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Math & Statisticsgeometry

Cylinder Calculator

Cylinder volume and area, with partial fill. A vertical cylinder is the one common shape that fills linearly, so half the height really is half the volume, which is not true of a horizontal tank or a cone.

Also called: cylinder volume calculator, tank volume.

%
Volume
2,261.95

2,261.95 litres at 100% full, of a total capacity of 2,261.95 litres. The cylinder is 2.26 m³, with 9.8 m² of surface and 7.54 m² of side. A vertical cylinder fills linearly, so depth and volume are proportional. A horizontal one does not.

Full capacity
2,261.95
Volume in m³
2.26
Total surface area
9.8
Side area
7.54
Base area
1.13
In US gallons
597.54
On partial filling
A vertical cylinder fills linearly, so depth and volume are proportional. A horizontal one does not.
How this is calculated
Method and background

How this is calculated

Volume is the base area times the height. The linearity matters practically: a sight glass on a vertical cylindrical tank can be marked evenly, where the same tank lying on its side needs a non-linear scale because the cross section changes with depth. The side area is the circumference times the height, which is what a label or a wrap of insulation has to cover.

a cylinder fills linearly with height, unlike a sphere or a cone
r
Radius
h
Height

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a 1.2 m tank two metres tall

Diameter
1.2
Height
2
In
Metres
Filled to
100 %

Volume2,261.95

pi x 0.36 x 2 x 1000

Open this example

half full is half the volume

Diameter
1.2
Height
2
In
Metres
Filled to
50 %

Volume1,130.97

boundary: the linearity that only a vertical cylinder has

Open this example

Method and limits

What it assumes

  • A vertical cylinder with a flat base.

What it deliberately does not model

  • A horizontal cylinder does not fill linearly and needs a different calculation.
  • Wall thickness means internal capacity is less than external dimensions suggest.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Is half the height half the volume?
For a vertical cylinder, yes. For a horizontal one, no: the cross section is widest at the middle, so depth and volume are not proportional.