Capsule Volume CalculatorFree online math calculator — instant results, no sign-up
Calculate a cylinder with two hemispherical ends.
Sign in to save results and favorites.
About the Capsule Volume Calculator
The Capsule Volume Calculator finds the volume of a cylinder capped by two hemispherical ends of the same radius. Enter the radius and the length of the straight cylindrical section to calculate the combined volume of the cylinder and rounded ends.
- Radius
- The radius is the distance from the central axis to the cylinder's curved surface, also the radius of each hemispherical end, measured in the same length unit as the cylindrical section length.
- Cylindrical section length
- The cylindrical section length is the length of the straight cylinder between the hemispherical ends, excluding both rounded caps, measured in the same length unit as the radius.
Formula and method
V = πr²L + (4/3)πr³; with r = 2 and L = 6, V = π(2²)(6) + (4/3)π(2³) = (104/3)π ≈ 108.9085453244.
- VTotal capsule volume, expressed in cubic units.
- rShared radius of the cylindrical section and both hemispherical ends.
- LLength of the cylindrical section only, excluding the hemispherical ends.
- πPi, the circle constant, approximately 3.141592653589793.
Calculate the cylindrical volume as πr²L. Combine the two hemispherical ends into one sphere with volume (4/3)πr³, then add the two volumes. For the default radius of 2 and cylindrical section length of 6, the cylinder contributes 24π and the ends contribute (32/3)π, giving a total of approximately 108.9085453244 cubic units.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Radius2
- Cylindrical section length6
Results
- Result108.9085453244
How to use the Capsule Volume Calculator
- 1Choose a common length unit for both dimensions.
- 2Enter the radius; use 2 for the default worked example.
- 3Enter the cylindrical section length without the rounded ends; use 6 for the default worked example.
- 4Calculate the volume by adding the cylinder volume to the combined volume of the two hemispheres.
- 5Read the Result row as the total capsule volume; the default inputs give 108.9085453244 cubic units.
Reading your result
The Result row reports the total volume enclosed by the capsule, including the cylindrical section and both hemispherical ends. With Radius = 2 and Cylindrical section length = 6, Result = 108.9085453244. Its unit is the cube of the input length unit: centimeters produce cubic centimeters, while meters produce cubic meters.
Limitations
The model assumes a straight circular cylinder with two exact hemispheres that share its radius and join without gaps or overlapping interiors. Both inputs must use the same unit and must be nonnegative; a physical capsule requires a positive radius. The cylindrical section length is not the overall end-to-end length. The calculation does not account for wall thickness, so capacity requires internal dimensions rather than external dimensions. The displayed decimal is an approximation, and its many digits do not imply equivalent measurement accuracy.
Common questions
Does the cylindrical section length include the rounded ends?+
No. Enter only the straight section. The overall capsule length is L + 2r, so the default inputs give an overall length of 6 + 2(2) = 10 length units.
Why does the formula include the volume of a full sphere?+
Each end is one hemisphere. Together, the two ends form a full sphere of radius r, so their combined volume is (4/3)πr³.
What happens if the cylindrical section length is zero?+
The cylinder contributes no volume, and the two hemispheres meet to form a sphere. The formula reduces to V = (4/3)πr³.
Can this calculator find the capacity of a capsule-shaped tank?+
Yes, if the interior is a circular cylinder with two hemispherical ends. Use the internal radius and internal cylindrical section length; external dimensions instead give the volume enclosed by the outer surface.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
You might also like
Slope Calculator
Slope, angle and line equation through two points.
Area Calculator
Area of common 2D shapes.
Volume Calculator
Volume of common 3D shapes.
Surface Area Calculator
Surface area of 3D shapes.
Circle Calculator
Radius, diameter, circumference and area.
Triangle Calculator
Solve a triangle from three sides.
Results are estimates for informational purposes and are not financial, medical or legal advice.