Capsule Volume Calculator
Find the volume of a capsule, the shape of a cylinder capped by two hemispheres: a medicine capsule, a horizontal storage tank with rounded ends, a pressure vessel. The shape is simple, but it punishes one specific mistake, entering the wrong height, and most calculators give you no way to catch it.
Enter the radius and either the cylinder height or the total end-to-end length, choose your unit, and the calculator returns the total volume in cubic units and in litres or gallons, the surface area, and the breakdown into cylinder and sphere parts, so you can see exactly where the volume comes from and spot a bad input before it costs you material.
Geometry aid. Volumes convert at 1,000 cm³ = 1 litre and 231 in³ = 1 US gallon.
Quick Answer
Key takeaways
- A capsule is a cylinder plus one sphere: the two hemispherical caps have the same radius as the cylinder, so their volumes add up to a single sphere volume.
- The height question is the whole game. Cylinder height excludes the caps; total length includes them (total = cylinder height + 2 x radius). This calculator has a mode for each, so use the one you actually measured.
- The part breakdown is an error detector: a wrong-looking sphere part means the radius is wrong, a wrong-looking cylinder part means the height is wrong.
- Surface area comes free with the volume here, which is what coating, painting and material estimates actually need.
- Quick Answer
- How to use the capsule volume calculator
- The formula: a cylinder plus a sphere
- Worked example, checked against this exact tool
- Cylinder height vs total length: the mistake this page is built around
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the capsule volume calculator
Measure the radius first, and be careful: most people measure the diameter, across the round end, and the radius is half of it. Entering the diameter as the radius does not double the answer, it multiplies the sphere part by eight and the cylinder part by four, so it is the most destructive slip available on this page. Next, decide which height you have. If you measured the straight section between the caps, stay on the cylinder height tab. If you measured end to end, switch to total length: the calculator subtracts the two radii for you and rejects any total length shorter than the diameter, because that shape cannot exist.
Pick the unit your measurements are in (centimetres, metres, inches or feet), press Calculate, and read the volume in cubic units plus its conversion: litres for centimetres and metres, US gallons and litres for inches and feet. The formula line under the result shows your actual numbers substituted into both parts, so you can check the arithmetic by hand in seconds.
The formula: a cylinder plus a sphere
A capsule is a cylinder of height h with a hemisphere on each end, and two hemispheres make one full sphere, as the geometry references for the capsule shape on Wolfram MathWorld set out. So the volume splits cleanly in two.
If your shape is only part of this family, the neighbours are covered separately: a plain ball on the ball volume calculator, a rectangular tank on the box volume calculator, and pour volumes for construction on the concrete volume calculator. The capsule sits between them: more than a cylinder by exactly one sphere.
Worked example, checked against this exact tool
| Part | Calculation | Volume |
|---|---|---|
| Cylinder (r = 3, h = 10) | π x 3² x 10 | 282.743 cm³ |
| Both caps = one sphere (r = 3) | (4/3) x π x 3³ | 113.097 cm³ |
| Total volume | 282.743 + 113.097 | 395.841 cm³ = 0.396 litres |
| Surface area | 2π(3)(10) + 4π(3²) | 301.593 cm² |
On this capsule the caps are not a rounding detail: at 28.6% of the total, treating the shape as a plain cylinder of height 10 would understate the volume by more than a quarter, and treating it as a cylinder of the full 16 cm length would overstate it by roughly 40%, because that counts the cap region twice at full cylinder width. The two-mode input exists precisely because both of those errors start from a reasonable measurement entered in the wrong place.
Cylinder height vs total length: the mistake this page is built around
Specifications disagree about which length they quote. Pharmaceutical capsule sizes are usually given as total length; tank drawings often dimension the straight shell section and the dish ends separately; a product listing may give overall length because that is what fits in a box. The relationship is fixed: total length = cylinder height + diameter, since each cap contributes exactly one radius. So a capsule of radius 3 with a 10 cm straight section is 16 cm long overall, and the two descriptions are interchangeable only if you convert. Enter a total length on the cylinder-height tab and the tool will silently add a phantom sphere-and-a-half worth of volume. Enter a cylinder height on the total-length tab and it will subtract caps that were never there, or refuse the input as shorter than the diameter. When a result looks surprising, checking which length you typed is the first diagnostic, and the part breakdown is the second: the sphere part depends only on the radius, so if it matches your expectation while the total does not, the height entry is the problem.
