Volume calculator
A cubic centimetre is a millilitre, so a box measured in centimetres gives you litres without a second conversion. The same box measured in inches or feet is converted for you.
Volume is the space a solid encloses. A box is length times width times height; a cylinder is π times the radius squared times the height; a sphere is four-thirds π times the radius cubed; a cone is a third of the matching cylinder. Each shape here also reports its surface area and its capacity in litres and US gallons.
How to use it
A cone is exactly one third of the cylinder that would contain it, and a pyramid is one third of its box. Neither is a coincidence or an approximation: both fall out of the same integral, and remembering it turns four formulas into two. The default cone here, radius 5 and height 12, comes out at 314.159 cm³ against the 942.478 cm³ of a cylinder with the same radius and height.
The capacity rows are the part most likely to catch someone out, because a gallon is not one thing. The figure here is the US liquid gallon, defined as 231 cubic inches and equal to 3.785412 litres. The imperial gallon still used in the UK and Canada is 4.546090 litres, a little over 20 per cent larger, so a tank that holds 100 US gallons holds about 83 imperial ones. Litres are simpler: a cubic centimetre is a millilitre by definition, so a box measured in centimetres gives its capacity with no conversion at all. Where a conversion is needed it is exact rather than approximate, because the inch has been defined as precisely 25.4 millimetres since 1959, which makes a foot 304.8 mm and a yard 914.4 mm with no rounding anywhere in the chain.
Every surface area on this page is the whole closed surface. A cylinder is 2πr(r + h), both flat ends included; a cone includes its base disc; a pyramid includes its rectangular base and assumes the apex sits over the centre of it. For an open-topped tank or a pyramid standing on the ground, subtract the one face you are not painting: the default cylinder loses 78.540 cm² of its 785.398 that way.
What people use it for
- Working out how many litres an aquarium or a water butt holds
- Ordering concrete, soil or gravel by the cubic metre
- Sizing a propane or pressure vessel from its cylindrical body and caps
- Getting the surface area to paint, clad or insulate a solid
- Comparing the capacity of two containers that are not the same shape
- Turning a delivery quoted in US gallons into litres before you buy it
Questions
Half the diameter. Measuring across a tank gives the diameter, so halve it before entering it here. Getting this wrong multiplies the volume by four.
The US liquid gallon of 231 cubic inches, 3.785412 litres. It is the smaller one.
Divide the US figure by 1.20095, or read the litres row and divide by 4.54609. An imperial gallon is just over 20 per cent larger than a US one.
Choose cylinder or capsule, enter the measurements in inches or feet, and read the gallons row. The conversion is done from the cubed unit, so the input unit does not have to be metric.
Yes. The inch is defined as exactly 25.4 millimetres, so a foot is 304.8 mm and a yard 914.4 mm with nothing rounded on the way through.
Because a cubic centimetre is a millilitre by definition. A box measured in centimetres gives a volume in millilitres, and a thousand of those is a litre.
Yes, on every shape here. These are closed solids. Subtract the face you are not covering if the object is open at one end or sits on the ground.
Take πr² off the figure shown. On the default cylinder that is 78.540 cm² off 785.398, leaving 706.858.
No. All the dimensions of a shape share one unit selector, so convert before you type. That is deliberate: mixed units in a volume are how a factor of a thousand gets lost.
A cylinder with a hemispherical cap on each end, the shape of a propane tank or a pressure vessel. Enter the radius and only the straight section; the caps are added for you.
No, only the straight middle. The overall length is that plus twice the radius, so the default capsule is 20 cm of body and 30 cm end to end.
Because integrating the area of its circular slices from tip to base gives exactly one third of the constant-radius case. The same relation makes a pyramid a third of its box.
The distance up the sloping side from the rim to the tip, which is Pythagoras on the radius and the height. The default cone gives 13 from a 5 radius and a 12 height, and it is what you need for the lateral surface or for cutting a template.
Inside for capacity, outside for material. A tank with 5 mm walls holds noticeably less than its external dimensions suggest, and the thicker the walls relative to the vessel the more it matters.
Not directly. An upright cylinder is easy: enter the height of the liquid instead of the height of the tank. A cylinder lying on its side is genuinely harder and needs a circular segment formula, not this one.
Split it into the solids here and add them, which is how a tank with domed ends is really a capsule. For something with no geometry at all, measure the water it displaces.
A thousand. Set the unit to metres and read the litres row: it is the same number with three zeros on it.
For water, one litre is one kilogram and the arithmetic stops there. Anything else needs its density: sand is roughly 1.6 kg per litre and petrol about 0.75.
Work in metres so the volume comes out in cubic metres, which is how it is sold, then add five to ten per cent for spillage and an uneven base.
So small volumes stay readable in litres without being rounded to zero. Round the answer yourself to whatever your tape measure justifies.
Use the box shape with the internal dimensions, then take off what the substrate and the rocks displace and the gap you leave below the rim. The glass figure is usually five to ten per cent above what actually goes in.
No, it multiplies it by four for a cylinder and by eight for a sphere, because the radius is squared or cubed. It is the most common mistake on this page.
No. The arithmetic runs in this page and nothing leaves your device.