A capsule is a cylinder with a hemisphere on each end, which together make one complete sphere. That makes the volume easy: the cylindrical body plus a full sphere of the same radius. The same logic gives the surface area as the curved cylinder wall plus a whole sphere surface, with no flat ends anywhere.
The shape matters far beyond pharmacy. Pressure vessels, propane tanks and dewars all use domed ends because a hemisphere carries pressure with half the wall stress of a cylinder of the same radius, and because a flat end would need heavy bracing. The total length is the cylindrical section plus twice the radius, which is a common source of confusion when specifying tanks.
Below the calculator sits the volume by radius and cylindrical length table: 5 rows — 2 at one end, 8 at the other — which is usually faster than entering a value you have seen before. The page opens with radius already set to 3, so there is a finished result on screen before anything is typed. Alongside the number, 4 bands label it — small capsule through very large capsule — because a bare figure rarely tells you whether it is unusual. Most visitors arrive here from, or leave for, Pythagorean Theorem Calculator and Torus Volume Calculator.
The formula
r- Radius of the cylinder and the hemispheres
h- Length of the cylindrical section only
Total length- h + 2r
How it works, step by step
- Enter the radius.
- Enter the length of the straight cylindrical section, not the overall length.
- The gauge shows the total volume.
- The split between body and ends appears below.
Worked examples
Radius 3, body length 10
The cylinder holds 282.7433 and the two hemispheres together hold 113.0973, giving 395.8407 in total. The overall length is 16, not 10.
A short, fat capsule
Radius 5 with a body of only 4 gives 314.1593 in the cylinder and 523.5988 in the ends — 62.5% of the volume is in the domes.
Checking the 4 row
The reference table lists Radius = 4, giving body 0: 268.08, body 5: 519.41, body 10: 770.74, body 20: 1,273.39. Entering that above should reproduce the same figures — if it does not, the input is being read differently to the way the table assumes.
How to read your score
Frequently asked questions
Why do the two hemispheres make a whole sphere?
Because they are identical halves of the same sphere, one on each end. Adding them gives exactly four thirds pi r cubed.
Is the length I enter the overall length?
No, it is the straight cylindrical part only. Add twice the radius to get the overall length, which the calculator reports for you.
Why do pressure vessels have domed ends?
A hemisphere of a given radius carries roughly half the wall stress of a cylinder under the same pressure, and a flat end would need heavy internal bracing.
Does this shape have the least surface area for its volume?
No, a plain sphere does. But a capsule is far more practical to manufacture and transport, and it beats a flat-ended cylinder on both stress and material.
What do the bands under the volume mean?
They label the figure so it can be read without a reference point of your own: Small capsule from 0 to 100; Medium capsule from 100 to 400; Large capsule from 400 to 1,500; Very large capsule from 1,500 upwards. The band is a reading aid only — the number itself is exact, and a value sitting just over a boundary is not meaningfully different from one just under it.
What formula does the Capsule Volume Calculator use?
It computes V = πr^2h + 4πr^3 ÷ 3, where r is radius of the cylinder and the hemispheres; h is length of the cylindrical section only; Total length is h + 2r. The same expression is printed on the page above the inputs, so the result can be reproduced by hand or in a spreadsheet.
Capsule volumes
| Radius | body 0 | body 5 | body 10 | body 20 | body 40 |
|---|---|---|---|---|---|
| 2 | 33.51 | 96.34 | 159.17 | 284.84 | 536.17 |
| 3 | 113.10 | 254.47 | 395.84 | 678.58 | 1,244.07 |
| 4 | 268.08 | 519.41 | 770.74 | 1,273.39 | 2,278.70 |
| 5 | 523.60 | 916.30 | 1,309.00 | 2,094.40 | 3,665.19 |
| 8 | 2,144.66 | 3,149.97 | 4,155.28 | 6,165.90 | 10,187.14 |
A body length of zero gives a plain sphere, which is the leftmost column.