The cylinder volume calculator above turns a base measurement and a height into a volume, a capacity and the surface areas that go with them. It accepts a radius, a diameter or a circumference for the base, because tanks, pipes and tins are far easier to measure around the outside than across the middle.
Arb Digital publishes this alongside a full set of free geometry tools. It also handles partial fills, which is the question people usually have in practice: not "how much does this tank hold" but "how much is in it right now".
What This Cylinder Volume Calculator Does
Choose how you measured the base, enter its value and the height, and the tool returns the volume in cubed units, converting to litres or gallons where the unit makes that meaningful. Three supporting figures come with it: the base area, the lateral surface area — the curved wall on its own, which is what a label or a coat of paint has to cover — and the total surface area including both end caps.
The fill level field gives the contained volume for an upright cylinder filled to a given percentage of its height. Because the cross-section of an upright cylinder is constant, that relationship is exactly linear: 80% of the height is 80% of the volume. That is not true for a cylinder lying on its side, and the page explains why.
How to Use It
- Choose your base measurement. Radius, diameter or circumference — whichever you can actually take with a tape or caliper.
- Enter the base value and the height, both in the same unit.
- Pick a unit. Volumes appear in cubed units, with a litre or gallon equivalent shown for metric and imperial units respectively.
- Set a fill level if you need one. Leave it at 100 for the full capacity of the vessel.
- Read the working line for the substituted formula, including the base-area step that the rest depends on.
The Formula / How It's Calculated
A cylinder is a circle extruded along a straight line, so its volume is simply the base area multiplied by the height:
- Volume V = πr2h
- Lateral surface area = 2πrh — the circumference multiplied by the height
- Total surface area = 2πr2 + 2πrh — two circular ends plus the wall
For the loaded example, a 10 cm diameter tin 25 cm tall: the radius is 5 cm, the base area is π × 52 = 78.54 cm², and the volume is 78.54 × 25 = 1,963.50 cm³, which is just under 2 litres. The lateral area is 2 × π × 5 × 25 = 785.40 cm², and adding the two ends at 78.54 cm² each gives a total of 942.48 cm². MathWorld's entry on the cylinder covers the general case, including oblique cylinders where the axis is not perpendicular to the base.
The lateral-area formula is worth understanding rather than memorising. Cut the wall vertically and unroll it and you have a rectangle: its width is the circumference 2πr and its height is h, so its area is 2πrh. Every label, wrap and sheet-metal shell is cut from that rectangle.
Wider Beats Taller, and by a Lot
The radius is squared in the volume formula while the height is not, so the two dimensions are not equally valuable. Increasing the radius by 20% multiplies the volume by 1.22 = 1.44 — a 44% gain. Increasing the height by 20% multiplies it by 1.2 — a 20% gain. The same proportional change in the width is worth more than twice as much.
This shows up in packaging design constantly. A slightly wider tin holds noticeably more than a slightly taller one of the same proportional increase, and conversely, a small reduction in diameter removes far more capacity than the same percentage off the height. If you are comparing two containers by their stated dimensions, the width difference is the one that matters most, and our percentage change calculator converts those dimension changes into the percentage terms people quote.
The Most Efficient Cylinder Shape
For a fixed volume, the cylinder that uses the least material has a height exactly equal to its diameter — that is, h = 2r. Any taller and the wall area grows faster than the ends shrink; any shorter and the two ends dominate. At the optimum, the shape looks square in profile.
Very few real cans are that shape, which tells you something useful: material cost is rarely the only constraint. Shelf presentation, hand grip, printing area, stacking and the standard sizes of the sheet metal all pull the design away from the mathematical optimum. Understanding the optimum is still worth having, because it tells you the direction in which a shape is inefficient and how much that inefficiency actually costs in material.
Partial Fills: Upright Versus Lying Down
An upright cylinder is the easy case. Because every horizontal slice is the same circle, the volume is exactly proportional to the depth: fill to 40% of the height and you have 40% of the capacity. A dipstick on a vertical tank can be a linear scale.
