Capsule Surface Area Calculator

Calculate the surface area of a capsule by entering the radius and cylindrical height. A capsule is a cylinder with hemispherical ends.

💊 Capsule Surface Area

Formula

Surface Area: SA = 4πr² + 2πrh
Alternative: SA = 2πr(2r + h)
Where r is the radius and h is the cylindrical height (excluding hemispheres)

Capsule Surface Area Formulas

Total Surface Area

SA = 4πr² + 2πrh

Sphere surface area plus cylindrical surface area

Spherical Ends

SA_sphere = 4πr²

Surface area of both hemispherical ends combined

Cylindrical Surface

SA_cylinder = 2πrh

Curved surface area of the cylindrical middle section

Volume

V = πr²h + (4/3)πr³

Cylinder volume plus sphere volume

Capsule Surface Area Examples

Example 1: Small Capsule

Given: Radius = 2 cm, Height = 6 cm

Spherical ends: 4π × 2² = 16π cm²

Cylindrical surface: 2π × 2 × 6 = 24π cm²

Total: SA = 16π + 24π = 40π ≈ 125.66 cm²

Example 2: Medium Capsule

Given: Radius = 3 cm, Height = 10 cm

Spherical ends: 4π × 3² = 36π cm²

Cylindrical surface: 2π × 3 × 10 = 60π cm²

Total: SA = 36π + 60π = 96π ≈ 301.59 cm²

Example 3: Large Capsule

Given: Radius = 5 cm, Height = 15 cm

Spherical ends: 4π × 5² = 100π cm²

Cylindrical surface: 2π × 5 × 15 = 150π cm²

Total: SA = 100π + 150π = 250π ≈ 785.40 cm²

Capsule Surface Area FAQ

What is a capsule?

A capsule (also called a spherocylinder) is a 3D shape consisting of a cylinder with hemispherical ends. It's commonly seen in pill shapes and some architectural elements.

How do you calculate capsule surface area?

Add the surface area of a complete sphere (4πr²) to the lateral surface area of the cylinder (2πrh). Total: SA = 4πr² + 2πrh.

What's the difference between total length and cylindrical height?

Total length includes the hemispheres (total = h + 2r), while cylindrical height (h) is just the straight middle section.

How is a capsule different from a cylinder?

A cylinder has flat circular ends, while a capsule has rounded hemispherical ends. This affects both surface area and volume calculations.