Cylinder Calculator
A cylinder with a radius of 3 and a height of 5 has a volume of about 141.37 cubic units and a total surface area of about 150.80 square units. This cylinder calculator works out volume, total surface area, lateral surface area, and base area from the radius and the height. Enter both measurements in the same unit and read the four results below.
Quick answer
Volume measures the space inside the cylinder.
What this tells you
- •Volume measures the space inside the cylinder.
- •Total surface area covers both circular ends plus the curved side.
- •Lateral surface area is the curved side only, without the two ends.
- •Base area is the area of one circular end.
How to Use
- 1Enter the radius of the cylinder.
- 2Enter the height of the cylinder.
- 3Use the same unit for both values, for example centimeters for radius and height.
- 4Click Calculate to see the volume, total surface area, lateral surface area, and base area.
How It Works
Formula
Volume: V = pi x r^2 x h. Total surface area: A = 2 x pi x r x (r + h). Lateral surface area: L = 2 x pi x r x h. Base area: B = pi x r^2.Here r is the radius of the circular end and h is the height of the cylinder. The volume multiplies the base area (pi x r^2) by the height. The total surface area adds the two circular ends (2 x pi x r^2) to the curved side (2 x pi x r x h), which factors to 2 x pi x r x (r + h). The lateral surface area is the curved side on its own.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Volume of a cylinder with radius 3 and height 5
The base area is pi x 3^2 = 28.2743. Multiply by the height: 28.2743 x 5 = 141.3717. The total surface area is 2 x pi x 3 x (3 + 5) = 150.7964.
Cylinder with radius 2 and height 5
The base area is pi x 2^2 = 12.5664. Volume is 12.5664 x 5 = 62.8319. Total surface area is 2 x pi x 2 x (2 + 5) = 87.9646.
Cylinder Volume and Surface Area
Sample volume and total surface area values for common radius and height pairs, rounded to 2 decimals.
| Radius (r) | Height (h) | Volume | Total Surface Area |
|---|---|---|---|
| 1 | 1 | 3.14 | 12.57 |
| 2 | 5 | 62.83 | 87.96 |
| 3 | 10 | 282.74 | 245.04 |
| 5 | 10 | 785.40 | 471.24 |
Values use pi as 3.14159 and assume radius and height share the same unit.
Common mistakes
- Using the diameter instead of the radius. The radius is half the diameter, so divide the diameter by 2 before entering it.
- Forgetting to square the radius. The base area uses r^2, not r, so a radius of 3 gives 9 inside the formula.
- Mixing length units. Keep the radius and the height in the same unit, otherwise the volume and area results are wrong.