About Spherical Cap Calculator (Formula)
A spherical cap is a portion of a sphere that is cut off by a plane. To calculate various properties of a spherical cap, such as its volume, surface area, and height, you can use the following formulas:
- Volume of a Spherical Cap (V):
The volume of a spherical cap can be calculated using the formula:
V = (1/3) * π * h * (3R^2 + h^2)
Where:
- V is the volume of the spherical cap.
- π is the mathematical constant pi (approximately 3.14159).
- h is the height of the spherical cap (the perpendicular distance from the cap’s base to the sphere’s center).
- R is the radius of the sphere.
- Surface Area of a Spherical Cap (A):
The surface area of a spherical cap can be calculated using the formula:
A = 2πR * h
Where:
- A is the surface area of the spherical cap.
- π is the mathematical constant pi (approximately 3.14159).
- h is the height of the spherical cap.
- R is the radius of the sphere.
- Height of a Spherical Cap (h):
If you have the volume and the radius of the spherical cap and want to calculate its height, you can rearrange the volume formula:
h = √((3V) / (πR^2) – 3R^2)
Where:
- h is the height of the spherical cap.
- V is the volume of the spherical cap.
- π is the mathematical constant pi (approximately 3.14159).
- R is the radius of the sphere.
These formulas are useful for various engineering, geometry, and physics problems where you need to work with spherical caps. Make sure to use consistent units (e.g., meters, inches, etc.) for the radius, height, and volume to obtain accurate results.