Volume and surface area of a cylinder.
Enter the radius and height of a right circular cylinder and read the whole shape at once: volume, base area, the curved side, total surface area, diameter and circumference. Every result updates live and shows its formula.
Dimensions
The unit is a label only. Volume comes out in cubic units and every area in square units of whatever you pick.
What each measure means
Full breakdown
The formulas, step by step
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Cylinders, explained
How to find the volume of a cylinder
A right circular cylinder is the shape of a can, a pipe or a water tank: two identical circles joined by a straight side. Its volume is the area of one circular base times the height, which is pi times the radius squared times the height, written V = pi * r^2 * h. Because you square the radius, doubling the radius makes the cylinder hold four times as much, while doubling only the height simply doubles the volume.
Volume is always in cubic units. If your radius and height are in centimeters the volume is in cubic centimeters, and 1000 cubic centimeters make one liter, a quick way to turn tank dimensions into a capacity you can picture.
Base area, lateral area and total surface area
The base area is the area of one circular end, pi * r^2. The lateral area is the curved side, which unrolls into a rectangle as tall as the height and as wide as the circumference, giving 2 * pi * r * h. The total surface area adds both flat ends to that side: 2 * pi * r^2 + 2 * pi * r * h.
Every area is in square units, never cubic. Surface area tells you how much material wraps the shape, so it is what you need for the sheet metal in a tank, the label on a can or the paint on a column, while volume tells you what fits inside.
Diameter, circumference and using the calculator
The diameter is twice the radius, and the circumference, the distance around the circular base, is 2 * pi * r. If you measured across the top of a pipe you have the diameter, so halve it to get the radius this tool asks for, or just switch the input to diameter mode and let the calculator do it.
Type any radius and height and every result updates at once: volume as the headline figure plus base area, lateral area, total surface area, diameter and circumference in the breakdown, each with its formula. The unit selector is a label, so the numbers stay the same whether you call them centimeters, inches, feet or meters.
Common questions
What is the formula for the volume of a cylinder?
Volume equals pi times the radius squared times the height, or V = pi * r^2 * h. Multiply the radius by itself, multiply by the height, then multiply by pi (about 3.14159). The answer is in cubic units.
What is the difference between lateral and total surface area?
Lateral surface area is only the curved side of the cylinder, 2 * pi * r * h. Total surface area adds the two circular ends to that side, giving 2 * pi * r^2 + 2 * pi * r * h. Use lateral area for a label that wraps just the side, and total area when both ends are also covered.
Why is volume in cubic units but surface area in square units?
Volume measures the space inside the cylinder, so it multiplies three lengths and comes out in cubic units such as cubic centimeters. Surface area measures a flat covering, which multiplies two lengths, so it is in square units such as square centimeters.
I only know the diameter, not the radius. What do I do?
The radius is half the diameter, so divide the diameter by 2 and enter that. This calculator also lets you switch the input to diameter mode, where you type the diameter directly and it converts to the radius for you.
All math runs in your browser using the exact value of pi. Results are for a right circular cylinder, the everyday can or pipe shape. Nothing is uploaded.