What is a capsule shape?

A capsule is a 3D solid formed by a cylinder with a hemisphere attached to each end. Both hemispheres have the same radius as the cylinder. Together the two hemispheres form one complete sphere.

What is the formula for the volume of a capsule?

Volume = πr²h + (4/3)πr³, where r is the radius and h is the height of the cylindrical section only. The first term is the cylinder volume and the second is the full sphere formed by the two hemispheres.

What is the surface area formula for a capsule?

Surface area = 2πrh + 4πr². The term 2πrh covers the lateral surface of the cylinder, and 4πr² covers the combined surface of the two hemispheres (equivalent to one full sphere).

Does the height include the hemispherical ends?

No. The height input refers to the cylindrical body height only. The total length of the capsule from end to end is h + 2r (cylinder height plus two radii for the two caps).

What units does this calculator support?

You can choose millimeters (mm), centimeters (cm), meters (m), inches (in), or feet (ft). Volume is shown in the corresponding cubic unit and surface area in the square unit.

What if the cylinder height is zero?

If h = 0, the capsule becomes a perfect sphere. The volume simplifies to (4/3)πr³ and the surface area to 4πr², which are the standard sphere formulas.

Volume of a Capsule Calculator

Enter a capsule's radius and cylindrical body height to instantly calculate its volume and surface area.

Capsule Dimensions

Unit

Radius (cm)

Cylinder Body Height (cm)

Height of the cylindrical section only, not including the hemispherical ends.

Formulas

Volume V = πr²h + (4/3)πr³

Surface A = 2πrh + 4πr²

Total L L = h + 2r

Results

Enter radius and height to see results.

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Summary

Enter a capsule's radius and cylindrical body height to instantly calculate its volume and surface area.

How it works

Enter the radius of the capsule (the radius of both the cylinder and the hemispheres).
Enter the height of the cylindrical body only (not including the hemispherical ends).
Select your preferred unit (mm, cm, m, in, ft).
Volume and surface area results appear instantly.
Click any result card to copy the value to your clipboard.

Use cases

Estimate volume of pharmaceutical capsules and drug delivery containers.
Calculate volume of propane or fuel tanks with domed ends.
Determine capacity of pressurized vessels used in engineering.
Compute volume of swimming pool lanes or capsule-shaped pools.
Verify geometry homework answers for capsule or stadium-of-revolution problems.
Model volume of biological cells with rounded cylindrical shapes.
Calculate material needed for capsule-shaped packaging or containers.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu