Cylinder Calculator
Calculate a cylinder's volume, total surface area, or lateral surface area from its radius and height. Perfect for working out tank capacities, pipe dimensions, and material requirements.
About this calculator
A cylinder is a 3D solid with two parallel circular bases connected by a curved lateral surface. Its volume is V = πr²h, where r is the base radius and h is the height — essentially the base area times the height. The lateral (side) surface area is LA = 2πrh, representing the curved wall unrolled into a rectangle. The total surface area depends on how many bases are included: with both bases it is SA = 2πrh + 2πr²; with one base, SA = 2πrh + πr²; and with no bases (open tube), SA = 2πrh. Choosing the right formula matters for tasks like calculating paint for a tank wall versus material for a sealed can.
How to use
Imagine a cylindrical water tank with radius 3 m and height 5 m. To find the volume, the formula gives V = π × 3² × 5 = π × 9 × 5 = 45π ≈ 141.37 m³. For the total surface area with both bases closed: SA = 2π × 3 × 5 + 2π × 3² = 30π + 18π = 48π ≈ 150.80 m². If the tank is open at the top (one base), subtract one circle: SA = 30π + 9π = 39π ≈ 122.52 m². Enter radius = 3 and height = 5 and select your preferred calculation type.
Frequently asked questions
How do I calculate the volume of a cylinder to find how much liquid it can hold?
Use the formula V = πr²h, where r is the inner radius and h is the height of the liquid column. For a tank with r = 0.5 m and h = 2 m, V = π × 0.25 × 2 ≈ 1.571 m³, which equals roughly 1,571 litres (since 1 m³ = 1,000 L). Make sure you use the inner radius, not the outer radius, to get the actual capacity. This calculator computes the result instantly once you enter the two dimensions.
What is the difference between lateral surface area and total surface area of a cylinder?
Lateral surface area covers only the curved side wall: LA = 2πrh. Total surface area adds one or both flat circular bases: full SA = 2πrh + 2πr². The distinction matters practically — if you are wrapping a label around a tin can, you need the lateral area; if you are manufacturing the entire sealed can, you need the total area. An open-topped container (like a cup) needs SA = 2πrh + πr², adding just the bottom circle.
When should I use diameter instead of radius when calculating cylinder dimensions?
Engineering drawings and physical measurements often give diameter because it is easier to measure across an object than to find its centre point. Simply divide the diameter by 2 to get the radius before entering it into the formula V = πr²h. For example, a pipe with a 6 cm diameter has r = 3 cm, giving a cross-sectional area of π × 9 ≈ 28.27 cm². Always check which measurement you have before calculating to avoid quadrupling your area or volume result by accident.