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Capsule Calculator

Calculate volume and surface area of a capsule (spherocylinder). A capsule is a cylinder with hemispherical caps.

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Radius (r)

Cylinder Height (h)

Capsule Diagram

Capsule Formulas

Volume Formulas:

Total Volume: V = πr²h + (4/3)πr³
Cylinder part: V₁ = πr²h
Sphere part: V₂ = (4/3)πr³
Total Length: L = h + 2r

Surface Area Formulas:

Total Area: SA = 2πrh + 4πr²
Cylinder part: A₁ = 2πrh
Sphere part: A₂ = 4πr²

Understanding Capsules

A capsule (also called spherocylinder or stadium solid) is a 3D shape consisting of a cylinder with hemispherical caps on both ends. When h = 0, it becomes a sphere.

Key Properties:

The two hemispherical ends combine to form one complete sphere
No edges or vertices - the surface is completely smooth
Has the minimum surface area for a given volume (efficient shape)
Common in physics for collision detection in games

Frequently Asked Questions

What are real-world examples of capsules?

Medication capsules, pills, propane tanks, pressure vessels, hot dog shapes, stadium roofs (2D), rounded-end swimming pools, and many industrial containers.

Why are pressure vessels capsule-shaped?

The hemispherical ends distribute pressure evenly without stress concentrations. Sharp corners would be weak points where cracks could start.

What's the difference from a cylinder?

A cylinder has flat circular ends, while a capsule has rounded hemispherical ends. The capsule's formula adds a sphere's volume and surface area to the cylinder's lateral parts.

How do I find h if I know total length?

Since L = h + 2r, you can solve for h = L - 2r. The cylinder height is the total length minus the two radii from the hemispherical caps.

Related Calculators

Cylinder Sphere Hemisphere Ellipsoid

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