What competing calculators miss
Miss 1: one input convention, take it or leave it. Most ranking capsule tools accept only the cylinder height, and at least one accepts only a loosely defined length. If your measurement is the other one, you are left to convert by hand, which is where the classic errors happen. This page takes either, labels them honestly, and validates the total-length case.
Miss 2: volume with no provenance. Several tools return a single number with no split. Without the cylinder and sphere parts shown, a wrong radius and a wrong height produce the same unexplained wrong total. The breakdown here localizes the error immediately.
Miss 3: no surface area, no usable conversions. Coating and material jobs need area, and tank jobs need litres or gallons, yet most capsule pages stop at cubic units. This calculator returns surface area with every volume and converts to litres (and gallons for imperial units) in the same result.
Frequently Asked Questions
V = πr²h + (4/3)πr³, where r is the radius and h is the height of the cylindrical section only. The first term is the cylinder; the second is the two hemispherical caps, which together make one complete sphere of the same radius. It can also be written as πr²(h + 4r/3).
Whichever you measured: the tool has a mode for each. Total length = cylinder height + 2 x radius, because each cap adds one radius. A capsule with radius 3 cm and a 10 cm straight section has a total length of 16 cm, and both entries give the same volume of 395.841 cm³.
Surface area = 2πrh + 4πr²: the lateral area of the cylinder plus the surface of the full sphere formed by the two caps. There are no flat end circles to add, because the caps close the shape. On the worked example it is 301.593 cm², and the calculator returns it with every volume.
One litre is 1,000 cm³, and one US gallon is 231 in³. The calculator converts automatically: centimetre and metre inputs report litres, inch inputs report US gallons and litres, and feet inputs report US gallons and litres. The worked example, 395.841 cm³, is 0.396 litres.
The result will be far too large, and unevenly so: the cylinder part grows with the square of the number you enter and the sphere part with its cube, so doubling the radius quadruples the cylinder part and multiplies the sphere part by eight. Halve any across-the-end measurement before typing it in. The sphere part in the breakdown is the tell: it depends only on the radius.
Yes. Spherocylinder is the mathematical name for the same solid: a cylinder with hemispherical ends of equal radius. It is also the shape engineers call a capsule tank or a dished-end pressure vessel, which is why the same formula serves pharmaceutical capsules and industrial vessels alike.
Yes. A short, fat capsule is perfectly valid, and in the limit of zero cylinder height the shape becomes a sphere. Only total-length mode constrains you: the total length must be at least the diameter (2 x radius), because the two caps alone account for that much length.
Half the total, if you cut it across the middle of the cylinder section: each half is a shorter cylinder plus one hemisphere. The part breakdown makes it easy to compute variants, for example a capsule cut off-centre, by taking the full sphere part for both caps or half of it (one cap) plus the cylinder volume at whatever straight length remains.
Add This Calculator to Your Website
References
- Wolfram MathWorld, “Capsule” – the formal definition of the capsule (spherocylinder) and its volume and surface area formulas. MathWorld: Capsule. Accessed October 2026.
- Wolfram MathWorld, “Sphere” – the volume (4/3)πr³ and surface area 4πr² of the sphere formed by the two caps. MathWorld: Sphere. Accessed October 2026.
- Wolfram MathWorld, “Cylinder” – the volume πr²h of the cylindrical mid-section. MathWorld: Cylinder. Accessed October 2026.
- Wolfram MathWorld, “Hemisphere” – the geometry of each end cap, half a sphere of the capsule radius. MathWorld: Hemisphere. Accessed October 2026.
- National Institute of Standards and Technology, “Guide for the Use of the International System of Units (SP 811)” – the unit framework behind the centimetre, litre and conversion factors used here. NIST: Guide to the SI (SP 811). Accessed October 2026.