A cylinder lying on its side behaves very differently. Near the bottom and top the cross-section is narrow, and in the middle it is at its widest, so the relationship between depth and volume is an S-shaped curve rather than a straight line. Filling a horizontal tank to half its diameter does give exactly half its volume — by symmetry — but filling it to a quarter of the diameter gives about 19.6% of the volume, not 25%. This is why horizontal fuel and water tanks need calibrated dip charts rather than a linear gauge, and why reading one as if it were linear systematically underestimates the contents in the lower half. The exact calculation uses the circular segment area, which brings the circle calculator and its sector arithmetic into play.
From Cubic Units to Litres and Gallons
A volume in cubic centimetres becomes litres by dividing by 1,000, since the litre is defined as one cubic decimetre. Cubic metres to litres is a multiplication by 1,000. On the imperial side, one US gallon is exactly 231 cubic inches, and one cubic foot is 1,728 cubic inches, or roughly 7.48 US gallons.
The NIST guide to SI units sets out how derived units like the cubic metre are formed and why the conversion factor for a volume is the cube of the length factor. That cubing is where most conversion errors come from: one cubic metre is 1,000,000 cubic centimetres, not 100. Our volume converter handles the arithmetic once you have the raw cubic figure.
Pipes, Shells and Hollow Cylinders
A pipe is the difference between two cylinders. Its internal capacity uses the inside radius, and the volume of the material in its wall is the outside-radius volume minus the inside-radius volume: π(R2 − r2)h. Using the outside diameter to estimate what a pipe carries is a standard and consistent error, and it matters most on small-bore pipe where the wall is a large fraction of the total width.
The gap between the two grows quickly, because the radius is squared. A 100 mm outside diameter pipe with 5 mm walls has an inside diameter of 90 mm, and it carries (90 ÷ 100)2 = 81% of what the outside dimension suggests — nearly a fifth less. Working out that inside radius from an outside measurement and a wall thickness is a subtraction people skip, and the square root calculator is useful when going the other way, from a required cross-sectional area back to a diameter.
Arb Digital publishes hundreds of free calculators and converters. All of them are free to use, need no account, and run entirely in your browser.
Browse All Free Tools Request a ToolCommon Mistakes to Avoid
- Using the diameter as the radius — the answer comes out four times too large, and it still looks plausible.
- Measuring a pipe's outside diameter for its capacity — the wall thickness has to be subtracted twice to get the inside radius.
- Treating a horizontal tank's depth as linear — only an upright cylinder fills in direct proportion to its depth.
- Cubing the unit conversion incorrectly — one cubic metre is a million cubic centimetres, not a hundred.
- Forgetting the end caps in a surface area — a wrap needs only the lateral area, but a full coating needs both circles as well.
Related Free Tools From Arb Digital
The base of a cylinder is a circle, so the circle calculator covers that step in isolation. Rounded containers are handled by the sphere volume calculator, unit changes by the volume converter, and the cube root needed to size a vessel from a target capacity by the cube root calculator. Dimension comparisons are quickest with the percentage change calculator, and going from an area back to a radius uses the square root calculator. See the full free online tools hub.
Frequently Asked Questions
Volume equals π times the radius squared times the height. A cylinder with a 5 centimetre radius and a 25 centimetre height holds π times 25 times 25, which is 1,963.5 cubic centimetres, or just under 2 litres.
Halve the diameter to get the radius before squaring it. Using the diameter directly makes the answer four times too large, because the error is squared along with the length.
Work out the volume in cubic centimetres and divide by 1,000, or work in cubic metres and multiply by 1,000. A litre is defined as exactly one cubic decimetre.
Yes, if it is standing upright, because every horizontal slice is the same circle. A cylinder lying on its side does not fill linearly, except at exactly half the diameter where symmetry makes it half full.
It is 2π times the radius times the height — the curved wall without the ends. Unrolled it is a rectangle as wide as the circumference and as tall as the cylinder, which is how labels and wraps are cut.
Wider adds more capacity, because the radius is squared while the height is not. A 20% wider cylinder holds 44% more, while a 20% taller one holds only 20% more.
Use the inside radius, not the outside. Subtract the wall thickness from the outside radius first, then apply π r squared times the length. A 100 mm pipe with 5 mm walls carries about 81% of what its outside diameter suggests.
This tool is provided for general educational and planning use. Real vessels have wall thickness, fittings and tolerances, so confirm capacities against the manufacturer's specification before relying on them.
