Cylinder Volume Calculator
A cylinder's volume is π r² h: the area of the circular end, π times the radius squared, multiplied by the height. Type the radius and the height and the answer appears with that formula beside the drawing and the working, your numbers put in, as the first row below it. The radius is half the diameter, and the Measure switch takes whichever one you actually measured. This page opens the calculator on the cylinder whatever shape you used last, and reads the answer out in litres, US gallons and UK gallons as well as the cube of the unit you typed in.
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
- Do I type the radius or the diameter?
- Either, but tell the tool which. The field is a radius by default, and the Measure switch beside it turns it into a diameter. The diameter is the full width across the circle, which is what a tape measure gives you, and the radius is half of it. Put a diameter into the radius field by mistake and the answer comes out four times too large, because the radius is squared. When you switch to Diameter the formula line reads π r² h, r = d/2 and the working shows the halving, for example r = 1 / 2 = 0.5, so you can check which number went into the sum.
- How do I get litres or gallons out of it?
- They are already under the answer. Whatever unit you measure in, the tool lists litres, US gallons and UK gallons, plus three cubic units for the scale you are working at. A cylinder of radius 0.5 m and height 1.2 m is π × 0.5² × 1.2 = 0.942478 m³, and the line under the figure reads 942.478 L · 248.976 US gal · 207.316 UK gal, each repeated in full in its own row below with a Copy button. The conversions use exact definitions: a litre is 1,000 cm³, a US gallon is 231 cubic inches (3.785411784 litres) and a UK gallon is 4.54609 litres.
- Can you work one through?
- A drum 60 cm across and 90 cm tall, measured in metres: set Measure to Diameter, type 0.6 for the diameter and 0.9 for the height. The radius is 0.6 / 2 = 0.3 m, so the volume is π × 0.3² × 0.9 = 0.254469 m³, which is 254.469 litres or 67.2236 US gallons. In feet it works the same way: a round tank of radius 3 ft and height 4 ft is π × 3² × 4 = 113.097 ft³, which the rows give as 3,202.56 litres and 846.027 US gallons.
- What about a hollow pipe?
- What a pipe holds is a cylinder of its inner diameter, so set Measure to Diameter, type the inside measurement, and type the pipe's length as the height. A pipe 10 cm inside and 300 cm long holds π × 5² × 300 = 23,561.9 cm³, which is 23.56 litres. There is no hollow shape here, so for the material in the wall run it twice and subtract: the same pipe with an 11 cm outside diameter is 28,510 cm³, and 28,510 − 23,561.9 leaves about 4,948 cm³, near enough 4.95 litres of pipe wall.
- The cylinder is only part full. What do I type?
- For a cylinder standing on its end, the liquid is a shorter cylinder: type the depth of the liquid as the height instead of the full height, and the volume falls in proportion, so half the height is exactly half the volume. A cylinder lying on its side is a different sum, because the liquid is a circular segment and not a shorter cylinder. Pick Tank on the shape row for that one: it takes the radius, the length and the fill depth measured up from the bottom.
- Which units can I measure in?
- Metres, centimetres, feet or inches, chosen on the Unit row. The volume comes back in the cube of that unit, m³ from metres and in³ from inches, with litres and both gallons underneath every time. The unit buttons change how your numbers are read rather than converting them, so if you switch from metres to feet, 0.5 becomes half a foot: retype the sides in the unit you picked.
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.