Volume of a Cylinder Calculator
Calculate the volume, total surface area, and lateral surface area of a cylinder from its radius and height. See also Volume of Cone Calculator and Volume of Sphere Calculator.
How to Calculate the Volume of a Cylinder
To find the volume of a cylinder, measure the radius of the circular base and the height (the perpendicular distance between the two bases). Square the radius, multiply by π, then multiply by the height. The total surface area includes both circular bases and the curved lateral surface. This calculator computes all three values automatically.
Cylinder Volume Formula
V = π × r² × h
Total SA = 2 × π × r × (r + h)
Lateral SA = 2 × π × r × h
Base Area = π × r²
Example
Find the volume of a cylinder with radius 4 and height 10:
V = π × r² × h
V = π × 4² × 10
V = π × 16 × 10
V ≈ 502.6548 cubic units
Cylinder Volume Reference Table
| Radius | Height | Volume | Surface Area |
|---|---|---|---|
| 1 | 5 | 15.7080 | 37.6991 |
| 2 | 5 | 62.8319 | 87.9646 |
| 3 | 5 | 141.3717 | 150.7964 |
| 4 | 5 | 251.3274 | 226.1947 |
| 5 | 5 | 392.6991 | 314.1593 |
| 2 | 10 | 125.6637 | 150.7964 |
| 4 | 10 | 502.6548 | 351.8584 |
| 5 | 10 | 785.3982 | 471.2389 |
| 6 | 10 | 1130.9734 | 603.1858 |
| 8 | 10 | 2010.6193 | 904.7787 |
| 5 | 15 | 1178.0972 | 628.3185 |
| 10 | 10 | 3141.5927 | 1256.6371 |
| 10 | 20 | 6283.1853 | 1884.9556 |
| 15 | 15 | 10602.8752 | 2827.4334 |
| 20 | 20 | 25132.7412 | 5026.5482 |
Frequently Asked Questions
What is the volume of a cylinder?
The volume of a cylinder is the total three-dimensional space enclosed within its two circular bases and curved surface. It is calculated as V = πr²h, where r is the base radius and h is the height.
What is the difference between total and lateral surface area?
The lateral surface area is only the curved side of the cylinder (2πrh). The total surface area adds the two circular bases (2πr²), giving 2πr(r + h).
How do I find the volume if I know the diameter?
Divide the diameter by 2 to get the radius, then use V = πr²h. For example, a cylinder with diameter 8 and height 10 has radius 4, so V = π × 16 × 10 ≈ 502.65.
Does the formula work for oblique cylinders?
Yes, the volume formula V = πr²h works for oblique cylinders as long as h is the perpendicular height (not the slant height). The surface area formula, however, only applies to right cylinders.