Hollow Cylinder Volume Calculator

Enter the outer radius, inner radius, and height of a hollow cylinder (pipe or tube) to get its volume (V = πh(R² − r²)), wall thickness, and an optional mass estimate.

Quick Facts

Volume formula
V = πh(R² − r²)
Outer cylinder volume minus the empty inner cylinder volume.
Equivalent form
V = πh(R + r)(R − r)
Useful when you know the wall thickness (R − r) directly.
Wall thickness
t = R − r
Inner radius must always be smaller than the outer radius.

Your Results

Calculated
Volume
-
V = πh(R² − r²)
Wall Thickness
-
t = R − r
Outer (Solid) Volume
-
πR²h, for reference
Estimated Mass
-
Volume × density

Ready

Enter the outer radius, inner radius, and height, then press Calculate.

Formula and Method for Hollow Cylinder Volume

Volume of a Hollow Cylinder (Pipe or Tube):

V = π × h × (R² − r²)

R = outer radius; r = inner radius; h = height (or length)

A hollow cylinder — like a pipe, tube, or washer extruded into a rod — is the solid that remains after a smaller cylinder (the bore) is removed from the center of a larger one. Its volume is simply the outer cylinder's volume minus the inner cylinder's volume: V = πR²h − πr²h = πh(R² − r²). This calculator also reports the wall thickness and, if you supply a material density, an estimated mass.

How the calculation works

Enter the outer radius (R), inner radius (r), and height or length (h), all in the same unit. The calculator squares each radius, subtracts the inner radius squared from the outer radius squared, multiplies by π and the height to get the volume, and also computes the wall thickness (R − r) and the volume of the equivalent solid cylinder (πR²h) for reference. If you provide a material density in grams per cubic centimeter, it converts the volume to cubic centimeters and multiplies by density to estimate mass.

Common mistakes

  • Diameter vs. radius: if you measured across the pipe (diameter), divide by 2 before entering it — using diameter as radius roughly quadruples the calculated volume.
  • Reversed radii: the outer radius must be larger than the inner radius; swapping them, or measuring the outer diameter but the inner radius, gives a negative or nonsensical result.
  • Mixed units: the outer radius, inner radius, and height must all use the same unit — convert everything to one unit system before entering values.

Real-world applications

  • Plumbing and piping use hollow cylinder volume to calculate the amount of metal or plastic in a pipe, or the fluid capacity inside it.
  • Manufacturing uses it to estimate the mass and material cost of tubes, bushings, sleeves, and rings before production.
  • Mechanical and structural engineering use it for hollow shafts and columns, where removing material from the center saves weight while retaining strength.
  • Construction uses it to estimate the concrete needed for hollow cylindrical forms, such as pipe piles or cylindrical tanks with a core void.

Frequently Asked Questions

What is the formula for the volume of a hollow cylinder?
V = π × h × (R² − r²), where R is the outer radius, r is the inner radius, and h is the height (or length) of the cylinder. This is the volume of the full outer cylinder minus the volume of the empty inner cylinder.
What if I only know the diameters instead of the radii?
Divide each diameter by 2 to get the radius: R = outer diameter ÷ 2 and r = inner diameter ÷ 2. Then apply V = πh(R² − r²) as usual.
How do I estimate the mass of a hollow cylinder like a pipe?
Multiply the volume by the material's density (mass = volume × density). For example, steel has a density of about 7.85 g/cm³, so a 1,000 cm³ steel pipe weighs about 7,850 g, or 7.85 kg.
Can the inner radius be zero or equal to the outer radius?
If the inner radius is 0, the shape is a solid cylinder and V = πR²h. The inner radius must always be smaller than the outer radius, otherwise there is no wall and the formula is invalid.

Related calculators