Capsule Calculator
Calculate the volume, surface area, and circumference of a capsule (stadium of revolution). Enter radius and side length to compute capsule properties instantly.
What is a Capsule Shape?
A capsule is a three-dimensional geometric shape consisting of a cylinder with hemispherical ends. It is also known as a stadium of revolution. The shape is formed by taking a sphere of radius r, cutting it in half through the center, and separating the two halves by a cylinder of the same radius r with height (or side length) a. For the individual shapes that make up a capsule, visit our Sphere Calculator and Cylinder Calculator tools.
The capsule shape appears in many real-world applications including pharmaceutical capsules, pressure vessels, storage tanks, diving oxygen tanks, and various industrial containers. Understanding its volume, surface area, and circumference is essential for manufacturing, material estimation, and capacity planning.
Formulas and Calculations
The capsule combines the volume of a sphere and a cylinder. The key formulas are:
Volume (V): V = πr²((4/3)r + a)
Where r is the radius and a is the side length (height of the cylindrical portion). The term (4/3)πr³ represents the volume of the two hemispheres combined (equivalent to a full sphere), and πr²a represents the volume of the cylindrical section.
Surface Area (S): S = 2πr(2r + a)
The total surface area consists of the surface area of the two hemispheres (equivalent to a sphere: 4πr²) plus the lateral surface area of the cylinder (2πra).
Circumference (C): C = 2πr
The circumference is simply the circumference of a circle with radius r, as the capsule has a constant circular cross-section.
How to Use the Capsule Calculator
Using this calculator is straightforward. Simply enter the radius (r) of the hemispherical ends and the side length (a) of the cylindrical section. The tool will instantly compute the total volume, surface area, and circumference of the capsule shape. All calculations are performed in real-time in your browser, so no data is sent to any server.
Both values must be positive numbers. You can enter whole numbers or decimals for precise calculations. The results display using the same units as your input values. For more general geometry calculations, try our Volume Calculator for other common 3D shapes.
Frequently Asked Questions
What is the difference between a capsule and a cylinder?
A capsule has hemispherical ends while a standard cylinder has flat ends. Capsules offer better pressure distribution and are commonly used for containing gases or liquids under pressure. The rounded ends also make capsules more efficient for certain storage applications.
When would the side length be zero?
When the side length (a) is zero, the capsule becomes a sphere. The calculator requires a minimum positive value for meaningful results. For a pure sphere calculation, you can use a dedicated sphere calculator.
What units does the calculator use?
This calculator works with any consistent unit of measurement. If you enter the radius and side length in meters, the volume will be in cubic meters, surface area in square meters, and circumference in meters. You can use inches, feet, centimeters, or any other unit as long as you are consistent.
Where are capsule shapes used in real life?
Capsule shapes are used in pharmaceutical capsules, scuba diving tanks, propane tanks, pressure vessels, storage silos, and many architectural designs. The shape is structurally efficient for containing internal pressure because the hemispherical ends distribute stress evenly.
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