Cylinder Calculator
Find a cylinder's volume, lateral surface area, and total surface area from its base radius and height. Perfect for engineering design, tank capacity calculations, and everyday geometry problems.
About this calculator
A right circular cylinder has two identical circular bases connected by a curved lateral surface. Its volume is V = π × r² × h, where r is the base radius and h is the height — essentially the base area multiplied by the height. The lateral (curved) surface area is A_lateral = 2 × π × r × h, which equals the circumference of the base times the height. The total surface area adds both circular caps: A_total = 2 × π × r × h + 2 × π × r² = 2πr(h + r). These formulas underpin calculations for pipes, tanks, cans, columns, and countless other cylindrical structures encountered in engineering and everyday life.
How to use
Consider a cylinder with radius r = 3 m and height h = 10 m. Volume: V = π × 3² × 10 = π × 90 ≈ 282.74 m³. Lateral surface area: 2 × π × 3 × 10 = 60π ≈ 188.50 m². Area of each circular base: π × 3² = 9π ≈ 28.27 m². Total surface area: 188.50 + 2 × 28.27 ≈ 245.04 m². This is handy for estimating, say, how much steel sheet is needed to fabricate a cylindrical tank. Enter r = 3 and h = 10 to reproduce these results.
Frequently asked questions
How do you calculate the volume of a cylinder using radius and height?
The formula is V = π × r² × h, where r is the base radius and h is the height. You first compute the area of the circular base (π × r²), then multiply by the height to get the total volume. For a cylinder with r = 5 cm and h = 20 cm, V = π × 25 × 20 ≈ 1570.80 cm³. This formula applies to any right circular cylinder regardless of size.
What is the difference between lateral surface area and total surface area of a cylinder?
Lateral surface area covers only the curved side of the cylinder: A_lateral = 2 × π × r × h. Think of it as unrolling the tube into a flat rectangle of width 2πr and height h. Total surface area includes both circular end caps: A_total = 2πrh + 2πr². You'd use lateral area when calculating material for a tube with open ends, and total surface area when the ends are closed, such as for a sealed can or pressure vessel.
How does changing the radius versus the height affect a cylinder's volume?
Volume scales with the square of the radius but only linearly with height: V = π × r² × h. Doubling the height doubles the volume, but doubling the radius quadruples the volume. This means radius has a far greater impact on capacity than height does. For example, increasing a tank's radius from 2 m to 4 m with the same height multiplies its volume by 4×, while doubling the height only doubles it. This is why wide, squat tanks are much more space-efficient than tall, narrow ones.