: An owner wants to know how much their rainwater tank can hold. The cylindrical tank has a radius of 2 feet and a height of 5 feet. The volume is π x (2^2) x 5 = 62.83 cubic feet.

~3.14 x (2 feet x 2 feet) x 5 feet = 62.83 cubic feet.

Finding the volume of an elliptical tank

V = π x A x B x H

• V = Volume in cubic units

• π = A constant approximately equal to 3.14

• A = Semi-major axis (half the longest diameter)

• B = Semi-minor axis (half the shortest diameter)

• H = Height of the tank

Example: You are installing a rooftop elliptical water storage tank and you need to tell the customer how much they can expect it to hold. If the semi-major axis is 3 feet, the semi-minor axis is 2 feet, and the height is 4 feet, the volume of the tank is 75.4 cubic feet.

~3.14 x 3 feet x 2 feet x 4 feet = 75.4 cubic feet.

Finding the volume of a spherical tank

V = (4/3) x π x R^3

• V = Volume in cubic units

• R = Radius of the sphere

• π = A constant approximately equal to 3.14

Example: You are working a pipe fitting job for an industrial gas metering station and need to understand the volume of the Horton sphere tanks. The tanks have a radius of 3 feet, meaning their volume is 113.1 cubic feet.

(4/3) x ~3.14 x (3 feet^3) = 113.1 cubic feet.

Finding the volume of a frustum tank

V = (1/3) x π x H x (R^2 + (R x r) + r^2)

• V = Volume in cubic units

• π = A constant approximately equal to 3.14

• R = Radius of the larger base

• r = Radius of the smaller base

• H = Height of the frustum

Example: You’re a master plumber tasked with the installation of frustum tanks for a heat exchanger. The engineers need you to tell them the volume of the hot side tanks. 

The largest end of the tank has a base radius of 4 feet, and the smaller end’s base radius is 2 feet. The height of the tank is 5 feet. The total volume of each tank is 209.4 cubic feet.

(1/3) x 3.14 x 5 feet x (4 feet^2 + (4 feet x 2 feet) + 2 feet^2) = 146.53 cubic feet.

If you’re looking for help with pipe volumes or conversions from imperial to metric units, our ServiceTitan Pipe Volume Tool has you covered. Simply input the values, and the app will calculate for you.

Area Calculation Formulas

Calculating the surface area of different shapes (especially pipes) means you can understand how much space needs to be cleared for insulation and estimate the cost of materials.

Area of squares and rectangles

A = L x W

• A = Area in square units

• L = Length of the square or rectangle

• W = Width of the square or rectangle

Example: You understand that the furnace for a commercial HVAC system requires at least 20 square feet for installation, and you know that the space set aside for the installation has a length of 6 feet and a width of 4 feet. The area of the rectangular floor is 24 square feet. 

6 feet x 4 feet = 24 square feet.

Area of circles

A = π x R^2

• A = Area in square units

• R = Radius of the circle

• π = A constant approximately equal to 3.14

Example: You need to get a pricing quote to clear an area of vegetation in a circular courtyard before work on a fountain plumbing system can commence. You know the radius of the circle is 3 feet, so the surface area will amount to 28.27 square feet.

~3.14 x (3 feet^2) = 28.27 square feet.

Perimeter/Circumference Calculation Formulas

When you need to know pipe size, boundaries, or surface edges, being able to calculate perimeters and circumferences will come in handy.

Circumference of a circle

C = π x D

• C = is the circumference,

• D = is the diameter (which is the radius x 2),

• π = is approximately 3.14

For example, you have to deal with some old underground piping and need to know the circumference of the pipe to install new foam insulation as it is above the frost line. You know the diameter is 4 inches, so the circumference must be 12.57 inches.

π x 4 inches = 12.57 inches.

Pressure/Height/Weight Calculation Formulas

These formulas calculate liquid pressure, pipe heights, and the weight of materials like soldering lead for pipe joining. 

Pounds per square inch (PSI)

PSI = Force ÷ Area

• PSI = Pounds per square inch, a measure of pressure

• Force = The amount of force applied (in pounds)

• Area = The surface area over which the force is applied (in square inches)

Example: You are installing piping from a submersible well pump to a home. You need to tell the owner what pressure they can expect inside the home at the accumulator tank. The pump specifies 600 pounds of force, which will be applied to 50 square inches, meaning the PSI is 12.

