About the Cylinder Calculator
This cylinder calculator handles the three questions people ask most about cylinders. Give the radius and height to get the volume, lateral area, base area and total surface area; or give a target volume with the radius to find the height needed, or with the height to find the radius needed. Choose a real unit and the capacity is also shown in liters and US gallons.
It is useful for tanks, drums, pipes, cans, pillars, round planters and water heaters — for example to find how many gallons a 3 ft round tank holds, how tall a 500 mL can must be, or how much paint the outside of a column needs.
The calculator assumes a right circular cylinder: straight sides at 90° to two equal circular ends. Measure the inside diameter for capacity and the outside diameter for surface area, and remember the radius is half the diameter.
With the default inputs, the volume is 28.2743. Change any value above to recalculate instantly.
How to use the cylinder calculator
- 1Choose what you know: radius and height, or a volume plus one dimension.
- 2Select the unit you measured in.
- 3Enter the values (use half the diameter for the radius).
- 4Read the volume, missing dimension, surface areas and capacity.
Formula and method
A cylinder is a stack of identical circles, so its volume is the area of one circular end, πr², multiplied by the height. Rearranging the same formula gives the height needed for a given volume (h = V ÷ πr²) or the radius needed (r = √(V ÷ πh)).
The curved side unrolls into a rectangle whose width is the circumference 2πr and whose height is h, so the lateral area is 2πrh. Adding both circular ends gives the total surface area 2πr² + 2πrh. Capacity conversions use 1 m³ = 1,000 L and 1 US gallon = 3.785411784 L.
- r
- Radius of the circular ends
- h
- Height (or length) of the cylinder
- V
- Volume
Worked examples
Round tank: radius 1.5 ft, height 4 ft
V = π × 1.5² × 4 = 9π ≈ 28.27 ft³, which is about 801 liters or 211.5 US gallons. The curved side is 2π × 1.5 × 4 ≈ 37.70 ft².
How tall must a 500 cm³ can with a 4 cm radius be?
h = 500 ÷ (π × 16) ≈ 9.95 cm. A can about 8 cm wide and 10 cm tall holds 500 mL.
Radius for a 1 m³ tank that is 2 m tall
r = √(1 ÷ (2π)) ≈ 0.399 m, so the tank needs to be about 0.80 m across to hold 1,000 liters.
Frequently asked questions
How do you calculate the volume of a cylinder?+
Multiply the area of the circular base by the height: V = πr²h. A cylinder with radius 3 and height 10 holds π × 9 × 10 ≈ 282.7 cubic units.
How many gallons are in a cylinder tank?+
Work out the volume in cubic feet and multiply by 7.48 to get US gallons, or in cubic inches and divide by 231. Choosing feet or inches here converts automatically.
What is the surface area of a cylinder?+
Total surface area = 2πr² + 2πrh: two circular ends plus the curved side. For an open-top container use πr² + 2πrh, and for a pipe use only 2πrh.
How do I find the height of a cylinder from its volume?+
Divide the volume by the base area: h = V ÷ (πr²). Choose “Volume and radius” in the calculator and it does this for you.
Should I use the inside or outside diameter?+
Use the inside diameter for how much a tank or pipe holds, and the outside diameter for painting, wrapping or insulating the outer surface.