Cylinder Calculator
Enter radius and height to calculate volume, total surface area, and lateral surface area.
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Cylinder Formulas Explained
A cylinder is a 3D shape with two parallel circular bases connected by a curved lateral surface. Cylinder calculations appear in engineering, manufacturing, architecture, and everyday problem-solving.
Volume
The volume of a cylinder equals the area of its circular base multiplied by its height: V = πr²h. If you know the diameter instead of the radius, use r = d/2. For example, a pipe with radius 0.05 m and length 2 m carries πr²h = π×0.0025×2 ≈ 0.0157 m³ of water.
Total Surface Area
Total SA = 2πr² + 2πrh. The first term (2πr²) is the combined area of both circular caps. The second term (2πrh) is the lateral (side) surface. Think of unrolling the side into a rectangle: its width is the circumference 2πr, and its height is h.
Lateral Surface Area
Lateral SA = 2πrh. This is the curved side only, used when calculating material for a tube, pipe label, or can wrapper. For a can with r=3.5 cm and h=12 cm: LSA = 2π×3.5×12 ≈ 263.9 cm².
Diagonal of a Cylinder
The longest diagonal inside a cylinder (from one rim point to the opposite rim point) is d = √((2r)² + h²) by the Pythagorean theorem applied to the rectangle formed by the diameter and height.
Worked Example: Water Tank Capacity
A cylindrical water tank has a radius of 1.5 m and a height of 4 m. Find its volume and total surface area.
Volume: V = πr²h = π × 1.5² × 4 = π × 2.25 × 4 = 9π ≈ 28.27 m³. Since 1 m³ = 1000 litres, the tank holds approximately 28,274 litres of water.
Total Surface Area: TSA = 2πr² + 2πrh = 2π(1.5²) + 2π(1.5)(4) = 2π(2.25) + 2π(6) = 4.5π + 12π = 16.5π ≈ 51.84 m².
Frequently Asked Questions
V = πr²h = π×3²×10 = 90π ≈ 282.74 cubic units.
Total SA = 2πr² + 2πrh. This includes both circular bases (2πr²) and the lateral curved surface (2πrh).
Lateral surface area is just the curved side, excluding the top and bottom caps: LSA = 2πrh.
Diameter = 2 × radius. For a cylinder with r=5, the diameter is 10.
Cans, pipes, water tanks, engine cylinders, columns, tree trunks (approximately), and candles are all cylinders or close approximations.
Doubling the radius quadruples the volume, since V = πr²h and r is squared. For example, a cylinder with r=2, h=5 has V = π×4×5 ≈ 62.83. Double the radius to r=4: V = π×16×5 ≈ 251.33 — exactly four times as large.
If you calculate volume in cubic metres, multiply by 1000 to get litres. If you use cubic feet, multiply by 7.481 to get US gallons. For cubic centimetres, divide by 1000 to get litres (since 1 litre = 1000 cm³).