Case 1
- Sphere radius R
- 5
- Cap height h
- 2
104.719755
Open with these valuesSpherical Sector Volume Calculator
104.719755units³
Result: 104.719755 units³A spherical sector is the cone from the centre of a sphere plus the cap that tops it, so V = 2πR²h/3. For R = 5 and h = 2 that is 100π/3, about 104.72 cubic units — nearly twice the 54.45 of the bare cap. The volume rises straight in line with h.
Worked examples
Case 2
- Sphere radius R
- 10
- Cap height h
- 3
628.318531
Open with these valuesCase 3
- Sphere radius R
- 3
- Cap height h
- 1.5
28.274334
Open with these valuesHow it's calculated
V = 2 × π × R² × h ÷ 3, h at most 2R
- StepEnter the radius of the sphere the sector is carved from.
- StepEnter the height of the cap that tops the sector.
- ResultRead the volume of cone plus cap in cubic units.
Reference table
| Radius, cap height | Exact | Volume |
|---|---|---|
| 1, 2 | 4π ÷ 3 (whole sphere) | 4.188790 |
| 3, 1.5 | 9π | 28.274334 |
| 5, 1 | 50π ÷ 3 | 52.359878 |
| 5, 2 | 100π ÷ 3 | 104.719755 |
| 10, 3 | 200π | 628.318531 |
Questions
How do I calculate the volume of a spherical sector?
Square the sphere radius, then multiply by 2π/3 and the cap height: V = (2/3) × π × R² × h. For a sphere of radius 5 and a cap height of 2 that is about 104.719755 cubic units.
What is a spherical sector?
A spherical sector is the solid swept from the centre of a sphere out to a cap on its surface — an ice-cream-cone shape with a rounded top and its point at the centre. It is a cone plus the cap that closes it.
How is a sector different from a spherical cap?
A cap is only the dome sliced off the top. A sector adds the cone reaching from the cap's base circle down to the centre of the sphere, so for R = 5 and h = 2 the sector holds 104.719755 against the cap's 54.454273.
Can the cap height be larger than the sphere?
No. At h = 2R the sector already fills the whole sphere, 4πR³/3, and there is nothing beyond that. This calculator therefore holds the answer at the full sphere instead of returning nonsense.
Which units does the answer use?
Whatever you entered, cubed. Radius and cap height in centimetres give cubic centimetres, in inches cubic inches.
Sources and last check
Information, not professional advice.