600 pounds ÷ 50 square inches = 12 PSI

Height when pressure is known

H = PSI ÷ (0.433 x Water Density)

• H = Height of the water column (in feet)

• PSI = Pounds per square inch (the water pressure)

• 0.433 = A constant for converting PSI to height in feet

• Water Density = The density of water (generally considered a value of 1)

Example: You are troubleshooting a submersible well pump. The pressure at the bore cap is reading 60 PSI. If you want to determine the height of the water column inside the well, divide 60 by 0.433 (x 1). This indicates the water column is about 138.6 feet, confirming that the water level is not the issue.

60 PSI ÷ 0.433 = 138.6 feet.

Lead needed for a given number of joints

Lead Weight = Joints x Lead per Joint

• Lead Weight = Total weight of lead needed

• Joints = The number of joints that require lead

• Lead per Joint = The weight of lead needed for one joint

Example: You have to replace lead pipes in a historic building. You know each joint requires 3 pounds of lead so you will need 36 pounds for 12 joints.

12 joints x 3 pounds = 36 pounds of lead required.

Total lead needed plus waste allowance

Total Lead = (Lead per Joint x Joints) + Waste Allowance

• Total Lead = Total amount of lead required, including waste

• Lead per Joint = Weight of lead per joint

• Joints = Number of joints

• Waste Allowance = An additional amount to account for waste

Example: In a historic building, you know that each joint requires 3 pounds of lead, and you have 12 joints to complete. You are allowed a 10% waste allowance for trimming and excess. You will need 39.6 pounds of lead.

(3 pounds x 12 joints) + 3.6 (10% of 36) = 39.6 pounds.

If all this manual plumbing arithmetic and fractions are a little too much, you can use our ServiceTitan Flow Rate calculator to calculate volumetric flow rates easily.

Pipe Calculation Formulas

If you want your plumbing installation to flow smoothly (literally) you need to understand pipe drops, pitches, and rolling offsets.

Drop of a pipe

Drop = Length x (Slope percentage)

• Drop = The vertical distance the pipe descends

• Length = The total length of the pipe 

• Slope = The incline percentage of the pipe

Example: When running a septic pipe to the tank, you need to install a line with a 2% slope over a 40-foot section to prevent solids from getting separated from liquids. The drop of the pipe will be 0.8 feet, meaning it drops 9.6 inches from the top of the pipe to the bottom.

40 feet x (2 ÷ 100) = 0.8 feet.

Pitch of a pipe

Pitch = Rise ÷ Run

• Pitch = The slope of the pipe (as either a ratio or percentage)

• Rise = The vertical height difference over the length of the pipe (in inches)

• Run = The horizontal distance of the pipe (in inches)

You’re working on a drainage system where the pipe has a rise of 6 inches over a 10-foot run (120 inches). The pitch is 0.05, or 5%. 

6 inches ÷ 120 inches = 0.05 or 5%

Run of a pipe

Run = Length of the Pipe x Slope

• Run = The total horizontal length of the pipe (height difference)

• Length = The total length of the pipe 

• Slope = The slope or pitch of the pipe

Example: You have a PVC drainage line with a slope of 1.5% over 50 feet. The run will be 0.75 feet.

50 feet x 0.015 = 0.75 feet.

Drop from % of fall

Drop = Length x Fall Percentage

• Drop = The total vertical fall of the pipe

• Length = The distance the pipe covers over the horizontal plane

• Fall Percentage = The slope percentage the pipe has

Example: You want to ensure proper drainage for outdoor piping. If a pipe has a fall percentage of 1.25% over a 30-foot length, the drop will be 0.375 feet or 4.5 inches.

30 feet x 0.0125 = 0.375 feet (~4.5 inches)

Ratio of larger to smaller pipe

Ratio = Larger Pipe Diameter ÷ Smaller Pipe Diameter

• Ratio = Comparison between the diameters of two pipes

Example: You are replacing an older pipe system with a 6-inch main and transitioning to a 3-inch branch. The ratio will be 2:1, meaning the larger pipe is twice the diameter.

6 inches ÷ 3 inches = 2 (2:1).

Degree of offset of a pipe fitting

Degree = arctan(Rise ÷ Run)

• Degree = The angle of the pipe offset

• Rise = The vertical distance of the offset (in inches or feet)

• Run = The horizontal distance of the offset (in inches or feet)

• arctan = the inverse function of the tangent function (tan) used to find the angle whose tangent is a given number 

Example: You need to calculate the rolling offset of a pipe with a rise of 8 inches and a run of 24 inches. The degree of offset will be 18.43 degrees.

arctan (8 inches ÷ 24 inches) = 18.43 degrees

Diagonal/Offset Calculation Formulas

If you have had to install a plumbing system around obstacles, these formulas will come in handy to ensure precision when measuring the length of a diagonal.

