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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.

r = 3 mh = 8 m
π setting: π = 3.14159265
π Precision:
m
Capsule Volume
339.292
Decimals:
Step-by-Step Mathematical Solution
Formula:V = π × r² × h + (4/3) × π × r³
Steps:
1.Radius (r) = 3 m, Straight Length (h) = 8 m
2.Formula: V = π × r² × h + (4/3) × π × r³
3.Square Radius: r² = 3² = 9
4.Cylinder Part: r² × h = 9 × 8 = 72
5.Sphere Part: (4/3) × r³ = (4/3) × 3³ = 36
6.Combined: h + (4/3) × r = 8 + 1.3333333333333333 × 3 = 12
7.Multiply by π ≈ 3.14159265: V ≈ 339.292 m³
Calculated Volume:339.292

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

Standard Formula
V = π × r² × h + (4/3) × π × r³

Formula Variables Explained:

rRadius

The radius of the hemispherical ends and the cylindrical middle section.

hStraight Length

The length of only the cylindrical middle section, excluding the rounded end caps.

LTotal Length

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?

  1. 1Measure the capsule radius r.
  2. 2Measure the straight cylindrical section length h, not the full end-to-end length.
  3. 3Calculate the cylinder volume π × r² × h.
  4. 4Calculate the sphere volume (4/3) × π × r³ for the two rounded ends together.
  5. 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.

Solution Steps:
  • 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
Final Volume:339.29 cubic meters

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.

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