Sphere Volume Calculator

Created by Luciano Mino
Last updated: Jul 06, 2022

Our sphere volume calculator can quickly find the volume of any sphere for you!

This tool will help you find:

  • The volume of any sphere from its radius;
  • The volume of any half-sphere or hemisphere;
  • The volume of any spherical cap; and
  • The height or radius of any spherical cap.

Read the following short article to learn more about how to find the volume of a sphere and the sphere volume formula!

Sphere volume formula

A sphere is a three-dimensional object where every point on its surface is at the same distance from its center (e.g., a ball). This distance is the sphere's radius.

If we know a sphere's radius, we can then calculate the volume it occupies with the sphere volume formula:

V=43πr3V = \frac{4}{3} \pi r^{3}

where:

  • rr is the radius of the sphere; and
  • VV is the sphere's volume.

As you can see, the sphere volume formula is straightforward. You only need the sphere's radius.

Try inputting any sphere's radius on the sphere volume calculator and experiment with it!

🙋 Remember to use the same length units when inputting the sphere's radius.

Volume of spherical cap

To find the volume of a portion of a sphere, we can either use:

  • The cap's height hh and sphere's radius rr; or
  • The cap's radius aa and height hh.

If we're using the cap's height hh and the sphere's radius rr, we should replace them in the following formula:

V=πh23(3rh)V = \frac{\pi h^{2}}{3}(3r - h)

However, if we're using only information about the cap (the cap's radius aa and height hh), we should use this formula instead:

V=16πh(3a2+h2)V = \frac{1}{6}\pi h (3a^{2}+h^{2})

You can use the sphere volume calculator with either parameter! Just fill in any two of them in the "Spherical cap / Hemisphere" section, and the sphere volume calculator will complete the missing parameter and output the spherical cap's volume.

Volume of a half-sphere

If you know how to find the volume of a sphere VV, then you know how to calculate the volume of a half-sphere VhV_{h}.

Simply divide by two inside the sphere volume formula, and that's it!

Vh=V2=23πr3V_{h} = \frac{V}{2} = \frac{2}{3}\pi r^{3}

Feel free to experiment with this or any of our geometrical tools, such as the cylinder volume calculator!

Luciano Mino
Sphere
Radius (r)
in
Circumference
in
Sphere with radius marked. Sphere volume



Volume
cu in
Spherical cap / Hemisphere
Cap height (h)
in
Sphere radius (r)
in
Cap base radius (a)
in
Spherical cap / hemisphere. Spherical cap volume

Volume
cu in
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