Sphere
Find the volume and surface area of a sphere from the radius, diameter, volume or area, and the volume of a spherical cap.
What is known:
Sphere radius r
x
Units:
Lengths are positive numbers (whole or decimal), angles are in degrees.
The sphere calculator finds the volume, the surface area, the diameter, the great circle circumference and area from the radius, diameter, volume or surface area, as well as the volume and area of a spherical cap.
Sphere formulas
| Value | Formula |
|---|---|
| Volume | V = ⁴⁄₃πr³ = πd³/6 |
| Surface area | S = 4πr² = πd² |
| Radius from volume | r = ∛(3V / (4π)) |
| Radius from area | r = √(S / (4π)) |
| Great circle circumference | C = 2πr |
Example. r = 3 cm.
V = ⁴⁄₃π · 27 = 36π ≈ 113.1 cm³, S = 4π · 9 = 36π ≈ 113.1 cm².
The surface area of a sphere is 4 times the area of its great circle. A sphere has the smallest surface area for a given volume, which is why drops and bubbles are round.
Spherical cap
The part of a ball cut off by a plane. If h is the cap height and r is the sphere radius:
| Volume | V = πh²(r − h/3) |
| Curved surface area | S = 2πrh |
| Base radius | a = √(h(2r − h)) |
Comments
No comments yet.