Tube / Pipe Wall Volume Calculator
This calculator finds the volume of the material that makes up a hollow tube or pipe, based on its outer diameter (D), inner diameter (d), and length (l). It also calculates the surface areas.
Enter the outer diameter, inner diameter, and the length of the tube/pipe below. Ensure all dimensions use consistent units. Note that this calculates the volume of the wall material itself, not the hollow space inside (which would be a simple cylinder volume using the inner diameter/radius).
Enter Tube/Pipe Dimensions
Understanding Tube/Pipe Wall Volume & Formulas
What is a Tube or Pipe (for this calculation)?
A tube or pipe, in this context, is a hollow cylinder. This calculator focuses on the volume of the *material* used to construct the tube wall itself, not the volume of the space inside. It's defined by its outer diameter (D), inner diameter (d), and its overall length (l).
The Tube/Pipe Wall Volume Formula
The volume of the tube material is found by calculating the volume of a solid cylinder with the outer diameter and subtracting the volume of a solid cylinder with the inner diameter (the hollow space).
V = Vouter - Vinner
Using radius (R = D/2, r = d/2): V = (π * R² * l) - (π * r² * l)
Using diameters directly (as used in the calculator):
V = (π * (D/2)² * l) - (π * (d/2)² * l) = (π/4) * D² * l - (π/4) * d² * l
Simplified:
V = (π * l / 4) * (D² - d²)
Where:
- V is the Volume of the material
- π (Pi) is approximately 3.14159...
- D is the Outer Diameter
- d is the Inner Diameter
- l is the Length of the tube
Other Tube/Pipe Formulas (Material Focus)
- Wall Thickness (t): Half the difference between outer and inner diameters.
t = (D - d) / 2 - Outer Surface Area (Side only): The area of the exterior curved surface.
OSA = π * D * l - Inner Surface Area (Side only): The area of the interior curved surface.
ISA = π * d * l - End Surface Area (ESA): The area of the two end rings (annuli).
ESA = 2 * (Areaouter_circle - Areainner_circle) = 2 * (π(D/2)² - π(d/2)²) = (π/2) * (D² - d²) - Total Surface Area (TSA): The sum of outer side, inner side, and the two end ring areas.
TSA = OSA + ISA + ESA = πDl + πdl + (π/2)(D² - d²)
Example Calculation (Provided in Original Text)
EX: Beulah builds a concrete pipe of outer diameter D = 3 feet, inner diameter d = 2.5 feet, and length l = 10 feet. Calculate the volume of concrete needed:
V = (π * l / 4) * (D² - d²) = (π * 10 / 4) * (3² - 2.5²) = (2.5π) * (9 - 6.25) = 2.5π * 2.75
Result: V ≈ 21.6 cubic feet (ft³).
Real-Life Tube/Pipe Wall Volume Examples
Click on an example to see the step-by-step calculation:
Example 1: PVC Pipe Section (1-inch Sch 40)
Scenario: Calculate the volume of plastic in a 1-foot length of 1-inch Schedule 40 PVC pipe.
1. Known Values: Outer Diameter (D) ≈ 1.315 in, Inner Diameter (d) ≈ 1.049 in, Length (l) = 1 ft = 12 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 12 / 4) * (1.315² - 1.049²) = (3π) * (1.7292 - 1.1004) = 3π * 0.6288
4. Result: V ≈ 5.92 cubic inches.
Conclusion: One foot of this PVC pipe contains about 5.9 cubic inches of plastic.
Example 2: Steel Pipe Section (2-inch Sch 40)
Scenario: Find the volume of steel in a 10-foot section of 2-inch Schedule 40 steel pipe.
1. Known Values: Outer Diameter (D) = 2.375 in, Inner Diameter (d) = 2.067 in, Length (l) = 10 ft = 120 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 120 / 4) * (2.375² - 2.067²) = (30π) * (5.6406 - 4.2725) = 30π * 1.3681
4. Result: V ≈ 128.9 cubic inches.
Conclusion: The 10-foot steel pipe section contains about 129 cubic inches of steel.
Example 3: Cardboard Tube (Paper Towel Core)
Scenario: Calculate the volume of cardboard in a standard paper towel core.
1. Known Values: Approx. Outer Diameter (D) ≈ 1.75 in, Inner Diameter (d) ≈ 1.60 in, Length (l) = 11 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 11 / 4) * (1.75² - 1.60²) = (2.75π) * (3.0625 - 2.56) = 2.75π * 0.5025
4. Result: V ≈ 4.34 cubic inches.
Conclusion: The cardboard core contains roughly 4.3 cubic inches of material.
Example 4: Copper Tubing (1/2" Type L)
Scenario: Find the volume of copper in a 5-foot length of 1/2" Type L copper tube.
1. Known Values: Outer Diameter (D) = 0.625 in, Inner Diameter (d) = 0.545 in, Length (l) = 5 ft = 60 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 60 / 4) * (0.625² - 0.545²) = (15π) * (0.390625 - 0.297025) = 15π * 0.0936
4. Result: V ≈ 4.41 cubic inches.
Conclusion: The 5-foot copper tube contains about 4.4 cubic inches of copper.
Example 5: Concrete Pipe Section
Scenario: Calculate the volume of concrete in a large pipe section.
1. Known Values: Outer Diameter (D) = 24 inches, Inner Diameter (d) = 18 inches, Length (l) = 8 ft = 96 inches.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V = (π * 96 / 4) * (24² - 18²) = (24π) * (576 - 324) = 24π * 252
4. Result: V ≈ 19000.3 cubic inches (or about 11 cubic feet).
Conclusion: The concrete pipe section uses approximately 19,000 cubic inches of concrete.
