Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate a cylinder's volume and surface area from its radius and height.
This tool calculates both the volume and total surface area of a right circular cylinder from its radius and height.
Enter the radius and height. Volume and surface area appear instantly.
Volume = πr²h
Surface Area = 2πr(r + h) (two circular ends plus the curved side)
The page gives the total surface area formula in its compact form. It helps to see the three pieces it is built from, especially if you only need part of the surface.
The page shows the volume for radius 2 and height 5. Here is the surface area for the same numbers, step by step.
Lateral area = 2 × π × 2 × 5 = 20π ≈ 62.83
Two ends = 2 × π × 2² = 8π ≈ 25.13
Total = 28π ≈ 87.96
Notice that the lateral area happens to equal the volume here. That is a coincidence of the chosen numbers, not a general rule. It is a useful reminder that volume and area use different units even when the digits look alike.
Suppose a cylindrical rain barrel has a radius of 0.5 meters and a height of 2 meters. These are hypothetical dimensions.
Volume = π × 0.5² × 2 = 0.5π ≈ 1.5708 cubic meters
At 1,000 liters per cubic meter, the barrel holds about 1,571 liters when filled to the brim. If it is only filled to 1.5 meters, use height 1.5 in the calculator to get the volume of the water itself. This is a handy way to estimate a partially filled upright cylinder.
The output is a geometric estimate. Real containers have wall thickness, rounded edges, and lids, so leave margin when ordering paint, wrap, or liquid-handling equipment.
Both circular end caps plus the curved lateral surface -- the full outer surface of the cylinder.
Enter the same radius and use the depth of the liquid as the height. The result is the volume of liquid, assuming the cylinder stands upright with a flat bottom.
Subtract one circular end, π × r², from the total surface area shown. If both ends are open, subtract two, which leaves only the lateral area 2πrh.
Enter the radius. If you know the diameter, divide it by 2 first.
Volume is π × r² × h, so it depends on the radius squared. Doubling r multiplies the volume by 2 squared, which is 4, as long as the height stays the same.
Reference: NIST Weights and Measures