Cylinder Volume Calculator
Widening beats heightening — radius is squared.
Work out Cylinder Volume. Widening beats heightening — radius is squared. Free, with no account and nothing to install.
Volume (cubic units)
282.743339
Surface area 245.0442
Volume scales with the square of the radius and only linearly with height, so widening a cylinder by 10% adds more volume than making it 10% taller. That is why a slightly wider glass holds noticeably more than a taller narrow one of the same nominal size.
How the Cylinder Volume Calculator works
Volume and surface area of a cylinder, with the base and curved areas separated and a litre conversion for centimetre inputs. Volume goes with the square of radius and only linearly with height.
Also known as: volume of a cylinder · tank capacity calculator · pipe volume calculator · cylinder litres calculator
Radius is squared and height is not
Volume is πr²h, so a 10% increase in radius adds 21% to the volume while a 10% increase in height adds exactly 10%. Widening beats heightening, and the gap grows with the size of the change.
That is why a slightly wider glass holds noticeably more than a taller narrow one of the same nominal size, and why doubling a pipe's bore quadruples what it holds rather than doubling it.
The same relationship governs flow. A pipe's cross-sectional area scales with the square of bore, so one size up carries roughly twice as much at the same velocity — which is the single most useful fact in domestic plumbing.
Surface area and the optimal can
Surface area is 2πr(r + h) — two circular ends plus the curved side, which unrolls into a rectangle of width 2πr and height h. That unrolling is why the curved area is so simple.
For a fixed volume, surface area is minimised when the height equals the diameter. That is the least-material can, and it is not the shape of any drinks can you have held.
Real cans are taller because they are designed to be gripped, stacked and printed on. The shape trades material efficiency for usability, which is a reminder that geometric optima are only one constraint among several.
The horizontal tank problem
An upright cylinder's volume from a liquid depth is trivial — depth times base area. A cylinder lying on its side is genuinely hard, because the cross-section of liquid is a circular segment.
That segment area requires an inverse trigonometric function of the fill depth, and the relationship between depth and volume is strongly non-linear. Half depth is half volume by symmetry, and no other point is intuitive.
Which is why dipstick charts exist. Rather than compute the segment each time, the relationship is tabulated once and read off — the practical answer to a genuinely awkward piece of geometry.
Where to go next
The Cylinder Volume question rarely arrives on its own. These are the ones that usually come with it:
- Cone Volume Calculator — Exactly one third of its cylinder, always.
- Sphere Volume Calculator — Two thirds of its cylinder — Archimedes' favourite result.
- Circle Area Calculator — A circle fills 78.54% of its square, always.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
What is the formula for cylinder volume?
πr²h — the area of the circular base times the height. Every prism follows the same pattern: base area times height.
Why does widening add more volume than heightening?
Because radius is squared and height is not. Increasing the radius by 10% adds 21% to the volume; increasing the height by 10% adds 10%.
How do I find the surface area?
2πr(r + h) — two circular ends plus the curved side, which unrolls into a rectangle of width 2πr and height h.
How do I convert cylinder volume to litres?
If the dimensions are in centimetres, divide the cubic centimetres by 1,000. A cylinder 10 cm across and 20 cm tall holds about 1.57 litres.
How do I calculate a partly full cylinder?
For an upright cylinder, use the depth of liquid as the height. For a cylinder on its side it is considerably harder — it needs the area of a circular segment.
What shape holds most for the least material?
For a cylinder, a height equal to the diameter minimises surface area for a given volume. Drinks cans are taller than that because they are designed to be held and stacked rather than to minimise metal.
How do I calculate a horizontal cylindrical tank?
It needs the area of a circular segment, which is considerably harder than the upright case. Dipstick charts exist precisely because the relationship between depth and volume is not linear.
What is a hollow cylinder's volume?
The outer cylinder minus the inner: π(R² − r²)h. It is the calculation for pipe wall material or a tube.
How do I find the volume of a pipe?
Use the internal radius, not the external one — the bore is what carries fluid. That is the most common error in pipe volume calculations.
Why are pressure vessels cylindrical?
Because a cylinder distributes hoop stress evenly and is far easier to manufacture than a sphere, which would be optimal. The hemispherical end caps are a compromise between the two.
How much does a cylinder of water weigh?
Its volume in litres, in kilograms, since water is 1 kg per litre. A cylinder 1 m across and 1 m tall holds about 785 litres and weighs 785 kg — which is why tank supports matter.
What is the optimal shape for a can?
Height equal to diameter minimises material for a given volume. Real cans are taller because they are designed to be gripped and stacked, so the shape trades material for usability.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/cylinder-volume-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Cylinder Volume Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/cylinder-volume-calculator" style="color:#64748b">Cylinder Volume Calculator</a> from The Calc Library</p>The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.
Related calculators
Cone Volume Calculator
Exactly one third of its cylinder, always.
OpenSphere Volume Calculator
Two thirds of its cylinder — Archimedes' favourite result.
OpenCircle Area Calculator
A circle fills 78.54% of its square, always.
OpenPercentage Calculator
Every common percentage question in one place.
Open