Cube
Compute cube volume, surface area, space diagonal, and face diagonal from side length. Free online 3D geometry calculator with formulas and instant results.
About This Calculator
The Cube Calculator computes four essential properties of a cube from a single input -- the side length a. A cube is a three-dimensional solid with six equal square faces, twelve equal edges, and eight vertices. All edges have the same length, making it one of the simplest 3D shapes to analyze.
The calculator returns the Volume (V = a^3), Surface Area (SA = 6a^2), Space Diagonal (d = asqrt3 -- the longest diagonal through the interior), and Face Diagonal (f = asqrt2 -- the diagonal across one face). Simply enter the side length in any unit and all four results update automatically.
This tool is essential for students studying 3D geometry, teachers preparing lesson materials, architects calculating material quantities, construction professionals estimating paint or concrete volumes, logistics workers determining shipping dimensions, and anyone needing quick cube measurements.
For related calculators, try the Cube Volume Calculator for volume-only results, the Cube Surface Area Calculator for surface area only, or the Cuboid Calculator for rectangular prisms with three different dimensions.
Frequently Asked Questions
What formulas does the Cube calculator use?
The calculator uses four standard cube formulas: Volume V = a^3, Surface Area SA = 6a^2, Space Diagonal d = asqrt3 (through the interior), and Face Diagonal f = asqrt2 (across a face). All results derive from the side length a.
What is the difference between face diagonal and space diagonal?
The face diagonal runs across one square face of the cube (f = asqrt2), while the space diagonal runs through the interior from one corner to the opposite corner (d = asqrt3). The space diagonal is always longer than any face diagonal.
How is cube volume different from surface area?
Volume measures the three-dimensional space inside the cube in cubic units (V = a^3). Surface area measures the total area covering all six faces in square units (SA = 6a^2). For a cube with side 4, volume is 64 cubic units and surface area is 96 square units.
What units should I use for the side length?
Use any consistent linear unit (meters, centimeters, inches, feet). Volume is in cubic units, surface area in square units, and diagonals in the same linear unit as the side length.
Can I calculate these from the volume instead?
Yes, if you know the volume V, the side length is a = V^(1/3). You can then plug that into the surface area and diagonal formulas. For a cube with volume 125, the side is 5, surface area is 150, and space diagonal is 8.66.
Is this cube calculator free to use?
Yes, all calculators on Calculy are completely free to use. There are no registration requirements or usage limits.
What are real-world applications of these cube measurements?
Cube volume is used for storage capacity and shipping, surface area for painting and material coverage, and diagonals for determining fit through doorways or packaging dimensions. Architects, engineers, and students use these formulas daily.