🔧 Hollow Cylinder Volume Calculator
Calculate volume, radii, wall thickness of pipes, tubes, and cylindrical shells
Enter Outer & Inner Radii
R = outer, r = inner,
t = wall (R-r)
📊 Results
Outer Radius (R)
10 cm
Inner Radius (r)
8 cm
Wall Thickness
2 cm
Height (h)
20 cm
Material Volume
2,262 cm³
Inner Capacity
4,021 cm³
Outer Volume
6,283 cm³
Cross-Section
113.1 cm²
📝 Step-by-Step Solution
Given: R = 10 cm, r = 8 cm, h = 20 cm
Wall thickness: t = R - r = 10 - 8 = 2 cm
Outer volume: V_out = πR²h = π × 100 × 20 = 6,283.19 cm³
Inner capacity: V_in = πr²h = π × 64 × 20 = 4,021.24 cm³
Material volume: V_mat = V_out - V_in = πh(R² - r²) = 2,261.95 cm³
📐 Hollow Cylinder Formulas
Material Volume: V = πh(R² - r²) = πh(R + r)(R - r)
Inner Capacity: Vinner = πr²h
Outer Volume: Vouter = πR²h
Wall Thickness: t = R - r
Cross-Section Area: A = π(R² - r²)
Understanding Hollow Cylinders
🔧 Pipes & Tubes
Hollow cylinders are pipes, tubes, bushings, sleeves. Material volume = wall material. Inner capacity = what fits inside.
📐 Two Radii
R = outer radius, r = inner radius. Wall thickness t = R - r. Both needed for material volume calculation.
🧮 Subtraction Method
V = πR²h - πr²h. Subtract inner cylinder from outer. Factored: V = πh(R² - r²).
⚖️ Weight Calculation
Weight = Material Volume × Density. Know the material (steel, copper, PVC) to calculate weight from volume.
Frequently Asked Questions
What is the hollow cylinder volume formula?
V = πh(R² - r²). Outer cylinder minus inner cylinder. R = outer
radius, r = inner radius, h = height.
What is material volume vs inner capacity?
Material volume = solid wall material (pipe itself). Inner
capacity = hollow space inside (what it can hold).
How do I find wall thickness?
t = R - r. Outer radius minus inner radius. If given diameters: t
= (D - d) / 2.
Can I use diameters instead of radii?
Yes. R = D/2 and r = d/2. Or use: V = (πh/4)(D² - d²). Our
calculator supports both.
What is an annular cylinder?
Same as hollow cylinder. Cross-section is an annulus (ring). Also
called cylindrical shell or pipe.
How do I calculate pipe weight?
Weight = Material Volume × Density. Steel: ~7.85 g/cm³, Copper:
~8.96 g/cm³, PVC: ~1.4 g/cm³.
What if inner radius equals outer radius?
Material volume = 0. No wall thickness. This would be an
infinitely thin shell (not possible in reality).
How do I find inner radius from volume?
r = √(R² - V/(πh)). Rearrange the formula. Need outer radius,
height, and material volume.
What is the cross-sectional area?
A = π(R² - r²). The ring-shaped area when you cut the cylinder.
Used for strength calculations.
Does height or length matter?
Same thing. Use "height" for vertical, "length" for horizontal
pipes. Formula is identical.
How do I convert to liters?
1 liter = 1000 cm³. Our calculator can output in liters, gallons,
or other volume units.
What is OD and ID in pipes?
OD = Outer Diameter, ID = Inner Diameter. Industry standard
naming. OD = 2R, ID = 2r.
Can the inner radius be zero?
Yes, then it's a solid cylinder. Material volume = πR²h. No hollow
space inside.
How accurate for real pipes?
Very accurate for straight sections. Real pipes have joints,
fittings, tolerances that may slightly affect total.
What about oval or non-circular tubes?
Different formulas needed. This calculator is for circular
cross-sections only. Oval tubes use different geometry.
How do I calculate surface area?
Total = 2πRh + 2πrh + 2π(R² - r²). Outer curved + inner curved +
two end rings.
What is Schedule in pipe sizing?
Wall thickness standard. Schedule 40, 80 etc. Higher schedule =
thicker wall. Determines inner diameter for given OD.