Quickly calculate the volume of a spherical sector using this spherical sector volume calculator. Input the radius and cone angle in radians.
R = radius of the sphere
θ = cone angle in radians
V = volume
This spherical sector volume formula computes the sector volume by multiplying 2/3 π by the cube of the radius and by (1 - cos θ).
| Radius (R) | Angle (θ rad) | Volume (V) |
|---|---|---|
| 5 | 0.5 | 20.588235 |
| 10 | 1 | 523.598776 |
| 7 | 0.7 | 114.428422 |
| 8 | 1.2 | 322.563381 |
| 6 | 0.9 | 81.936156 |
To compute spherical sector volume manually:
1. Measure the sphere radius (R) and cone angle (θ).
2. Calculate cos θ.
3. Subtract cos θ from 1.
4. Multiply by (2/3) π R³.
This spherical sector volume calculator provides accurate results with six decimal places. Ideal for students, engineers, and mathematicians working with spheres and spherical cones.
• A spherical sector is like a “cone” inside a sphere.
• Its volume is proportional to the solid angle.
• Spherical sectors are used in astronomy and optics.
• The formula derives from integrating the sphere volume.
• They are applied in calculating portions of planetary atmospheres.