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Spherical Cap Volume Calculator

Quickly calculate the volume of a sliced section of a sphere.

V = \frac{\pi h^2}{3} (3R - h)
r = ?
h = ?
Diagram updates instantly as you type.

What is a Spherical Cap?

A portion of a sphere cut off by a plane.

A spherical cap is the region of a sphere which lies above (or below) a given flat plane. If the plane passes through the center of the sphere, the cap becomes a hemisphere.

Key Information
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spherical cap volume calculator

How to Find the Volume of a Spherical Cap

You need the radius of the original sphere and the height of the cap.

1
Determine the radius of the original whole sphere.
2
Measure the height of the cap itself.
3
Apply the mathematical formula to find the volume.

Spherical Cap Volume Formula

The equation for a spherical cap.

V = \frac{π h^2}{3} (3R - h)
V Volume
r Base Radius
h Height

Where 'h' is the height of the cap and 'R' is the radius of the original sphere.

Frequently Asked Questions

What if I only know the radius of the cap's base, not the whole sphere?

You can use an alternative formula: V = (πh/6) × (3a² + h²), where 'a' is the radius of the flat base of the cap.

Is a hemisphere a type of spherical cap?

Yes, a hemisphere is a special case of a spherical cap where the height of the cap is exactly equal to the radius of the sphere.

What is a spherical sector?

A spherical sector is a cone shape connecting the center of the sphere to the cap. A cap is just the top 'slice' part.

Why is this formula useful?

It is highly useful for finding the volume of liquid in a spherical tank that is only partially full.