1,470.2654
cubic units
2,412.7432
cubic units
942.4778
cubic units
3
units
122.5221
square units
1,470.2654
cubic units
2,412.7432
cubic units
942.4778
cubic units
3
units
122.5221
square units
The Hollow Cylinder Volume Calculator determines the volume of material in a hollow cylinder (also called a cylindrical shell or annular cylinder) given the outer radius, inner radius, and height. Hollow cylinders are ubiquitous in engineering -- from pipes and tubes to bearings, bushings, and structural columns.
The volume of a hollow cylinder is given by:
$$V = \pi h (R^2 - r^2)$$
where $$R$$ is the outer radius, $$r$$ is the inner radius, and $$h$$ is the height. This formula subtracts the volume of the inner void from the volume of the complete outer cylinder. It can also be factored as:
$$V = \pi h (R + r)(R - r)$$
This factored form reveals that the volume depends on both the average radius $$(R+r)/2$$ and the wall thickness $$(R-r)$$, which is particularly useful in thin-wall approximations used in mechanical engineering.
Hollow cylinders appear in countless practical scenarios. Pipes and tubing are hollow cylinders where the volume of material determines weight, cost, and structural capacity. Water mains, oil pipelines, and HVAC ducts are all dimensioned using hollow cylinder geometry. The volume of material in a pipe section directly affects its weight per unit length, which is critical for support structure design.
In manufacturing and machining, hollow cylinder calculations determine how much raw material is needed to produce cylindrical parts. When boring out a solid cylinder to create a hollow one, the removed material volume equals the inner void volume. CNC programmers and machinists rely on these calculations for material estimation and waste minimization.
Civil engineering uses hollow cylindrical columns for structural support because they provide excellent strength-to-weight ratios. The moment of inertia of a hollow cylinder is nearly as large as a solid one of the same outer diameter, but with significantly less material. This principle is why steel structural columns and bridge piers are often hollow.
In thermal engineering, the cross-sectional area of a hollow cylinder (the annular region $$\pi(R^2 - r^2)$$) determines heat conduction rates through cylindrical walls. Insulation thickness calculations for pipes rely directly on these hollow cylinder volume and area formulas.
This calculator also reports the outer cylinder volume, inner void volume, and wall thickness for complete analysis. Remember that the inner radius must always be less than the outer radius for a physically meaningful result.
The calculator computes the outer cylinder volume as $$\pi R^2 h$$ and the inner void volume as $$\pi r^2 h$$, then subtracts to get the hollow cylinder volume: $$V = \pi h(R^2 - r^2)$$. Wall thickness is simply $$R - r$$. All computations use Math.PI for precision.
The Hollow Cylinder Volume represents the actual material volume in the shell. The Outer Cylinder Volume is what the volume would be if the cylinder were solid. The Inner Void Volume is the empty space inside. The Wall Thickness is the radial distance between outer and inner surfaces. Ensure the outer radius is greater than the inner radius.
Inputs
Results
V = pi*12*(64-25) = 468*pi ~ 1470.27 cu units. Wall thickness = 8-5 = 3 units.
Inputs
Results
V = pi*20*(100-90.25) = 195*pi ~ 613.59. The thin wall means the material volume is small relative to the outer volume.
A hollow cylinder (or cylindrical shell) is a three-dimensional shape formed by two concentric cylinders sharing the same axis. The space between the outer radius $$R$$ and inner radius $$r$$ constitutes the material, while the inner region is empty. Common examples include pipes, tubes, rings, and bushings.
Start with the volume of the outer solid cylinder $$V_{\text{outer}} = \pi R^2 h$$, then subtract the volume of the inner void $$V_{\text{inner}} = \pi r^2 h$$. The result is $$V = \pi R^2 h - \pi r^2 h = \pi h(R^2 - r^2)$$. This can be factored as $$\pi h(R+r)(R-r)$$.
Yes. If you have outer diameter $$D$$ and inner diameter $$d$$, use $$R = D/2$$ and $$r = d/2$$. The formula becomes $$V = \frac{\pi h}{4}(D^2 - d^2)$$.
If $$r = R$$, the wall thickness is zero and the volume is zero. This represents an infinitely thin shell with no material. In practice, there must always be some positive difference between outer and inner radii.
Multiply the material volume by the density of the material: $$\text{Weight} = \rho \cdot \pi h(R^2 - r^2)$$. For steel (density ~7850 kg/m3), use meters for dimensions to get weight in kilograms.
When the wall thickness $$t = R - r$$ is much smaller than the radius, the volume can be approximated as $$V \approx 2\pi \bar{r} \cdot t \cdot h$$, where $$\bar{r} = (R+r)/2$$ is the mean radius. This simplification is widely used in pressure vessel and pipe design.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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