Volume Calculator: Cube, Cylinder, Cone, Sphere

Volume Calculator

Solid Length unit

Radius (r)

Height (h)

Volume:

Isometric reference drawing: proportions are approximate.

Volume in liters:

Calculation:

With this volume calculator you pick a solid (cylinder, cone, sphere, hemisphere, cube, rectangular prism, square pyramid or triangular prism), enter its dimensions and get the volume right away. The solid is drawn with its dimensions labeled and, if you choose a unit, the result also appears in liters.

Below you will find the formulas, worked examples, a liters conversion table and the most common questions.

How to use the volume calculator

Step 1: Pick the Solid from the list. The input boxes and the drawing change with your choice.

Step 2: Pick the length unit (mm, cm, m, in, ft or yd) to see the volume in liters too. If you pick none, the volume comes out in cubic units.

Step 3: Enter the dimensions. A decimal point or comma both work, for example 2.5 or 2,5.

Step 4: Click Calculate or press Enter. You get the volume, the drawing with your dimensions and, in the Calculation box, every step.

Volume formulas for solids

Volume measures how much space a solid takes up and is given in cubic units (cm³, m³, ft³). For prisms and cylinders you multiply the area of the base by the height; for cones and pyramids, one third of that:

Solid	Formula
Cube	V = a³
Rectangular prism	V = a × b × c
Cylinder	V = π × r² × h
Cone	V = (1/3) × π × r² × h
Sphere	V = (4/3) × π × r³
Hemisphere	V = (2/3) × π × r³
Square pyramid	V = (1/3) × a² × h
Triangular prism	V = (1/2) × b × h × L

In the triangular prism, b is the base of the triangle, h its height and L the length of the prism. In the pyramid, a is the side of the square base and h is the perpendicular height, not the slanted edge.

Volume examples

Example 1: A fish tank (rectangular prism)

A tank is 60 cm long, 30 cm wide and 40 cm tall. The volume of the prism is length times width times height:

V = a × b × c = 60 × 30 × 40 = 72000 cm³

Since 1 liter is 1000 cm³, the tank holds 72 liters when filled to the brim.

Example 2: A cylindrical tank

A cylinder has radius 3 cm and height 5 cm. We multiply the area of the base by the height:

V = π × r² × h = π × 3² × 5 = π × 9 × 5 ≈ 141.37 cm³

The volume is 141.37 cm³, or 0.1414 liters.

Example 3: A cone

An ice cream cone has radius 4 cm and height 9 cm. Its volume is one third of a cylinder with the same base and height:

V = (1/3) × π × r² × h = (1/3) × π × 4² × 9 = (1/3) × π × 16 × 9 ≈ 150.8 cm³

It holds 150.8 cm³, which is 0.1508 liters.

Example 4: A sphere

A ball has radius 6 cm:

V = (4/3) × π × r³ = (4/3) × π × 6³ = (4/3) × π × 216 ≈ 904.78 cm³

The ball takes up 904.78 cm³. A hemisphere with the same radius takes up half of that: 452.39 cm³.

Converting volume to liters

One liter is one cubic decimeter (1 dm³ = 1000 cm³). These conversions are exact, because 1 in = 2.54 cm and 1 ft = 0.3048 m are exact:

Volume	Liters
1 mm³	0.000001 L
1 cm³	0.001 L
1 in³	0.016387064 L
1 m³	1000 L
1 ft³	28.316846592 L
1 yd³	764.554857984 L

Frequently asked questions

How do you find the volume of a cylinder?

Multiply the area of the base (π × r²) by the height. With radius 3 and height 5, V = π × 9 × 5 ≈ 141.37.

Why is the volume of a cone one third of a cylinder?

Because a cone takes up exactly one third of a cylinder with the same base and height. With radius 3 and height 4, the cylinder is 113.1 and the cone is 37.7.

How do I convert cm³ to liters?

Divide by 1000: 1000 cm³ is 1 liter. And 1 m³ is 1000 liters. The calculator does it for you when you pick a unit.

What is the difference between a sphere and a hemisphere?

A hemisphere is half a sphere, so its volume is half: (2/3)πr³ versus (4/3)πr³.

What units does the volume come in?

The length unit cubed: if you measure in cm, the volume comes out in cm³. Mixing units (cm with m) gives wrong results, so convert every measurement to the same unit before calculating.

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