Volume Calculator

Volume is the three-dimensional quantity representing the capacity of an enclosed space or container. This free Volume Calculator computes the cubic c

Mathematics

3D Solid Shape

Dimension 1 (Length / Radius)

Dimension 2 (Width / Height)

Dimension 3 (Height for Box)

Formula & Methodology

Rectangular Box: V = Length × Width × Height Cylinder: V = π × Radius² × Height Sphere: V = 4/3 × π × Radius³ Cone: V = 1/3 × π × Radius² × Height

To calculate the volume of a 3D object: 1. Measure the defining cross-sectional and vertical dimensions. 2. For uniform extrusions (boxes and cylinders), multiply the base area by height: Volume = Base Area × Height. 3. For tapering cones and pyramids, volume is exactly 1/3 of the base area times height. 4. For spheres, volume is 4/3 π r³.

3D Volume (BOX)

200

Overview

Volume is the three-dimensional quantity representing the capacity of an enclosed space or container. This free Volume Calculator computes the cubic capacity of boxes, cylinders, spheres, and cones, with instant conversions to fluid gallons and liters.

Volume calculations are essential in civil engineering (concrete pouring and gravel transport), shipping logistics (freight container packing), swimming pool water capacity planning, and chemical manufacturing.

Worked Examples

Example 1: Volume of a Shipping Container (20 × 8 × 8.5 ft)

Solid: Box, L = 20, W = 8, H = 8.5

Multiply dimensions: 20 × 8 × 8.5 = 1,360 cubic feet.

Final Answer: 1,360.00 cu ft

Example 2: Volume of a Water Tank Cylinder (Radius 4 ft, Height 10 ft)

Solid: Cylinder, Radius = 4, Height = 10

Base area: π × 4² = 50.2655 sq ft.
Multiply by height: 50.2655 × 10 = 502.65 cu ft.
Convert to gallons: 502.65 × 7.48 = 3,760 gallons.

Final Answer: 502.65 cu ft

Example 3: Volume of a Basketball (Radius 4.7 inches)

Solid: Sphere, Radius = 4.7

Apply formula: (4/3) × π × 4.7³ ≈ 434.89 cubic inches.

Final Answer: 434.89 cu in

Solid	Dimensions	Formula	Cubic Volume
Box	5 × 4 × 10	5 × 4 × 10	200.00
Cylinder	R = 3, H = 10	π × 9 × 10	282.74
Sphere	Radius = 5	(4/3)π(125)	523.60
Cone	R = 3, H = 10	(1/3)π × 9 × 10	94.25
Cube	Side = 6	6³	216.00

Solid

Dimensions

Formula

Cubic Volume

Box

5 × 4 × 10

200.00

Cylinder

R = 3, H = 10

π × 9 × 10

282.74

Sphere

Radius = 5

(4/3)π(125)

523.60

Cone

R = 3, H = 10

(1/3)π × 9 × 10

94.25

Cube

Side = 6

6³

216.00

Frequently Asked Questions

What units is volume expressed in?

Volume is expressed in cubic units such as cubic inches (in³), cubic feet (ft³), cubic meters (m³), or fluid units like liters and gallons.

How do you convert cubic feet to gallons?

One cubic foot holds approximately 7.48052 US liquid gallons. Multiply cubic feet by 7.48 to find gallons.

How do you convert cubic inches to gallons?

One US liquid gallon equals exactly 231 cubic inches. Divide cubic inches by 231 to obtain gallons.

How does volume scale when an object is enlarged?

Volume scales cubically by the factor cubed (k³). If you double all linear dimensions of an object, its volume increases eightfold (2³ = 8×).

What is the relationship between a cylinder and a cone of the same radius and height?

A cone holds exactly one-third (1/3) of the volume of a cylinder with identical radius and height.