What is the formula for the surface area of a capsule?

SA = 2πr(2r + h), where r is the radius and h is the height of the cylindrical section. This combines the lateral cylinder surface (2πrh) with a full sphere surface (4πr²).

What is the cylinder height in a capsule?

It is only the straight middle section between the two hemispherical caps — not the total length of the capsule. If you know the total length L, then h = L − 2r.

What happens when h = 0?

When the cylinder height is zero the capsule becomes a perfect sphere. The formula reduces to SA = 4πr², which is the standard sphere surface area.

Does the result include the inside surface?

No. The calculator gives the outer surface area only. For a hollow capsule, you would need the inner radius as well.

How do I convert the result to different units?

Select the unit before calculating and the result is already in that unit squared (e.g., cm²). To convert afterward, multiply by the appropriate area conversion factor.

Surface Area of a Capsule Calculator

Name: Surface Area of a Capsule Calculator
Availability: InStock
Author: Nham Vu

Enter the radius and cylinder height of a capsule to instantly compute its total surface area.

Capsule Dimensions

Unit

Radius (r) — radius of cylinder and hemispherical caps

Cylinder Height (h) — straight middle section only

Enter dimensions and press Calculate.

Formula Reference

Total formula

SA = 2πr(2r + h)

Sphere caps

4πr² (two hemispheres)

Cylinder side

2πrh

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Summary

Enter the radius and cylinder height of a capsule to instantly compute its total surface area.

How it works

Enter the radius (r) of the capsule — the radius of both the cylinder and the hemispherical caps.
Enter the cylinder height (h) — the straight cylindrical section between the two hemispherical ends.
Select your preferred unit (mm, cm, m, in, ft).
The calculator applies SA = 2πr(2r + h) and displays the result in the same unit squared.
Copy the result or adjust inputs to explore different dimensions.

Use cases

Engineering: sizing capsule-shaped pressure vessels or tanks.
Pharmaceuticals: estimating coating surface area of capsule-shaped tablets.
Architecture: material estimates for barrel vault structures.
3D printing: surface area estimation for resin or filament cost.
Physics homework: verifying geometric surface area computations.
Sports science: modeling surface area of capsule-shaped equipment.
Medical devices: calculating surface area of implants or stents.
Education: visualizing the relationship between geometry and formulas.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu