Last updated: July 31, 2026
Hollow Cylinder Volume Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
volume = π·h·(R²−r²), wall thickness = R−r, total surface area = 2π(R+r)h + 2π(R²−r²)
Where:
- R=Outer radius(length)
- r=Inner radius(length)
- h=Height of the cylinder(length)
Worked Examples
Standard pipe dimensions
Use R = 5, r = 3, h = 10.
- 1Compute R² − r² = 25 − 9 = 16.
- 2Volume = π × 10 × 16 = 160π ≈ 502.654824.
- 3Wall thickness = 5 − 3 = 2.
- 4Lateral area = 2π(5+3)10 = 160π ≈ 502.654824.
- 5Top-bottom area = 2π(16) ≈ 100.530965.
Thin-walled tube
Small wall thickness compared with height.
- 1Compute the radius difference 4.2 − 4 = 0.2.
- 2Find annular cross-section area using π(R²−r²).
- 3Multiply by height for volume.
- 4Add inner and outer curved areas for lateral area.
Short hollow spacer
A squat cylinder with thicker walls.
- 1Compute R² − r² = 64 − 6.25 = 57.75.
- 2Volume = π × 3 × 57.75.
- 3Wall thickness = 8 − 2.5 = 5.5.
- 4Total area combines curved sides and both annular caps.
Introduction
A hollow cylinder models pipes, tubes, sleeves, spacers, and shells. This calculator separates the empty core from the solid material so you can compute both enclosed material volume and useful surface measurements.
Geometry of a Hollow Cylinder
A hollow cylinder is an outer cylinder with a concentric inner cylinder removed.
Outer radius is R.
Inner radius is r.
Height is h.
The wall occupies the annular cross-section.
All formulas assume consistent units.
Volume Formula
The material volume equals the outer cylinder volume minus the inner empty core volume.
Outer volume is πR²h.
Inner void volume is πr²h.
Subtract to get πh(R²−r²).
Volume grows linearly with height.
Larger wall area means more material.
Surface Area Components
Surface area is split into curved sides and the two annular end caps.
Outer curved area contributes 2πRh.
Inner curved area contributes 2πrh.
Combined lateral area is 2π(R+r)h.
Two caps contribute 2π(R²−r²).
Total surface area is the sum of both parts.
Wall Thickness
Wall thickness helps engineers judge strength, flow capacity, and weight.
Thickness equals R − r.
Thicker walls generally mean more material.
Small thickness can indicate lightweight tubing.
Thickness affects both volume and cap area.
Always compare it with the overall radius.
Validation Rules
The calculator enforces the geometric constraints of a real hollow cylinder.
R must be positive.
r must be positive.
h must be positive.
Inner radius must be strictly less than outer radius.
Invalid values return zero defaults with a clear error.
How to Use the Calculator
Enter the outer radius, inner radius, and height, then review the primary output first.
Measure or select R.
Measure or select r.
Enter the height h.
Confirm that R > r.
Read the volume and supporting area results.
Common Applications
The calculator is useful in design, fabrication, and inventory planning.
Pipes and tubing
Machine bushings and spacers
Storage sleeves and liners
3D-print shell estimates
Material-cost calculations
FAQs
What is the volume formula for a hollow cylinder?
Volume = π·h·(R²−r²), which subtracts the inner void from the outer solid cylinder.
Why must the inner radius be smaller than the outer radius?
If r is equal to or larger than R, there is no positive wall thickness and the shape is not a valid hollow cylinder.
What does wallThickness represent?
It is the radial thickness of the material, computed as R − r.
What is included in lateralSurfaceArea?
It includes both the outer and inner curved surfaces: 2π(R+r)h.
What is topBottomArea?
It is the area of the two annular caps together: 2π(R²−r²).
Do I need matching units?
Yes. Use the same length unit for outer radius, inner radius, and height so all outputs stay meaningful.
Can I use decimals?
Yes. Any positive finite decimals are allowed as long as the inner radius stays smaller than the outer radius.
How can I check the total surface area?
Add lateralSurfaceArea and topBottomArea; the sum should equal totalSurfaceArea.