Cylinder Volume & Surface Area
Volume, surface area, curved side and end of a cylinder from radius and height, or the radius or height from a volume: V = πr²h and A = 2πr(h + r). How it works
Use the Cylinder Volume & Surface Area
About the Cylinder Volume & Surface Area
A cylinder with radius 5 and height 10 has a volume of 785.3982 cubic units and a total surface area of 471.2389 square units. Volume is π × r² × h, and total surface area is 2πrh + 2πr²: the curved side plus the two circular ends. The answer is in the unit you typed, cubed or squared. It also finds the radius or the height from a volume.
Cylinder volume and total surface area
| Radius | Height | Volume | Total surface area |
|---|---|---|---|
| 1 | 1 | 3.1416 | 12.5664 |
| 3 | 7 | 197.9203 | 188.4956 |
| 2.5 | 12 | 235.6194 | 227.7655 |
| 5 | 10 | 785.3982 | 471.2389 |
| 10 | 20 | 6,283.1853 | 1,884.9556 |
As the tool shows them, to four decimals, in cubic and square units of whatever unit the radius and height are in.
How to use this tool
- Under Find, keep volume and areas or pick the radius or the height from a volume. Enter the radius, which is half the diameter, and the height, both in the same unit.
- Read the volume (cubic units), the total surface area (square units), the curved side and one end. They update as you type.
- Read the units from what you entered: centimeters give cm³ and cm², inches give cubic and square inches. For capacity, 1 cm³ is 1 mL.
Frequently asked questions
- How do I find the volume of a cylinder?
- Square the radius, then multiply by π and by the height. With radius 4 and height 6 that is 16 × π × 6 = 301.5929 cubic units. To go the other way choose a Find option: 1,000 cubic units at height 10 needs a radius of 5.6419, and at radius 5 a height of 12.7324.
- What is the surface area formula for a cylinder?
- Total surface area is 2πrh + 2πr², or 2πr(h + r). With radius 3 and height 7 the curved side is 2π × 3 × 7 = 131.9469 and the two ends add 56.5487, a total of 188.4956 square units.
- What if I know the diameter, not the radius?
- Halve it. A can 8 cm across has a radius of 4 cm, so with a height of 12 cm its volume is 603.1858 cm³.
- How many milliliters or liters is the volume?
- With the radius and height in centimeters the volume is in cm³, and 1 cm³ is 1 mL. Radius 3.25 cm and height 12 cm give 398.1969 cm³, so the cylinder holds 398.1969 mL, about 0.4 L. A liter is 1,000 cm³.
- How do I find the lateral surface area of a cylinder?
- The lateral (curved) area is 2πrh and each end is πr². The tool shows both beside the total: radius 4 and height 6 give a curved side of 150.7964 and ends of 50.2655 each, which add up to the total of 251.3274.
- Does it work for a pipe or hollow tube?
- No, it gives a solid cylinder. For a hollow tube, enter the outer radius and then the inner radius with the same height, and subtract the two volumes. With height 10, an outer radius of 5 gives 785.3982 and an inner radius of 4 gives 502.6548.
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