Geometry

Volume Calculator

Calculate the volume of any 3D shape including cylinders, pipes, boxes, cubes, spheres, and cones with instant unit conversions.

Instant results

Real-time calculation

Accurate & reliable

Standard SI formulas

Free to use

No sign up required

Technical Dimension Schematic100% Vector

Select 3D Geometric Solid

Dimension Input Mode

Radius (r)

Height (h)

Output Volume Unit

3D Geometric Solid PreviewOpen Dedicated Cylinder Calculator

Universal Shape Volume Results

Decimals:

Volume in M3Live Output

6.2832m3

Equivalent Standard Volume Units

Liters (L)

6,283.1853 l

Cubic Centimeters (cm³)

6,283,185.3072 cm3

Cubic Feet (ft³ / cu ft)

221.8886 ft3

Cubic Inches (in³)

383,423.4923 in3

Cubic Yards (yd³)

8.2181 yd3

US Liquid Gallons (gal)

1,659.842 us_gal

Imperial Gallons (UK gal)

1,382.1075 imp_gal

Mathematical Formula & Step-by-Step Derivation

SI Standard Math

General Formula:

V = π × r² × h

Live Calculation With Your Input Values:

11. Calculate Radius

Formula: r = radius

Substituted: r = 1 m

Step Result: Radius = 1 m

22. Cylinder Volume Formula

Formula: V = π × r² × h

Substituted: V = π × (1 m)² × (2 m)

Step Result: V = 6.2832 m3

Normalized to SI units: V = π × (1 m)² × (2 m) = 6.2832 m³

33. Total Surface Area

Formula: A = 2πrh + 2πr²

Substituted: A = (2 × π × 1 × 2) + (2 × π × 1²)

Step Result: A = 18.8496 m²

3D Volume Formulas Reference Table

Shape	Volume Formula	Parameters
Cube	V = a³	a = side length
Rectangular Box	V = l × w × h	l=length, w=width, h=height
Cylinder	V = π × r² × h	r=radius, h=height
Sphere	V = ⁴⁄₃ × π × r³	r=radius
Cone	V = ⅓ × π × r² × h	r=radius, h=height

Worked Example: Inscribed 3D Solids Comparison (2m Cube Boundary)

Comparing different 3D shapes fitted inside an identical 2.0 m × 2.0 m × 2.0 m bounding cube (radius r = 1.0 m):

• Cube (Side a = 2 m): V = 2³ = 8.0000 m³ (8,000 Liters / 2,113.38 US gal)

• Cylinder (r = 1 m, h = 2 m): V = π × 1² × 2 = 6.2832 m³ (6,283.19 Liters / 1,659.88 US gal) — 78.54% fill

• Sphere (r = 1 m): V = ⁴⁄₃ × π × 1³ = 4.1888 m³ (4,188.79 Liters / 1,106.53 US gal) — 52.36% fill

• Cone (r = 1 m, h = 2 m): V = ⅓ × π × 1² × 2 = 2.0944 m³ (2,094.40 Liters / 553.29 US gal) — 26.18% fill

Common Use Cases

Specialized Volume Calculators: While this general volume calculator computes regular 3D solids, specific industries and applications use specialized tools:

For shipping boxes, cargo freight, and pallet loading, use the CBM Calculator or the Cubic Meter Calculator (m³).
For circular columns, drums, and barrels, use our dedicated Cylinder Volume Calculator.
For plumbing, water mains, and tubing holding capacity, use the Pipe Volume Calculator.
For vertical and horizontal liquid storage vessels, use the Tank Volume Calculator.

How to Calculate Volume of 3D Geometric Shapes

Volume measures the three-dimensional space enclosed by a boundary or occupied by an object. Calculating volume depends on the geometric solid:

1. Prisms & Cubes

Multiply base area by vertical height: Cube (V = a³), Rectangular Box (V = l × w × h).

2. Cylinders

Multiply the circular base area by height: V = π × r² × h.

3. Spheres

Two-thirds of circumscribing cylinder: V = ⁴⁄₃ × π × r³.

4. Cones

One-third of corresponding cylinder: V = ⅓ × π × r² × h.

Frequently Asked Questions

What is a volume calculator?

A volume calculator is an online mathematical tool that determines the total three-dimensional capacity and space occupied by geometric shapes (such as cylinders, cubes, spheres, and prisms) or containers, providing instant results across cubic units, litres, and gallons.

How do you calculate volume for different 3D shapes?

To calculate volume, measure the solid's primary dimensions in uniform units and apply its specific formula: V = a³ for cubes, V = l × w × h for rectangular boxes, V = πr²h for cylinders, V = ⁴⁄₃πr³ for spheres, and V = ⅓πr²h for cones.

How do I calculate cylinder or pipe volume?

To calculate the volume of a cylinder or pipe, multiply the circular cross-sectional base area by its length or height (V = π × r² × h). For pipes, always use the inside diameter (ID) to find the internal fluid capacity.

How do I calculate volume for shipping freight in cubic meters (CBM)?

To calculate shipping volume in CBM (cubic meters), multiply length × width × height in meters, then multiply by the total carton quantity. If dimensions are in centimeters, multiply them together and divide by 1,000,000.

What is the difference between volume and capacity?

Volume refers to the physical 3D space occupied or enclosed (measured in cubic meters, cubic feet, or cubic inches). Capacity refers to the maximum volume of liquid or bulk fluid a container can hold (measured in liters or gallons).

How do I convert cubic meters to liters and gallons?

1 cubic meter (m³) contains exactly 1,000 Litres or approximately 264.172 US liquid gallons (219.969 Imperial gallons). To convert m³ to litres, multiply by 1,000.

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