A cylinder is a solid with two congruent circular ends joined by a curved surface, like a can, pipe section, tank, or post. This calculator finds its volume from the radius of a circular end and the cylinder's height or length. Volume estimates support storage planning, liquid capacity, concrete and material calculations, packaging, and geometry work where the space inside or occupied by a cylindrical object matters.
Quick Answer
The volume of a cylinder is V = ΟrΒ²h, where r is the radius of the circular base and h is the perpendicular distance between the two ends.
Base Area Extended Through the Height
The formula can be understood in two stages. First, the circular base has area ΟrΒ². Second, that area is extended uniformly through the height, so volume is base area times height. Unlike a cone, the cross-section does not shrink along the way; every slice parallel to the base has the same circular area in an ideal right cylinder. This is why a cylinder with the same radius and height as a cone holds three times the cone's volume.
The radius is measured from the center of a circular face to its rim. Specifications often give diameter instead, because diameter is easier to measure across a pipe or can. Divide it by two before entering the value. Height is the straight separation between faces along the cylinder's axis. For a horizontal tank, that dimension may be described as length, but geometrically it plays the role of h as long as it is measured from one end to the other.
All inputs must share a unit. The result is in the corresponding cubic unit: cubic inches for inches, liters after conversion from cubic centimeters or cubic meters, and so on. To compare this shape with its tapered counterpart, use the Cone Volume Calculator.
How to Use the Cylinder Volume Calculator
- Measure across a circular end through its center to get the diameter, unless the radius is already known.
- Divide the diameter by two if necessary.
- Measure the cylinder's height or axial length from one flat end to the other.
- Convert the radius and height to the same unit.
- Enter both measurements.
- Read the volume in cubic units and convert afterward if a capacity unit such as liters is required.
Capacity of a Cylindrical Tank
Consider a tank with a radius of 5 feet and a height of 12 feet. Square the radius: 5Β² = 25. Multiply by Ο and by the height: Ο Γ 25 Γ 12 = 300Ο. The volume is 942.48 cubic feet, rounded to two decimal places. Keeping the expression as 300Ο until the last step makes the structure clear and limits rounding error.
Unit conversion should happen deliberately. A cylinder with radius 10 centimeters and height 30 centimeters has volume Ο Γ 100 Γ 30 = 9,424.78 cubic centimeters. Since 1,000 cubic centimeters equal 1 liter, its geometric capacity is about 9.42 liters. A real tank's safe working capacity may be lower because it should not be filled to the brim.
- A radius of 2 units and height of 10 units give 125.66 cubic units.
- A radius of 7 units and height of 4 units give 615.75 cubic units.
- A radius of 1 unit and height of 1 unit give 3.14 cubic units.
Solid Volume Versus Hollow Capacity
Do not enter the outside diameter when the required result is the usable inside volume of a thick-walled pipe or tank. Wall thickness reduces the interior radius. For an open cylindrical shell or pipe, the material volume or flow capacity may require an inner-cylinder calculation and, for the wall material itself, a subtraction of inner volume from outer volume. A single solid-cylinder result cannot represent all three quantities at once.
Diameter-radius confusion remains the biggest arithmetic risk. If a can is 10 units wide, its radius is 5, not 10. Entering 10 multiplies the volume by four. Also distinguish height from a slanted measurement on an oblique cylinder. Standard tank and can problems use a right cylinder with ends perpendicular to its axis; if the container leans or has domed ends, the plain formula covers only the cylindrical portion.
Surface area is a different question. It measures the material needed to cover the outside, including or excluding the ends depending on the object, whereas volume measures enclosed space. Confusing the two can lead to buying paint when the task requires liquid capacity, or vice versa. A rounded solid without flat ends calls for the Volume of a Sphere Calculator, and the wider Mathematics Calculators category groups related measures.
Converting Cubic Measurements Into Working Capacity
A geometric result often needs conversion before it can be used. One liter equals exactly 1,000 cubic centimeters, so divide a cubic-centimeter result by 1,000 to obtain liters. One cubic meter contains 1,000 liters. In US customary work, one US gallon is approximately 3.78541 liters; convert liters with that factor only when US gallons, rather than imperial gallons, are intended. Mixing the two gallon systems introduces an error of roughly 20 percent, far larger than most rounding choices.
For a partly filled upright cylinder, the same formula applies with the liquid depth in place of the full height, assuming the circular cross-section is constant and the surface is level. A horizontal cylindrical tank is more complicated: equal increments of depth do not contain equal volumes because the width of the liquid surface changes as it rises. Use the full-cylinder result for total capacity, but do not treat a depth percentage as a volume percentage in a horizontal tank without a proper circular-segment calculation.
If the cylinder is a container, note whether dimensions describe the outside or the cavity. A drawing for fabrication may use outside measurements, while a capacity specification usually refers to the inside. Writing "inside radius" or "outside radius" beside the entry prevents a correct formula from being applied to the wrong circle. The same note helps when results are passed to another person for ordering, filling, or machining.
Reading a Cylinder Result With Confidence
Check that the answer scales sensibly: a modest increase in radius should produce a noticeable jump because the radius is squared, while the same proportional increase in height scales the result only by that proportion. If the result moves in the opposite way, a diameter, radius, or unit has likely been mixed up.