Why does the surface area only grow by 2.67 when the volume quadruples?

Because the surface has two parts that grow at different rates. The two circular ends grow with the square of the radius, like the volume, while the curved side grows only in proportion to the radius since its height did not change. Doubling the radius here takes the surface from 471.2 to 1,256.6, a factor of 2.67 rather than 4, and the mixture is why a bigger tank costs proportionally less material per litre stored. That relationship — volume outrunning surface as things get bigger — is the reason large containers are cheaper per unit and large animals lose heat more slowly than small ones.

How much does a partly filled cylinder hold?

Standing upright, in exact proportion to the depth: half the height is half the volume, and a dipstick reads linearly. Lying on its side it is not proportional at all — a horizontal tank half full by depth is half full by volume, but a quarter of the depth holds noticeably less than a quarter of the contents, because the cross-section is narrow at the bottom and widest in the middle. That is why horizontal fuel and oil tanks come with a calibrated chart rather than a ruler, and why estimating a side-lying drum by eye always overstates what is left near the bottom.

Twice as Wide Holds Four Times as Much; Twice as Tall Holds Twice

Published 10/12/2026 · 3 min read · Everyday calculators

Marco Bianchi — Home, DIY & motoring writer at OneKitly

Renovation · Materials

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In short

The volume of a cylinder is π × r² × h, and the whole practical consequence sits in that little two. The radius is squared and the height is not, so the two dimensions do not trade equally: taking the radius from 5 to 10 multiplies the volume by four, from 785.4 to 3,141.6, while taking the height from 10 to 20 merely doubles it to 1,570.8. A water butt that is twice as wide as another holds four times as much; one twice as tall holds twice. That is why storage tanks are squat rather than slender, why a wider pipe carries so much more than a slightly wider one appears to, and why widening a cylindrical hole for a post is far more expensive in concrete than deepening it.

A cylinder of radius 5 and height 10 holds 785.4 units of volume. Double the radius and it holds 3,141.6; double the height instead and it holds 1,570.8.

Radius, not diameter

Tanks, pipes and post holes are sold and measured by diameter, and the formula wants the radius. Entering a diameter where a radius belongs multiplies the answer by four, and the resulting number is plausible enough to survive a glance — a container that should hold 200 litres reports 800, which is wrong by a factor that nobody notices until the delivery arrives. Halve the figure on the label before typing it, and take the internal diameter rather than the external one where the wall thickness is a real fraction of the size, as it is on small-bore pipe.

The tool has no units, so you supply them

Feed it centimetres and the answer is in cubic centimetres; feed it metres and the answer is in cubic metres. The two are a million apart, and the useful bridges are that a cubic centimetre is a millilitre and a cubic metre is a thousand litres. A tank of radius 5 cm and height 10 cm therefore holds 785 cm³, which is 0.785 litres — a large mug. The error that actually happens is mixing the two in one calculation, a radius in centimetres with a height in metres, which is off by a hundred and produces an answer with no obvious tell. Convert everything to one unit before entering anything.

Volume

Starting from radius 5, height 10
Change	Volume	Times the original
none	785.4	1.0
height doubled	1,570.8	2.0
radius doubled	3,141.6	4.0

Worked with our own calculator

Cylinder volume calculator

Given

Radius: 10
Height: 20

Result

Volume: 6,283
Surface area: 1,885

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

Run it on your own figures →

Frequently asked questions

Why does the surface area only grow by 2.67 when the volume quadruples?: Because the surface has two parts that grow at different rates. The two circular ends grow with the square of the radius, like the volume, while the curved side grows only in proportion to the radius since its height did not change. Doubling the radius here takes the surface from 471.2 to 1,256.6, a factor of 2.67 rather than 4, and the mixture is why a bigger tank costs proportionally less material per litre stored. That relationship — volume outrunning surface as things get bigger — is the reason large containers are cheaper per unit and large animals lose heat more slowly than small ones.
How much does a partly filled cylinder hold?: Standing upright, in exact proportion to the depth: half the height is half the volume, and a dipstick reads linearly. Lying on its side it is not proportional at all — a horizontal tank half full by depth is half full by volume, but a quarter of the depth holds noticeably less than a quarter of the contents, because the cross-section is narrow at the bottom and widest in the middle. That is why horizontal fuel and oil tanks come with a calibrated chart rather than a ruler, and why estimating a side-lying drum by eye always overstates what is left near the bottom.

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Sources

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