How this calculation works
Convert the supplied length convention to the straight middle length, then combine one cylinder with two hemispheres. The junction disks are internal and do not belong to the external curved surface.
Overall length = L+2r; V = πr²L + 4πr³/3; outer area = 2πrL + 4πr²A worked example
Radius 2 m with a 6 m straight middle gives an overall 10 m capsule. Volume is 104π/3 ≈ 108.908545 m³ and outer surface is 40π ≈ 125.663706 m². Entering overall 10 m gives the same geometry.
Good to know
Ideal cylindrical middle with two matching hemispheres only. No ellipsoidal ends, wall thickness, cavity or fill fraction. Overall length must be at least the diameter; a zero straight middle gives a sphere.
Reference: MathWorld: geometry definitions and formulas (opens in a new tab) ↗
The straight middle does not include the rounded ends
At radius 2 m, each hemispherical end adds 2 m to the axial length. A 6 m straight cylindrical middle therefore gives 10 m overall. Choosing overall-length mode with 10 m reproduces the same shape; entering 6 m as overall would leave only a 2 m straight middle.
The overall input cannot be shorter than the 4 m diameter in that example. At exactly the diameter the straight middle is zero and the two hemispheres form a sphere. The tool validates the length convention rather than silently treating a negative middle as a physical part.
The cylinder calculator checks the straight-middle volume, while the sphere calculator checks the combined hemispherical end contribution.
The two hemispheres contribute one sphere
For radius 2 m and straight length 6 m, cylinder volume is 24π m³ and combined end volume is 32π/3 m³. Total volume is 104π/3, about 108.908545 m³. The separate contributions help check which length entered the cylinder formula.
Outer surface is the cylinder’s curved area plus one sphere’s area: 24π + 16π = 40π m². The flat cylinder disks lie inside the joined solid. Adding them would count internal junctions as exposed outer material.
Capsule geometry does not specify a hollow vessel
The cylinder calculator and sphere calculator can check the two ideal component terms separately. A capsule with a zero straight middle reduces to the sphere result. Ellipsoidal end caps or domes with another profile require different formulas.
These dimensions describe a mathematical solid. They do not infer wall thickness, internal capacity, a fill fraction, seams or manufacturing allowances. Changing the common unit label also does not convert numbers already entered.
A few questions, answered
Which length should I enter?
Choose whether it is the straight cylindrical middle or the full end-to-end length. The other length is then derived.
Are cylinder end disks included in outer surface?
No. They are internal junctions where the hemispheres meet the cylinder.
Can the straight middle be zero?
Yes. The shape then becomes a sphere.
Does this support ellipsoidal end caps?
No. Both ends are hemispheres with the same radius as the cylinder.