Capsule Volume Calculator
Calculate the volume of a capsule (cylinder with hemispherical ends) using its radius and height.
Capsule Volume and Surface Area Calculator
Calculate the volume and surface area of a capsule (cylinder with hemispherical ends) with our easy-to-use calculator. Learn about capsule formulas, applications, and explore interactive examples.
A capsule shape, also known as a spherocylinder, consists of a cylinder with hemispherical ends. This elegant shape combines the properties of cylinders and spheres, making it ideal for various applications in engineering, pharmaceuticals, and product design.
Formula
Volume = πr²h + (4/3)πr³
Surface Area = 2πrh + 4πr²
Where:
- r:radius of the cylinder and hemispheres
- h:length of the cylindrical portion (not including hemispheres)
How to Calculate Capsule Volume
The volume is the sum of the cylindrical portion (πr²h) and the two hemispherical ends (each contributing (2/3)πr³). The total combines to πr²h + (4/3)πr³.
Understanding Surface Area
The surface area includes the curved surface of the cylinder (2πrh) and the surface area of the two hemispheres (each contributing 2πr²), totaling 2πrh + 4πr².
Real-World Applications
Capsule shapes are used in pharmaceutical pills, space vehicle design, pressure vessels, and product packaging. Their smooth profile and structural efficiency make them ideal for containers and aerodynamic applications.
Frequently Asked Questions
Why use a capsule shape instead of a cylinder?
Capsule shapes offer better aerodynamics and stress distribution than cylinders with flat ends. The rounded ends reduce pressure concentrations and provide smoother fluid flow, making them ideal for pressure vessels and high-speed vehicles.
How does a capsule compare to a cylinder and sphere?
A capsule combines features of both shapes: the storage efficiency of a cylinder with the smooth transitions of a sphere. This makes it stronger than a simple cylinder while being more space-efficient than a sphere for the same length.
What industries use capsule shapes?
Capsules are common in pharmaceuticals (pill design), aerospace (fuel tanks, spacecraft), manufacturing (pressure vessels), and consumer products (packaging). Their shape provides an optimal balance of strength, volume, and manufacturability.