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!

• 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.

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:

$V = \frac{4}{3} \pi r^{3}$

where:

• $r$ is the radius of the sphere; and
• $V$ 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 $h$ and sphere's radius $r$; or
• The cap's radius $a$ and height $h$.

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

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

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

$V = \frac{1}{6}\pi h (3a^{2}+h^{2})$

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 $V$, then you know how to calculate the volume of a half-sphere $V_{h}$.

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

$V_{h} = \frac{V}{2} = \frac{2}{3}\pi r^{3}$

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

Luciano Mino
Sphere
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Circumference
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Volume
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Spherical cap / Hemisphere
Cap height (h)
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Volume
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