$Cylinder$

Cylinder

Find the volume, base area, lateral and total surface area of a cylinder from the radius or diameter and height. Exact answer in terms of π.

What is known:

Radius and height

Diameter and height

Radius and volume

Radius and lateral surface area

Base radius r

Height h

Units:

Lengths are positive numbers (whole or decimal), angles are in degrees.

Test yourself

The cylinder calculator finds the volume, base area, lateral and total surface area and the diagonal of the axial section from the radius or diameter and the height, and also the height from the volume or the lateral area. The answer is shown exactly — in terms of π — and approximately.

Cylinder formulas

Value	Formula
Volume	V = πr²h
Base area	S_base = πr²
Lateral surface area	S_lat = 2πrh
Total surface area	S = 2πr(r + h)
Height from volume	h = V / (πr²)
Diagonal of the axial section	d = √(4r² + h²)

Example. r = 3 cm, h = 5 cm.
V = π · 9 · 5 = 45π ≈ 141.37 cm³
S_lat = 2π · 3 · 5 = 30π ≈ 94.25 cm², S = 2π · 3 · 8 = 48π ≈ 150.8 cm².

The lateral surface of a cylinder is a rectangle rolled into a tube: one side equals the height h, the other equals the circumference of the base 2πr. Hence S_lat = 2πrh.

Volume in liters: if the dimensions are in decimeters, the volume comes out in dm³, which is liters — this is how the volume of a barrel or a tank is found.