Example 6: Drinking Straw Wall Volume
Scenario: Estimate the volume of plastic in a typical drinking straw.
1. Known Values: Approx. Outer Diameter (D) ≈ 0.24 in, Inner Diameter (d) ≈ 0.20 in, Length (l) = 8 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 8 / 4) * (0.24² - 0.20²) = (2π) * (0.0576 - 0.04) = 2π * 0.0176
4. Result: V ≈ 0.11 cubic inches.
Conclusion: A drinking straw uses about 0.11 cubic inches of plastic.
Example 7: Garden Hose Wall Volume
Scenario: Find the volume of rubber/vinyl in a 50-foot garden hose.
1. Known Values: Typical Outer Diameter (D) ≈ 0.75 in, Inner Diameter (d) = 0.625 in (for 5/8" hose), Length (l) = 50 ft = 600 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 600 / 4) * (0.75² - 0.625²) = (150π) * (0.5625 - 0.390625) = 150π * 0.171875
4. Result: V ≈ 80.98 cubic inches.
Conclusion: The 50-foot garden hose contains about 81 cubic inches of material.
Example 8: Hollow Structural Section (HSS Round)
Scenario: Calculate the volume of steel in a 20-foot length of round HSS.
1. Known Values: HSS 4 x 0.25 => Outer Diameter (D) = 4 in, Wall Thickness (t) = 0.25 in. Inner Diameter (d) = D - 2t = 4 - 2*0.25 = 3.5 in. Length (l) = 20 ft = 240 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V = (π * 240 / 4) * (4² - 3.5²) = (60π) * (16 - 12.25) = 60π * 3.75
4. Result: V ≈ 706.86 cubic inches.
Conclusion: The 20-foot HSS tube contains about 707 cubic inches of steel.
Example 9: Telescope Tube Wall Volume
Scenario: Find the volume of aluminum in a telescope's main tube.
1. Known Values: Outer Diameter (D) = 8 inches, Wall Thickness (t) = 0.1 inches => Inner Diameter (d) = 8 - 2*0.1 = 7.8 inches. Length (l) = 48 inches.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V = (π * 48 / 4) * (8² - 7.8²) = (12π) * (64 - 60.84) = 12π * 3.16
4. Result: V ≈ 119.1 cubic inches.
Conclusion: The telescope tube is made of approximately 119 cubic inches of aluminum.
Example 10: Industrial Pipe (6-inch Sch 80)
Scenario: Calculate the volume of steel in a 40-foot section of 6" Schedule 80 pipe.
1. Known Values: Outer Diameter (D) = 6.625 in, Inner Diameter (d) = 5.761 in, Length (l) = 40 ft = 480 in.
2. Formula: V = (π * l / 4) * (D² - d²)
3. Calculation: V ≈ (π * 480 / 4) * (6.625² - 5.761²) = (120π) * (43.8906 - 33.1891) = 120π * 10.7015
4. Result: V ≈ 4034.3 cubic inches.
Conclusion: The 40-foot pipe section contains about 4034 cubic inches of steel.
Understanding Volume Measurement
Volume is the quantification of the three-dimensional space...
Common Volume Units Reference
Ensure your input diameters and length use a consistent unit...
Frequently Asked Questions about Tube/Pipe Volume
1. What volume does this calculator find?
This calculator finds the volume of the solid material that makes up the walls of a hollow tube or pipe. It does *not* calculate the volume of the hollow space inside (the capacity).
2. How do I calculate the volume of the hollow space inside the pipe?
That's simply the volume of a solid cylinder using the *inner* diameter (d) or inner radius (r = d/2). Use the Cylinder Volume formula: Vinside = π * r² * l = (π * d² / 4) * l.
3. What is the formula for the volume of the pipe wall?
The volume (V) is V = (π * l / 4) * (D² - d²), where 'l' is the length, 'D' is the outer diameter, and 'd' is the inner diameter.
4. Can I use radii (Outer R, Inner r) instead of diameters?
Yes. The formula becomes V = π * l * (R² - r²). This calculator uses diameters as input, but they are equivalent (D=2R, d=2r).
5. How is Wall Thickness (t) calculated?
The wall thickness is half the difference between the outer and inner diameters: t = (D - d) / 2. This calculator shows the calculated thickness.
6. What do the different Surface Areas represent?
- Outer Surface Area: Area of the curved outside surface (πDl).
- Inner Surface Area: Area of the curved inside surface (πdl).
- End Surface Area: Area of the two end "rings" or annuli ((π/2)(D² - d²)).
- Total Surface Area: The sum of all the above areas, representing the total surface of the pipe material itself.
7. What units should I use for diameters and length?
Use any consistent unit of length (e.g., inches, mm, feet). The volume result will be in the corresponding cubic units (in³, mm³, ft³), areas in square units, and thickness in linear units.
8. What if my pipe is square or rectangular (like HSS)?
This calculator is only for cylindrical pipes/tubes with circular cross-sections. Calculating the wall volume for square or rectangular tubes requires subtracting the inner prism volume from the outer prism volume.
9. How do I find the inner diameter if I know the outer diameter and wall thickness (t)?
The inner diameter is d = D - 2t.
10. Does this account for pipe threads or end fittings?
No, this calculates the volume for a straight, uniform tube section based on the provided diameters and length. Threads, flanges, or bends are not included.
11. What are pipe "Schedules" (like Schedule 40, Schedule 80)?
Pipe schedules refer to standard wall thicknesses for specific nominal pipe sizes. A higher schedule number generally means a thicker wall (and smaller inner diameter) for the same outer diameter, making the pipe stronger.
