Cylinder Calculator
Calculate the volume, lateral surface area, total surface area, and base area of a cylinder from its radius and height.
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How to use this calculator
Cylinder volume is the base circle area times height. Lateral surface area is the rectangle formed by "unrolling" the curved wall: width = circumference = 2πr, height = h.
- 1
Enter the base radius r (half the diameter of the circular end).
- 2
Enter the height h (length of the cylinder from one circular end to the other).
- 3
Volume, surface areas, and base circumference are displayed immediately.
Frequently asked questions
How do I find the volume of a hollow cylinder (pipe)?
Subtract the inner cylinder's volume from the outer: V = π(R² − r²)h, where R is the outer radius and r is the inner radius. This gives the volume of material in the pipe walls, useful for calculating pipe weight or material needed.
What is the "space diagonal" of a cylinder?
The space diagonal is the longest straight-line distance between two points inside the cylinder — from one rim of the base to the opposite rim of the top. Using the Pythagorean theorem: d = √(diameter² + height²) = √((2r)² + h²). This tells you the longest item that will fit inside the cylinder.
How does a cylinder compare to a cone with the same base and height?
The cylinder holds exactly three times the volume of the cone. This is why a cone-shaped paper cup (at a water cooler) holds so much less than it looks — its volume is V = (1/3)πr²h compared to πr²h for a cup that is fully cylindrical.
What is the lateral surface area used for?
Lateral surface area (2πrh) represents just the curved wall of the cylinder, excluding the two circular ends. It is used when calculating the material needed for a label on a can, the paint needed for a pipe exterior, or the insulation wrap for a cylindrical water heater — all cases where the flat ends are not included.
Cylinder calculator — volume and surface area
Why cylinder volume is so useful
Cylinders are among the most common shapes in engineering: pipes, tanks, columns, cans, barrels, and engines are all cylindrical or close to it. The volume formula V = πr²h is a direct product of base area and height — every horizontal cross-section is identical. Doubling the radius quadruples the volume (since r is squared), while doubling the height only doubles it.
Unrolling the cylinder: lateral surface area
If you cut a cylinder along a vertical line and flatten it, you get a rectangle of width equal to the base circumference (2πr) and height h. Its area is 2πrh — the lateral surface area. This "unrolling" trick is used in manufacturing: calculating the sheet metal needed for a cylindrical tank wall, or the label paper for a tin can.
Cylinders in everyday engineering
Engine displacement — the combined swept volume of all pistons — is calculated as V = (π/4) × bore² × stroke × cylinders, directly from the cylinder formula with bore = diameter. Water towers are cylindrical to distribute hydrostatic pressure evenly in all directions. Grain silos combine a cylinder body with a conical hopper bottom; total capacity = cylinder volume + cone volume.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →