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Capsule Volume Calculator

Calculate the volume of a capsule using its radius and straight length.

V = \pi r^2 (\frac{4}{3}r + a)
r = ?
a = ?
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What is a Capsule?

A cylinder capped by two hemispheres.

A capsule is a basic three-dimensional geometric shape consisting of a cylinder with hemispherical ends. It is commonly seen in pill capsules and certain pressure vessels.

Key Information
Shape Focus
capsule volume calculator

How to Find Capsule Volume

A capsule's volume is the sum of a cylinder and a sphere.

1
Calculate the volume of the cylindrical middle section.
2
Calculate the volume of a sphere (which makes up the two hemispherical ends).
3
Add the two volumes together.

Capsule Volume Formula

The combined equation for a capsule.

V = π r^2 (\frac{4}{3}r + a)
V Volume
r Radius
a Cylinder Length

Where 'r' is the radius and 'a' is the length of the straight cylindrical section.

Frequently Asked Questions

Can I just use the total length of the capsule?

Yes, but the formula changes slightly. If 'L' is total length, the straight part 'a' is equal to L × 2r.

Why does the formula include 4/3?

Because the two ends of the capsule form a complete sphere, and the formula for a sphere's volume includes the fraction 4/3.

Are medicine pills perfect capsules?

Usually yes, many medicinal pills are manufactured in standard geometric capsule shapes for easy swallowing.

What if the two ends have different radii?

Then it is not a standard capsule. You would have to calculate the volume of each hemisphere separately and add them to a conical frustum.