Length of a diagonal for 45 degree angles and offsets

Diagonal Length = Rise x 1.414

• Diagonal Length = The length of the pipe required to cover the offset

• Rise = The vertical distance between two points

• 1.414 = A constant (the square root of 2) used for 45 degree angles

Example: You’re working with a 45 degree fitting and have a vertical rise of 10 inches. You will need a diagonal length of 14.14 inches to properly fit around the offset at a 45 degree angle.

10 inches x 1.414 = 14.14 inches

Length of all other diagonals

Diagonal Length = √(Rise^2+ Run^2)

√ = The square root symbol

• Diagonal Length = The length of the diagonal pipe/fitting

• Rise: The distance between two vertical points

• Run: The distance between two horizontal points

Example: You’re installing a water heater in a tight space and need to route a pipe around a support beam. The vertical rise is 6 inches and the horizontal run is 8 inches. The diagonal length required will be 10 inches.

√(6 inches+ 8 inches)^2 = √(36 + 64) = √100 = 10 inches

Measurement/Scale Calculation Formulas

Just like their builder counterparts, plumbers need to convert measurements from scaled blueprints into real-world sizes. This formula translates scaled-down measurements into the ones you will be using in real life.

Actual length from scale

Actual Length = Scale Length x Scale Factor

• Actual Length = The real-world measurement

• Scale Length = The measurement on the blueprint

• Scale Factor = The ratio between the drawing scale and real-world dimensions (example: 1:100, 1:50, etc.)

Example: Say you are working with blueprints for a new housing development and a pipe length is shown as 5 inches on the drawing. If the scale is 1:50, then the actual pipe length you will be working with is 250 inches.

5 inches x 50 = 250 inches

Manpower Calculation Formulas

When you have big-scale jobs lined up, it’s not just the tools you need to think about ahead of time. The following formulas also allow you to anticipate the hours needed to get the work done. 

Man hours per joint

Labor Hours = Number of Joints x Time per Joint

• Labor Hours = The total time required to get the job done

• Number of Joints = The number of joints to be completed

• Time per Joint = How long, on average, it takes a plumber to complete a joint (in hours)

Example: Your team is working on a commercial restroom plumbing job and needs to complete 10 pipe joints. If each joint takes about half an hour, then the total labor hours for the entire job is 5.

10 joints x 0.5 hours each = 5 hours.

At ServiceTitan, we’re all about empowering your plumbers to do more with technology. To perform more complex labor calculations, use our ServiceTitan Plumbing Labor Rate Calculator. 

Empowering Plumbing Techs Beyond The Technical Staff

Yes, technical skills are one of the most important aspects of any plumbing tech. But there’s more to success than just the know-how. 

To truly succeed in the modern age, you need to equip your technicians and administrators with the right digital tools in the field and the office.

Equip them with technology

Gone are the days when plumbing techs had to carry around clipboards with their augers. With ServiceTitan’s Field Service App, your techs arrive at the worksite with all the information they need right at their fingertips. 

The app syncs directly with your base of operations, so techs have access to everything they need to get on with the work. Customer details, work history, and even premises information are all available to help your team deliver a personalized service every time. 

With dedicated software for plumbers, ServiceTitan makes paperwork a thing of the past. 

Teach them how to sell

Your techs know everything they need to get the job done right—but they also know everything about what your business sells. So, why not use their industry knowledge in the field to communicate value?

ServiceTitan’s Pricebook Pro allows your plumbing techs to show customers exactly what they’re buying, with clear pricing and detailed images in an easy-to-understand format. 

With Pricebook Pro, your techs have access to data-backed and intelligent recommendations that will drive upsells and have your customers hanging on their every word. 

Pricebook Pro lets you close more sales and impress customers with a modern buying experience.

Over to You

Now you have all the essential plumbing formulas to help you tackle the fundamentals. 

If you’re a seasoned plumbing pro, then hopefully they help you remember the fundamentals, and if you’re a plumber-in-training, they’ll serve you well during your plumbing exam.

Technology like ServiceTitan is here to make your life easier by giving you the tools you need to succeed in the plumbing industry. From managing jobs and estimates to building trust with your customers, ServiceTitan helps you run your plumbing business smarter.