Calculate pipe volume
To calculate pipe volume, multiply the bore's area by the length: a 10 ft run of pipe with a 4 in inside diameter holds 480π ≈ 1,507.964 in³, which is 6.528 US gallons.
Volume
- Volume The exact answer is the form before the ≈ sign. Keep it that way until the last step if more arithmetic follows.
- 480π ≈ 1,507.964 in³
- Formula The space inside a pipe is a cylinder with the inside diameter: the area of the bore, (π/4)d², times the length.
- V = (π/4)d²L = (π/4) × 4² × 120 = 480π ≈ 1,507.964
- Measurements used
- outside diameter D = 4.5 in, inside diameter d = 4 in, length L = 120 in
- Total surface area A = π(D + d)L + (π/2)(D² - d²): the outside and inside walls plus the two ring-shaped ends.
- 3,211.1 in²
- Wall volume (the material) (π/4)(D² - d²)L = (π/4) × (4.5² - 4²) × 120: the outer cylinder minus the bore. Times the material's density, it is the pipe's weight.
- 400.5531 in³
- Outer cylinder (π/4)D²L, the space the pipe takes up, bore included.
- 1,908.518 in³
- Wall thickness (D - d) ÷ 2.
- 0.25 in
- In liters 1 liter is 1,000 cubic centimeters, the volume of a 10 cm cube.
- 24.71111 L
- In US gallons A US gallon is defined as exactly 231 cubic inches, 3.785411784 liters. An imperial gallon is about 20% larger.
- 6.527985 gal
- In other cubic units Cubic conversions cube the length factor: a yard is 3 feet, so a cubic yard is 27 cubic feet.
- 0.02471111 m³ = 0.8726646 ft³ = 0.03232091 yd³
| Every length times | Volume | Surface area |
|---|---|---|
| 0.5 | 188.4956 in³ (×0.125) | 802.7751 in² (×0.25) |
| 1 | 1,507.964 in³ (×1) | 3,211.1 in² (×1) |
| 2 | 12,063.72 in³ (×8) | 12,844.4 in² (×4) |
| 3 | 40,715.04 in³ (×27) | 28,899.9 in² (×9) |
| 10 | 1,507,964 in³ (×1,000) | 321,110 in² (×100) |
- Volume scales with the cube of length and surface area with the square. Double every measurement and the volume goes up 8 times while the surface only goes up 4. That is why large animals keep heat better and why small ice cubes melt faster.
How the Volume Calculator works
The volume a pipe holds is a cylinder with the pipe's inside diameter: V = (π/4) × d² × L, which is πr²L written with the diameter. That is the figure for filling, draining or flushing a line. The wall is the ring between the inside and outside diameters, (π/4) × (D² - d²) × L.
Worked example: a 10 ft (120 in) run with a 4 in inside diameter and a 4.5 in outside diameter. Inside, V = (π/4) × 4² × 120 = 480π ≈ 1,507.964 in³. A US gallon is exactly 231 in³, so the pipe holds 1,507.964 ÷ 231 = 6.528 gallons, or 24.71 liters. The wall is (π/4) × (4.5² - 4²) × 120 = 127.5π ≈ 400.553 in³ of material, with a wall thickness of 0.25 in.
To calculate the volume of water in a pipe by the foot, use gallons per foot = 0.0408 × d², with d the inside diameter in inches. The constant is (π/4) × 12 ÷ 231 = 0.0408, and the d² means doubling the diameter holds four times the water.
Measure the inside diameter for the capacity. A nominal pipe size is a label rather than a measurement, and the bore of two pipes with the same nominal size differs with the material and wall thickness, so read it from the manufacturer's table or measure it. The outside diameter matters only for the wall: the pipe's weight, which is the wall volume times the material's density, and the hole it passes through.
Keep the units together. Diameters in inches and a length in feet give a mixed answer; put the length in inches as well, or everything in centimeters, where 1,000 cm³ is a liter.
Volume Calculator FAQ
How many gallons are in a foot of pipe?
0.0408 × d² US gallons, with d the inside diameter in inches. A 2 in pipe holds 0.0408 × 4 = 0.163 gallons per foot, so 100 ft of it holds 16.3 gallons.
How do I calculate pipe volume in liters?
Measure in centimeters and divide the cubic centimeters by 1,000. A 10 cm inside diameter over 3 m (300 cm) holds (π/4) × 10² × 300 = 7,500π ≈ 23,561.94 cm³, which is 23.56 liters.
What is the volume of a hollow cylinder?
The outer cylinder minus the inner one: V = (π/4) × (D² - d²) × L with diameters, or π(R² - r²)L with radii. For the 10 cm pipe with an 11 cm outside diameter and a 300 cm length, the wall is 1,575π ≈ 4,948.008 cm³ of material.
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