Skip to main content
VolumeCalcKit
Geometry

Cube Volume Calculator

Calculate cube volume, surface area, face diagonal, and space diagonal from edge length with instant unit conversions.

Instant results
Real-time calculation
Accurate & reliable
Standard SI formulas
Free to use
No sign up required
a (side)aa
Technical Dimension Schematic100% Vector
Cube Geometrya (side)aa

V = a³ • A = 6a²

Cube Calculation Results
Decimals:
Volume in M3Live Output
8m3
Additional Computed Dimensions
Total Surface Area
24 m²
Face Diagonal
2.8284 m
Space Diagonal (Corner to Corner)
3.4641 m
Equivalent Standard Volume Units
Liters (L)
8,000 l
Cubic Centimeters (cm³)
8,000,000 cm3
Cubic Feet (ft³ / cu ft)
282.5173 ft3
Cubic Inches (in³)
488,189.9528 in3
Cubic Yards (yd³)
10.4636 yd3
US Liquid Gallons (gal)
2,113.3764 us_gal
Imperial Gallons (UK gal)
1,759.754 imp_gal

Mathematical Formula & Step-by-Step Derivation

SI Standard Math
General Formula:
V = a³ = a × a × a
Live Calculation With Your Input Values:
11. Cube Volume Formula
Formula: V = a³
Substituted: V = (2 m)³
Step Result: V = 8 m3

Normalized in SI: (2 m)³ = 8 m³

22. Total Surface Area
Formula: A = 6a²
Substituted: A = 6 × (2 m)²
Step Result: A = 24 m²
33. Space Diagonal
Formula: d = a√3
Substituted: d = 2 × √3
Step Result: d = 3.4641 m (3.4641 m)
Cube Geometric Formulas
Volume:V = a³
Total Surface Area:A = 6 × a²
Corner-to-Corner Space Diagonal:d_space = a × √3 ≈ 1.73205 × a
Worked Example: 2-Meter Side Cube

Calculating the volume, surface area, and diagonals for a cube with edge length a = 2.0 meters:

• Volume V = 2³ = 8.0000 m³ (8,000 Liters / 2,113.38 US gal)

• Total Surface Area = 6 × 2² = 24.0000 m²

• Face Diagonal = 2 × √2 ≈ 2.8284 meters

• Space Diagonal = 2 × √3 ≈ 3.4641 meters

Common Use Cases

Geometric Relationships: A cube is a special case of a rectangular prism where length = width = height. For boxes with unequal sides, use our Rectangular Prism Calculator; for spherical solids inscribed in a cube, see the Sphere Volume Calculator.

How to Calculate the Volume of a Cube

A cube is a regular three-dimensional geometric polyhedron bounded by six congruent square faces, twelve equal edges, and eight vertices. Because all edges have identical length (a), calculating cube volume is as simple as raising the edge length to the third power: V = a³.

  1. Measure any single edge length (a).
  2. Multiply the edge length by itself three times (a × a × a).
  3. To calculate total surface area, multiply the area of one face (a²) by 6: A = 6a².
  4. To calculate the 3D space diagonal connecting opposite corners, multiply side length by √3: d = a√3.

Frequently Asked Questions

How do you calculate the volume of a cube?
Multiply the edge length by itself twice: Volume = side³ (V = a × a × a).
How do you find the volume of a cube from surface area?
Divide total surface area by 6 to find the area of one face (a² = A / 6), take the square root to find side length (a), and cube the result (V = a³).
What is the difference between face diagonal and space diagonal?
A face diagonal connects opposite corners on one 2D square face (d = a√2). A space diagonal cuts through the 3D center of the cube connecting opposite corners in 3D space (d = a√3).
How many liters are in a 1-meter cube?
Exactly 1,000 liters. A cube measuring 1m × 1m × 1m equals exactly 1 cubic meter (1 m³), which holds 1,000 liters of fluid.
Custom Solutions

Need a branded Cube Volume calculator for your business?

Get a custom calculator with your branding, units, formulas, and custom workflows. Perfect for logistics, manufacturing, and ecommerce.

Tailored dimensions & conversion units
Seamless website or ERP embed
Request a Custom CalculatorContact Us

Related Volume & Capacity Calculators

All Calculators
geometry

Rectangular Prism Volume Calculator

Calculate the volume, surface area, and space diagonal of rectangular prisms, boxes, and cuboids.

Open calculator
geometry

Sphere Volume Calculator

Calculate sphere volume, surface area, and circumference from radius or diameter with full mathematical derivation.

Open calculator
geometry

Volume Calculator

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

Open calculator
conversion

Volume Converter

Convert instantly between liters, milliliters, cubic meters, cubic feet, cubic inches, US gallons, and imperial gallons.

Open calculator