What is the formula for the volume of a cylinder?

Volume equals pi times the radius squared times the height: V = pi x r^2 x h. Using full-precision pi (~3.14159265) gives a more accurate result than the approximation 3.14.

How do I find the radius if I only know the volume and height?

Rearrange V = pi x r^2 x h to get r = sqrt(V divided by (pi x h)). Choose "Volume + Height" mode and enter those two values; the calculator solves for radius automatically.

How do I find the height if I only know the volume and radius?

Rearrange V = pi x r^2 x h to get h = V divided by (pi x r^2). Choose "Volume + Radius" mode; the calculator returns the height.

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

Lateral surface area is the curved side wall only: 2 x pi x r x h. Total surface area adds both circular end caps (each pi x r^2), giving 2 x pi x r x (r + h). For an open-top tank you only need the lateral area plus one base.

Can I use this for a cylindrical tank or pipe?

Yes. A cylindrical tank is exactly a right circular cylinder. Enter the internal radius and length (height) to get the capacity in your chosen cubic unit. To convert cubic centimetres to litres, divide by 1000.

Does it matter which units I use?

All inputs must use the same unit. If you enter radius in centimetres, height must also be in centimetres; the volume will then be in cubic centimetres (cm^3) and surface areas in square centimetres (cm^2). Convert first if your measurements are in different units.

Cylinder Volume Calculator

A right circular cylinder appears everywhere in engineering, construction, and everyday life — storage tanks, pipes, cans, pillars, and rollers are all cylinders. To size a tank, estimate paint coverage on a pipe, or check how much concrete a column needs you must be able to go from the dimensions you have to the ones you need. This calculator handles all four common scenarios: enter radius and height to get volume and area; enter diameter and height when that is what you measure; enter volume and height to find the required radius; or enter volume and radius to find the required height.

How it works

A right circular cylinder has two congruent circular bases connected by a curved side wall. Three formulas cover everything:

Quantity	Formula
Volume	V = pi x r^2 x h
Lateral (side) area	A_L = 2 x pi x r x h
Total surface area	A_T = 2 x pi x r x (r + h)

where r is the radius of the base and h is the perpendicular height. The total surface area is the lateral area plus the two circular end caps, each of area pi x r^2, so:

A_T = 2 x pi x r x h + 2 x pi x r^2 = 2 x pi x r x (r + h)

When you need to solve for a dimension the same formulas rearrange cleanly:

Solving for radius from volume and height: r = sqrt(V divided by (pi x h))
Solving for height from volume and radius: h = V divided by (pi x r^2)

The tool uses JavaScript’s built-in Math.PI (~3.141592653589793) rather than any rounded approximation, so results are accurate to at least 12 significant figures.

Worked example

Suppose you have a storage drum with an internal diameter of 60 cm and a height of 90 cm and you want to know its volume in litres.

Diameter = 60 cm, so radius r = 30 cm.
V = pi x 30^2 x 90 = pi x 900 x 90 = 81 000 x pi ≈ 254 469 cm^3.
254 469 cm^3 ÷ 1 000 = ~254.5 litres.

The lateral area (how much sheet metal forms the curved wall):

A_L = 2 x pi x 30 x 90 = 5 400 x pi ≈ 16 965 cm^2 (~1.70 m^2)

Total surface area (both end caps included):

A_T = 2 x pi x 30 x (30 + 90) = 2 x pi x 30 x 120 = 7 200 x pi ≈ 22 619 cm^2 (~2.26 m^2)

Now suppose you know the drum must hold 300 litres (300 000 cm^3) and the height is fixed at 90 cm — what radius is needed?

r = sqrt(300 000 divided by (pi x 90)) ≈ sqrt(1 061.03) ≈ 32.57 cm (diameter ~65.1 cm)

Select “Volume + Height” mode, enter 300 000 in the volume field and 90 in the height field to confirm instantly.

Formula note

The volume formula V = pi x r^2 x h can be derived by imagining the cylinder as a stack of infinitely thin circular discs, each of area pi x r^2 and thickness dh. Integrating over the full height h gives pi x r^2 x h. The result is exact for a perfect right circular cylinder (flat, parallel, congruent bases perpendicular to the axis). For a hollow cylinder (pipe) you subtract the inner-bore volume: V = pi x (R^2 - r_inner^2) x h, where R is the outer radius and r_inner is the inner radius — a quick calculation you can do with two runs of this tool.