Capsule Volume Calculator
Calculate the volume of a capsule using radius and straight cylinder length with our capsule volume calculator. Get results with the capsule formula and steps.
What Is a Capsule?
A capsule, also called a spherocylinder, is a three-dimensional shape made from a cylinder with a hemisphere attached to each end.
Common examples include medicine capsules, pressure vessels, storage tanks, rounded containers, and aerodynamic components.
Volume of a Capsule Formula
Formula Variables Explained:
The radius of the hemispherical ends and the cylindrical middle section.
The length of only the cylindrical middle section, excluding the rounded end caps.
The full end-to-end capsule length, where L = h + 2r.
The volume of a capsule equals the volume of the cylindrical middle plus the volume of a full sphere formed by the two hemispherical ends.
The standard formula is V = π × r² × h + (4/3) × π × r³, where r is the radius and h is the straight cylindrical length. You can also write it as V = π × r² × (h + 4r/3).
How to find the volume of a Capsule?
- 1Measure the capsule radius r.
- 2Measure the straight cylindrical section length h, not the full end-to-end length.
- 3Calculate the cylinder volume π × r² × h.
- 4Calculate the sphere volume (4/3) × π × r³ for the two rounded ends together.
- 5Add both parts and express the final answer in cubic units.
Example: Calculate the Volume of a Capsule
Example 1: Calculate capsule volume with radius 3 m and straight length 8 m
Problem: A capsule-shaped tank has radius 3 meters and a straight cylindrical middle section 8 meters long. Find its volume.
- Formula: V = π × r² × h + (4/3) × π × r³
- Substitute r = 3 and h = 8
- Cylinder part = π × 3² × 8 = 72π
- Rounded ends part = (4/3) × π × 3³ = 36π
- Total V = 72π + 36π = 108π
- V ≈ 339.29 m³
Frequently Asked Questions (FAQ)
Q: Is a capsule just a cylinder plus two hemispheres?
Yes. The two hemispheres combine into one full sphere, so capsule volume is cylinder volume plus sphere volume.
Q: Do I use total capsule length in the formula?
This calculator uses the straight cylindrical length h. If you only know total length L, first subtract the two radii: h = L - 2r.
Q: What if the straight length is zero?
Then the capsule becomes a sphere, and the formula reduces to V = (4/3) × π × r³.