About the spherical cap calculator
A spherical cap is the piece of a sphere cut off by a plane, such as a dome or the liquid in a round-bottom flask. The practical question is often “I can measure the base width and height; what sphere is this?” Enter the base radius a and height h to get the sphere radius r = (a² + h²)/(2h).
Formulas
| Volume | V = πh²(3r − h)/3 = πh(3a² + h²)/6 |
| Base radius | a = √(h(2r − h)) |
| Cap area | S꜀ = 2πrh |
| Sphere radius | r = (a² + h²)/(2h) |
Frequently asked questions
What is the volume of a spherical cap?
V = πh²(3r − h)/3, or equivalently πh(3a² + h²)/6 using the base radius.