Capsule Volume: worked example
| Radius (r) | 3 |
|---|---|
| Cylinder length (L) | 8 |
| Volume | 339.3 |
| Surface area | 263.9 |
Capsule Volume: formula
Enter the radius of the rounded ends and the straight length of the cylinder section, not including the two hemispherical caps. The capsule is a cylinder with a hemisphere at each end. The volume is the cylinder's plus a full sphere's, and the surface area is the cylinder's curved side plus a sphere's.
The total length is the straight section plus two radii.
Capsule Volume: changing Radius (r)
| Radius (r) | Volume | Surface area |
|---|---|---|
| 2.4 | 202.7 | 193 |
| 2.7 | 265.7 | 227.3 |
| 3 (example) | 339.3 | 263.9 |
| 3.3 | 424.2 | 302.7 |
| 3.6 | 521.2 | 343.8 |
Capsule Volume: compare input ranges
| Input | Tested from | To | Volume: low input | Volume: high input | Swing |
|---|---|---|---|---|---|
| Radius (r) | 2.7 | 3.3 | 265.7 | 424.2 | 158.6 (47%) |
| Cylinder length (L) | 7 | 9 | 311 | 367.6 | 56.5 (17%) |
Capsule Volume: individual input comparisons
| Input | Value | Volume | Surface area |
|---|---|---|---|
| Radius (r) | 2.4 | 202.7 | 193 |
| 2.7 | 265.7 | 227.3 | |
| 3 | 339.3 | 263.9 | |
| 3.3 | 424.2 | 302.7 | |
| 3.6 | 521.2 | 343.8 | |
| Cylinder length (L) | 6 | 282.7 | 226.2 |
| 7 | 311 | 245 | |
| 8 | 339.3 | 263.9 | |
| 9 | 367.6 | 282.7 | |
| 10 | 395.8 | 301.6 |
Capsule Volume: combined input changes
| Radius (r) / Cylinder length (L) | 6 | 8 | 10 |
|---|---|---|---|
| 2.4 | 166.5 | 202.7 | 238.9 |
| 2.7 | 219.9 | 265.7 | 311.5 |
| 3 | 282.7 | 339.3 | 395.8 |
| 3.3 | 355.8 | 424.2 | 492.7 |
| 3.6 | 439.7 | 521.2 | 602.6 |
Capsule Volume: which assumptions move the result?
Capsule Volume: values and definitions
| Quantity and definition | Value used |
|---|---|
| Radius (r) | 3 |
| Cylinder length (L) — The straight part only, without the two rounded ends. | 8 |
| Volume | 339.3 |
| Surface area | 263.9 |
Capsule Volume: half and double Radius (r)
| Radius (r) | Volume |
|---|---|
| 1.5 | 70.7 |
| 3 | 339.3 |
| 6 | 1,809.6 |
Common error: Measuring the overall length and using it as the cylinder length. The overall length includes both caps, which makes the volume larger than the real one.
The length field excludes the two hemispherical ends. Wall thickness makes inside capacity different from the external envelope. An elliptical or other tank-head profile is a different shape; this model does not estimate a partly filled vessel.
Geometry calculators: Triangular Prism Volume Calculator, Law of Sines Calculator, Cube Calculator, Equilateral Triangle Calculator, Trigonometry Calculator, Golden Ratio Calculator.
A capsule is a cylinder capped by two half-spheres, so its volume is a cylinder plus one full sphere. With a radius of 3 and a straight section 8 long, the cylinder holds about 226 and the two ends together about 113, for roughly 339 cubic units. The surface is the same story: the cylinder wall plus the surface of one sphere, about 264 square units.
Enter only the straight length. The rounded ends are already counted, so adding them to the length double counts about two radii at each end.
See the cylinder, sphere and hemisphere calculators for the parts, the cone frustum page for tapered shapes, and the annulus calculator for the wall's cross-section. The unit conversion calculators turn volume into gallons or liters, and the aquarium volume page handles rectangular tanks.
How do I find the volume of a capsule?
Add the volume of the cylinder, pi r squared times its length, to the volume of a sphere with the same radius, four thirds pi r cubed.
What is the total length of a capsule?
The straight cylinder length plus twice the radius, one radius for each rounded end, so a capsule with radius 3 and a straight section of 8 is 14 long.
Where are capsule shapes used?
A cylinder joined to two hemispherical ends is a useful idealization of some tanks, packages and rounded objects. The cylinder-length input excludes the end caps. This geometry computes ideal dimensions and areas; it does not establish vessel pressure capacity, shell thickness or structural safety.