Case 1
- Bottom base radius (a)
- 4
- Top base radius (b)
- 3
- Height between the planes (h)
- 2
82.728607
Open with these valuesSpherical Segment Volume Calculator
82.728607units³
Result: 82.728607 units³Cut a sphere with two parallel planes and the slice between them holds πh ÷ 6 times (3a² + 3b² + h²), where a and b are the two flat faces and h the distance between them. With a = 4, b = 3 and h = 2 the bracket is 79 and the volume 82.73 cubic units. The sphere's own radius is never needed.
Worked examples
Case 2
- Bottom base radius (a)
- 5
- Top base radius (b)
- 5
- Height between the planes (h)
- 3
249.756616
Open with these valuesCase 3
- Bottom base radius (a)
- 10
- Top base radius (b)
- 8
- Height between the planes (h)
- 5
1,353.502835
Open with these valuesHow it's calculated
V = π × h ÷ 6 × (3a² + 3b² + h²)
- StepMeasure the radius of the lower flat circle, not the sphere.
- StepMeasure the radius of the upper flat circle.
- StepMeasure the straight distance between the two planes.
- ResultRead the volume in the cube of the unit you entered.
Reference table
| a, b, h | Bracket 3a² + 3b² + h² | Volume |
|---|---|---|
| 1, 1, 1 | 7 | 3.665191 |
| 2, 1, 4 | 31 | 64.926248 |
| 4, 3, 2 | 79 | 82.728607 |
| 6, 2, 3 | 129 | 202.632726 |
| 5, 5, 3 | 159 | 249.756616 |
| 10, 8, 5 | 517 | 1353.502835 |
Questions
How do I calculate the volume of a spherical segment?
Use V = πh ÷ 6 × (3a² + 3b² + h²), where a and b are the two base radii and h the height between the parallel planes. For a = 4, b = 3 and h = 2 the bracket is 48 + 27 + 4 = 79, so the volume is about 82.728607 cubic units.
What is the difference between a spherical segment and a spherical cap?
A segment is cut by two parallel planes and has two flat circular faces; a cap is cut by one plane and has only one. Setting b to zero in the segment formula gives the cap.
What are a and b in the formula?
They are the radii of the two flat circular faces, measured where each plane cuts the sphere. They are not the sphere's radius — that value is not needed here at all.
Can I use this for a partly filled spherical tank?
Yes, the liquid in a horizontal band of a spherical tank is exactly a spherical segment. Measure the radius of the liquid surface, the radius at the lower boundary and the vertical depth between them.
What units does this calculator use?
Any single length unit for all three inputs. Centimetres in, cubic centimetres out; inches in, cubic inches out.
Sources and last check
Information, not professional advice.