Capsule Volume Calculator
Calculate the volume of a capsule (cylinder with hemispherical ends) by entering its radius and cylindrical height.
Formula:
Volume=πr²h + (4/3)πr³
Where:
- r = Radius of the capsule
- h = Height of the cylindrical section
- π = Pi (approximately 3.14159)
Unit of Measurement:
cm
Radius of the capsule (and hemispheres)
cm
Height of cylindrical section (excluding hemispheres)
Result
(Cylinder volume + Sphere volume)
About Capsule Volume
A capsule is a three-dimensional geometric shape that consists of a cylinder with hemispherical ends. It is commonly seen in pharmaceutical pills, spacecraft designs, and various engineering applications.
The volume of a capsule is calculated as the sum of the cylinder's volume (πr²h) and the volume of a sphere (4/3πr³), where the sphere volume accounts for both hemispherical ends. This gives us the formula V = πr²h + (4/3)πr³, where r is the radius andh is the height of the cylindrical section.
For example, if the radius is 2 cm and the cylinder height is 5 cm, the volume would be π × 2² × 5 + (4/3) × π × 2³ = 20π + (4/3) × 8π ≈ 96.08 cm³.
How to Calculate Capsule Volume
Step 1: Calculate the Cylinder Volume
First, calculate the volume of the cylindrical part using the formula: V_cylinder = πr²h, where r is the radius and h is the height of the cylindrical section.
Step 2: Calculate the Sphere Volume
Next, calculate the volume of a complete sphere using the formula: V_sphere = (4/3)πr³. Since the capsule has two hemispheres, this accounts for both ends.
Step 3: Add the Volumes
Add the cylinder volume and the sphere volume to get the total capsule volume: V_capsule = V_cylinder + V_sphere = πr²h + (4/3)πr³.
Practical Applications
Pharmaceutical Industry
Used to calculate the volume of capsule pills and medical dosages.
Aerospace Engineering
Applied in spacecraft and fuel tank design where capsule shapes are common.
Manufacturing
Used to determine material requirements for capsule-shaped components and containers.
Pressure Vessels
Important for designing and analyzing capsule-shaped pressure vessels and storage tanks.
Tips and Common Mistakes
- Cylinder Height vs Total Height: Remember that the cylinder height (h) is only the height of the cylindrical part, not including the hemispheres. The total height of the capsule is h + 2r.
- Radius Consistency: The radius must be the same for both the cylindrical part and the hemispherical ends.
- Zero Cylinder Height: If the cylinder height is zero, the capsule becomes a sphere, and you should use the sphere volume formula instead.
- Units: Ensure all measurements use the same unit system before calculating. The result will be in cubic units.
Frequently Asked Questions
A capsule is a geometric shape consisting of a cylinder with hemispherical caps at both ends, while a cylinder has flat circular ends. The capsule has rounded ends that are perfect hemispheres with the same radius as the cylindrical portion. This smooth, continuous shape gives the capsule improved aerodynamics and even stress distribution compared to a cylinder. In terms of volume calculation, a capsule's volume includes both the cylindrical middle section (πr²h) and the volume of a complete sphere (4/3πr³), accounting for both hemispherical ends.
Advertisement
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.
Need Help?
Check out our guide on how to use this calculator properly and understand the concepts behind it.
Learn more about calculating volume