The cylinder is the most-used 3D shape in everyday engineering and packaging.
About this calculator
The cylinder is the most-used 3D shape in everyday engineering and packaging. Water bottles, soda cans, pipes, drums, batteries, gas tanks, silos, syringes -- all are cylinders. Mathematically a right circular cylinder is defined by just two numbers: the radius of its circular base and its perpendicular height. From these, every volume and surface property follows from a handful of clean formulas.
The cylinder also has the elegant property that its volume formula is simply 'base area × height'. This is the same rule that applies to any prism with a uniform cross-section, which is why cylinders are intuitive: they're prisms with a circular cross-section. The total surface area splits into three parts: the top circle, the bottom circle and the lateral curved surface that, when unrolled, is just a rectangle of width 2πr and height h.
Real-world cylinder problems usually involve volume in litres, surface area for material costs, or finding optimal proportions for a fixed volume (the answer to 'cheapest cylindrical can for 1 litre' is height = 2 × radius -- a famous calculus problem). For tanks and storage, divide volume in cubic centimetres by 1000 to get litres directly. A cylinder's volume is exactly three times that of a cone with the same base and height -- a fact you can use as a quick sanity check. Pair this with the [[cone]] calculator for tapered shapes, the [[sphere]] calculator for round shapes, the [[area]] calculator for 2D footprints and the [[paint]] calculator for surface coverage in real units.
Common uses
- Class 9/10 geometry homework -- cylinder volume and surface problems
- Volume of cylindrical water tanks, drums and storage containers (in litres)
- Surface area for paint, fabric or insulation needed to cover pipes and tanks
- Engineering calculations for pressure vessels, syringes and rolling pins
- Packaging design and label sizing for cylindrical product containers
Frequently asked questions
How do I convert volume to litres?
If you entered dimensions in centimetres, divide cubic-cm volume by 1000 to get litres. The calculator does this automatically. For metres, the same volume in cubic metres is already in kilolitres -- multiply by 1000 to get litres.
What's the difference between lateral area and total area?
Lateral area is just the curved side (2πrh). Total area includes the lateral area plus the two circular ends (2πr² + 2πrh = 2πr(r + h)). Use lateral area when you don
How is a cylinder related to a cone and sphere with the same radius?
If a cylinder, cone and sphere all have the same radius and the cylinder/cone height equals the sphere
What is the cylinder of revolution?
It
What if I have diameter, not radius?
Just divide the diameter by 2 to get radius. A 20 cm diameter pipe has radius 10 cm. The calculator uses radius to keep formulas clean, which is the standard mathematical convention.