MultiConvers

Volume Calculator

Ask how much space sits inside a cube, box, sphere, cylinder, cone or rectangular pyramid; every input is a length and the answer is that length cubed — litres of water, grain in a silo, air in a ball.

How to use

  1. Pick the solid that matches the hollow you are filling: a cube or rectangular box, a sphere, a standing cylinder, a cone, or a pyramid with a rectangular base.
  2. Convert every dimension to one length unit before you type. A centimetre radius with a metre height is not a legal pair on this form.
  3. Enter the lengths that solid needs — one side; l, w and h; a radius; radius and height; or base length, base width and height.
  4. Read unit³. That is capacity, not paint on the outside and not the flat area of a floor plan.

How it works

Volume is the amount of space a solid occupies. A storage cube of side 2 is 8 unit³. A crate is length × width × height. A sphere of radius 3 is ⁴⁄₃π(27) = 36π ≈ 113.097 unit³ of interior. A standing tank that is a cylinder is the circular base πr² times the height. Those numbers tell you how much water, grain, concrete or air fits inside, not how much coating the outside wants.

A cone with the same base radius and height as a cylinder holds one-third of that cylinder. A rectangular pyramid is one-third of the box with the same base and height: V = ⅓lwh. That Euclidean factor is easy to forget when you scale a hopper or an ice-cream cone from a cylindrical jar of the same footprint. Height on the cone and pyramid is the perpendicular from apex to base, not a slanted edge along the face.

This tool is not surface area. Paint, foil, plating and gift wrap are the skin of the solid (unit²) on the surface-area page. A cube of side 2 has volume 8 and surface area 24 — different dimensions, different jobs. It is also not the 2-D area calculator: a circular lid’s area πr² is only the base of a cylinder, not the cylinder’s contents.

Solids not listed — a triangular prism, a hemisphere, a frustum, an irregular hopper — are outside this form. You would split those into listed pieces or use another formula by hand. A “pyramid” here is rectangular-based, not a cone and not a regular tetrahedron.

π is Math.PI. Zero or negative edges are rejected because they do not enclose a positive interior. After you have unit³ you can convert to litres or gallons yourself (1,000 cm³ = 1 L); this page does not change the volume unit family for you.

Formula

Cube: V = s³
Box: V = lwh
Sphere: V = ⁴⁄₃πr³
Cylinder: V = πr²h
Cone: V = ⅓πr²h
Pyramid: V = ⅓lwh

Worked examples

  • A 2-unit cube

    cube, side 2 → 8 unit³

  • A sphere of radius 3

    sphere, r = 3 → 36π ≈ 113.097 unit³

Useful notes

  • π is the JavaScript constant Math.PI.
  • For the wrapping area of the same solid, use surface area.
  • Cone and pyramid height is the perpendicular from apex to base, not a face’s slant.
  • Pyramid mode is a rectangular base (⅓lwh), not a tetrahedron or a cone.
  • The result stays in unit³ of the length unit you picked; litre conversion is a separate step.

FAQ

How do I find the volume of a cylinder?

Multiply the base area πr² by the height. V = πr²h.

Why is a cone one-third of a cylinder?

A cone with the same base radius and height occupies one-third of that cylinder’s volume. That is the standard Euclidean result used here.

Can I mix cm and inches?

No. Pick one length unit for every measurement. The volume unit is then that unit cubed.

Does this tell me how much paint the outside needs?

No. Paint coverage is surface area (unit²). Volume is the interior. A cube of side 2 is 8 unit³ inside and 24 unit² of skin.

Is the pyramid the same as the cone?

Both use the one-third factor, but the cone has a circular base (⅓πr²h) and the pyramid has a rectangular base (⅓lwh). Pick the matching solid.

Related tools

See all Geometry tools.