Case 1
- Sphere radius
- 5
- Wedge angle
- 90°
130.899694
Open with these valuesSpherical Wedge Volume Calculator
130.899694units³
Result: 130.899694 units³A spherical wedge is one segment of an orange: the piece between two half-planes meeting along a diameter. Its volume is ⅔R³ times the angle in radians, so a 90° wedge of a radius-5 sphere holds 130.90 cubic units. At 360° the formula returns the whole sphere, ⁴⁄₃πR³.
The numbers at a glance
Held fixed: Sphere radius 5.000.
| Wedge angle (°) | Result |
|---|---|
| 25.0 | 36.361026 |
| 50.0 | 72.722052 |
| 75.0 | 109.083078 |
| 90.0Your value | 130.899694 |
| 100.0 | 145.444104 |
| 125.0 | 181.805130 |
| 150.0 | 218.166156 |
| 175.0 | 254.527183 |
Worked examples
Case 2
- Sphere radius
- 2
- Wedge angle
- 180°
16.755161
Open with these valuesCase 3
- Sphere radius
- 10
- Wedge angle
- 30°
349.065850
Open with these valuesHow it's calculated
V = ⅔ × R³ × α, with α = angle × π ÷ 180
- StepEnter the radius of the whole sphere the wedge is cut from.
- StepEnter the angle between the two flat faces, in degrees.
- ResultRead the volume in the cube of the length unit you used.
Reference table
| Radius, angle | Share of the sphere | Volume |
|---|---|---|
| 1, 90 | one quarter | 1.047198 |
| 3, 45 | one eighth | 14.137167 |
| 2, 180 | one half | 16.755161 |
| 5, 90 | one quarter | 130.899694 |
| 10, 30 | one twelfth | 349.065850 |
| 5, 360 | the whole sphere | 523.598776 |
Questions
How do I calculate the volume of a spherical wedge?
Convert the angle to radians with α = degrees × π ÷ 180, then use V = ⅔ × R³ × α. For a radius of 5 and a 90° wedge, α is 1.570796 and the volume is about 130.899694 cubic units.
What is a spherical wedge?
It is the piece of a solid sphere between two flat half-planes that meet along a diameter — exactly one segment of an orange. Its size depends only on the sphere radius and the angle between those two faces.
Is the angle in degrees or radians?
Enter it in degrees, from 0 to 360. The calculator converts to radians itself before applying the formula.
What angle gives the whole sphere?
360°, which puts α = 2π into the formula and returns ⅔R³ × 2π = ⁴⁄₃πR³, the standard sphere volume. A 180° wedge is half a sphere and 90° is a quarter.
What units does the spherical wedge calculator use?
Any length unit for the radius, and the volume comes back in the cube of it. The angle carries no length unit and is always in degrees.
Sources and last check
Information, not professional advice.