Volume Calculator
Pick a shape, type its sides in metres, centimetres, feet or inches, and read the volume with the formula it came from, in litres and gallons at once. Seven solids from box to pyramid, a horizontal tank with a fill depth, rectangular and oval pools with a shallow and a deep end, and a concrete slab with its thickness in inches or centimetres, every answer listed in six more units underneath.
Cylinder · π r² h942.478 L · 248.976 US gal · 207.316 UK gal
A drum, a can, a round tank on its end. A pipe is a cylinder too: use its inner diameter, and the length as the height.
The formula is on the stage, and the working is the first row. Every answer here is one textbook formula with your numbers put in, printed so you can check it: a cylinder is π r² h, a sphere is (4/3) π r³, a pool is length times width times the average of its two depths. The horizontal tank uses the exact circular-segment formula for a partial fill, so half way up is exactly half and a quarter of the way up is less than a quarter, because the bottom of a circle is narrow. Conversions use exact definitions: a litre is 1,000 cm³, a US gallon is 231 cubic inches and a UK gallon is 4.54609 litres.
Common questions
- How do I get litres from measurements in centimetres?
- Choose cm as the unit and type the sides in centimetres. The volume comes out in cubic centimetres, and the first row under it is litres: 1,000 cubic centimetres make exactly one litre. An aquarium 40 cm long, 25 cm wide and 30 cm tall is 30,000 cm³, which is 30 litres, and the US gallons row gives the same water as 7.93 gallons.
- How much water is in my pool, for dosing chemicals?
- The volume is the number a chemical label asks for. Pick Pool for a rectangular pool, or Oval pool for an oval or round one, and type the length, the width and the depth at the shallow end and at the deep end; the tool uses the average of the two depths, which is the floor a sloping pool actually has. A 10 m by 5 m pool running from 1 m to 2 m deep holds 75 m³, and the rows under it read 75,000 litres and about 19,813 US gallons. A pool of one depth throughout: type that depth in both fields.
- How does the partly filled tank work?
- Tank is a cylinder lying on its side, and the fill depth is the height of the liquid measured up from the bottom. The tool works out the exact area of the circular segment the liquid covers, r² acos((r − f)/r) − (r − f) √(2rf − f²), and multiplies it by the tank's length. It is not a simple fraction of the tank: half way up is exactly half, but a quarter of the way up is less than a quarter, because a circle is narrow at the bottom. A tank of radius 1 m and length 2 m filled to 0.5 m holds 1,228 litres, 19.6% of the 6,283 litres it holds full, and the When full row shows that capacity.
- How do I work out concrete in cubic yards?
- Pick Concrete slab and the unit ft. Type the length and width in feet and the thickness in inches, since that is how a slab is specified; the tool divides the inches by 12 before multiplying. A 10 ft by 10 ft slab 4 inches thick is 33.33 cubic feet, and the Cubic yards row reads 1.2346, because a cubic yard is 27 cubic feet. In metres the thickness is typed in centimetres and the answer comes out in cubic metres, which is how concrete is ordered in metric countries. The tool gives the geometric volume only; it does not add an allowance for waste or an uneven base.
- How do I find the volume of a pipe?
- A pipe is a cylinder: pick Cylinder, switch the measure to Diameter, type the inner diameter (not the outer, which includes the wall), and type the pipe's length as the height. A pipe with a 10 cm inner diameter and 300 cm of length holds π × 5² × 300 = 23,562 cm³, which the litres row gives as 23.56 litres.
- Do I enter the radius or the diameter?
- Either. The cylinder, sphere, hemisphere, cone and tank take a radius by default, and a switch beside the field turns it into a diameter. The diameter is halved before it goes into the formula, and the formula line says so: it reads π r² h, r = d/2. A radius of 0.5 m and a diameter of 1 m are the same cylinder, and with a height of 1.2 m both give 0.942478 m³.
- Which units come out?
- The volume is in the cube of the unit you typed in, and the rows under it give litres, US gallons and UK gallons every time, plus three cubic units chosen for the scale you are working at: cubic feet, cubic yards and cubic inches for metres, for instance. The conversions use exact definitions: a litre is 1,000 cm³, a cubic foot is 28.316846592 litres, a US gallon is 231 cubic inches (3.785411784 litres) and a UK gallon is 4.54609 litres, so a UK gallon is about 1.2 US gallons.
Volumes are computed from the formulas shown, exact for the dimensions you type; a horizontal tank's partial fill is the exact circular-segment result. A US gallon is 231 cubic inches and a UK gallon 4.54609 litres.