Cylinder Calculator

Calculate the volume and surface area of any cylinder from radius and height.

What is a Cylinder?

A cylinder is a three-dimensional geometric solid with two parallel, circular bases connected by a curved lateral surface. The line connecting the centers of the two circular bases is called the axis of the cylinder. When the axis is perpendicular to the bases, the shape is a right circular cylinder - the most common type and the one this calculator handles.

To fully describe a right circular cylinder, you need just two measurements: the radius (r) of the circular base and the height (h) - the perpendicular distance between the two bases. From these two values, the volume, lateral surface area, and total surface area can all be calculated.

The volume of a cylinder measures how much three-dimensional space it encloses - practically, how much liquid or material it can contain. The formula V = πr²h is intuitive: it is simply the area of the circular base (πr²) multiplied by the height - as if you were stacking thin circular slices of height h.

The lateral surface area (LSA) is the area of the curved side wall only, excluding the two circular ends. If you were to cut the cylinder along its length and unroll the side, it would form a rectangle with width equal to the circumference of the base (2πr) and height h. Therefore LSA = 2πrh.

The total surface area (TSA) adds the two circular end caps to the lateral area: TSA = 2πrh + 2πr² = 2πr(r + h). This is the total area of material needed to enclose the cylinder completely.

Cylinders are ubiquitous in engineering and manufacturing: pipes and tubes carry fluids and gases; engine cylinders convert combustion energy to mechanical work; cans and containers use the cylindrical form for structural efficiency; columns and pillars in architecture often take a cylindrical shape. The cylinder optimises the ratio of volume to lateral surface area among shapes with circular cross-sections, making it efficient for storage.

Formula

Volume of a Cylinder:

V = π × r² × h

r = Base radius

h = Height

V = Volume (cubic units)

Lateral (Curved) Surface Area:

LSA = 2 × π × r × h

The curved side wall only - equivalent to unrolling into a rectangle of width 2πr and height h

Total Surface Area:

TSA = 2 × π × r × (r + h)

= Lateral area + 2 circular end caps = 2πrh + 2πr²

How to Use This Calculator

Enter the radius of the circular base in the first field.
Enter the height (the length) of the cylinder in the second field.
Click Calculate to get volume, lateral surface area, and total surface area.
Interpret results - volume is in cubic units (use for capacity), lateral area is in square units (use for painting or wrapping the side only), total area is in square units (use for manufacturing the complete enclosed shape).
Unit flexibility - use any unit (cm, m, mm, inches) as long as both inputs use the same unit.

Example Calculations

Example 1 - Tin Can

A cylindrical tin can has a radius of 3.5 cm and a height of 12 cm.

r = 3.5 cm, h = 12 cm

Volume = π × 3.5² × 12 = π × 12.25 × 12 = 461.81 cm³ ≈ 461.81 mL

Lateral Surface Area = 2 × π × 3.5 × 12 = 263.89 cm² (label area)

Total Surface Area = 2 × π × 3.5 × (3.5 + 12) = 2 × π × 3.5 × 15.5 = 340.88 cm²

Volume = 461.81 cm³ | Lateral SA = 263.89 cm² | Total SA = 340.88 cm²

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Example 2 - Water Tank Pipe

A water pipe has a radius of 0.25 m and a length (height) of 50 m.

r = 0.25 m, h = 50 m

Volume = π × 0.0625 × 50 = 9.817 m³ = 9,817 litres of water capacity

Lateral Surface Area = 2 × π × 0.25 × 50 = 78.54 m² (outer pipe surface)

Total Surface Area = 2 × π × 0.25 × (0.25 + 50) = 79.28 m²

Volume = 9.8175 m³ | Lateral SA = 78.5398 m² | Total SA = 79.1522 m²

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Frequently Asked Questions

What is the formula for the volume of a cylinder?+

Volume = π × r² × h, where r is the base radius and h is the height. For a cylinder with radius 4 cm and height 10 cm: V = π × 16 × 10 = 502.65 cm³. Volume is in cubic units.

What is the difference between lateral surface area and total surface area?+

Lateral (curved) surface area covers only the side wall: LSA = 2 × π × r × h. Total surface area includes the two circular end caps: TSA = 2 × π × r × (r + h) = LSA + 2 × π × r². For a cylinder with r = 4 cm and h = 10 cm: LSA = 251.33 cm², TSA = 351.86 cm².

How do I find the radius of a cylinder if I know the volume and height?+

Rearrange the volume formula: r = √(V / (π × h)). For V = 500 cm³ and h = 10 cm: r = √(500 / (π × 10)) = √(15.915) = 3.99 cm ≈ 4 cm.

What are everyday examples of cylinders?+

Cans, pipes, tubes, batteries, columns, rollers, engine cylinders, and drinking glasses are all approximately cylindrical. The cylinder is one of the most common shapes in manufacturing because it is easy to produce by rotating a rectangle around an axis.

Is a cylinder a prism?+

A cylinder is considered a circular prism - a prism with a circular cross-section rather than a polygonal one. Like all prisms, its volume is base area × height. As the number of sides of a regular polygon prism increases toward infinity, the prism approaches a cylinder.

How do you calculate the volume of a cylinder?+

Volume of a cylinder = pi x r^2 x h, where r is the radius of the circular base and h is the height. Example: a cylinder with radius 4 cm and height 10 cm has volume = 3.14159 x 16 x 10 = 502.65 cm^3. If you are given the diameter instead of radius, divide by 2 first. Volume is in cubic units.

How is the surface area of a cylinder calculated?+

Total surface area of a cylinder = 2 x pi x r x h + 2 x pi x r^2. The first term (2 x pi x r x h) is the lateral (curved side) surface area. The second term (2 x pi x r^2) is the area of both circular bases (top and bottom). Example: cylinder with radius 3 cm and height 8 cm: lateral = 2 x 3.14159 x 3 x 8 = 150.8 cm^2. Bases = 2 x 3.14159 x 9 = 56.55 cm^2. Total = 207.3 cm^2.

How does a cylinder relate to a cone and sphere?+

Three important volume relationships: a cone with the same base and height as a cylinder has exactly 1/3 the volume. A sphere inscribed in a cylinder (touching the top, bottom, and sides) has exactly 2/3 the volume of the cylinder. These relationships were discovered by Archimedes and inscribed on his tombstone. For a cylinder with r and h = 2r: sphere volume = (4/3) x pi x r^3 = (2/3) x cylinder volume = (2/3) x pi x r^2 x 2r.

🔗 Related Calculators

📌 Quick Tips

💡The volume of a cylinder is simply the area of the circular base multiplied by the height: V = π × r² × h. Think of it as stacking many thin circular discs.

💡The lateral surface area is the area of the curved side wall only - imagine cutting the cylinder vertically and unrolling it into a rectangle of width 2πr and height h.

💡Doubling the radius increases the volume by a factor of 4 (because of r²), while doubling the height only doubles the volume. Radius has a stronger effect than height on capacity.