Geometry

Volume Calculator

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

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 Normalized 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

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.

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

Units and Measurement Conversions

Base Unit	Cubic Meters (m³)	Liters (L)	Cubic Feet (ft³)	US Gallons (gal)
1 Cubic Meter (m³)	1.0000	1,000.00	35.3147	264.172
1 Liter (L)	0.0010	1.0000	0.03531	0.26417
1 Cubic Foot (ft³)	0.02832	28.3168	1.0000	7.48052
1 US Gallon (gal)	0.003785	3.78541	0.13368	1.0000

Practical Notes & Guidelines

Common Volume Calculations: Different applications require specific geometric models. For shipping boxes and freight containers, use the CBM Calculator; for industrial cylinders and barrels, use the Cylinder Volume Calculator; and for storage tanks, use the Tank Volume Calculator.

Frequently Asked Questions

What is volume?▼

Volume is the quantity of three-dimensional space occupied by a liquid, solid, or gas, measured in cubic units (m³, ft³, in³) or capacity units (liters, gallons).

How do you calculate volume?▼

Identify the solid shape, measure necessary dimensions (e.g. length, width, radius, height) in the same unit, and apply the geometric volume formula for that shape.

What is the difference between volume and capacity?▼

Volume refers to the physical 3D space occupied or enclosed (e.g., m³ or cubic feet). Capacity refers to the maximum volume of liquid or bulk material a container can hold (e.g., 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).

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