Cube Calculator

Enter any one known cube measurement — edge length, volume, surface area, or space diagonal — and calculate all the others using V = a³ and SA = 6a².

Quick Facts

Core formulas
V = a³, SA = 6a², d = a√3
Every cube measurement derives from a single edge length a; enter any one known value to solve for the rest.
Face vs. space diagonal
Face diagonal = a√2 ≈ 1.4142a
Space diagonal (corner to opposite corner through the interior) = a√3 ≈ 1.7321a — always the longer of the two.

Your Results

Calculated
Edge length (a)
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Length of one side
Volume (V = a³)
-
Space enclosed by the cube
Surface area (SA = 6a²)
-
Total area of all 6 faces
Space diagonal (d = a√3)
-
Corner-to-opposite-corner distance

Ready

Choose what you know about the cube, enter its value, then press Calculate.

How the Cube Calculator works

A cube is a three-dimensional solid with six identical square faces, twelve equal edges, and eight vertices. Every measurement of a cube — its volume, surface area, and diagonals — can be derived from a single number: the length of one edge, usually written a. This calculator lets you enter whichever measurement you already know and solves for the edge length, then uses that edge length to compute everything else.

Formula and method

Given the edge length a, the standard cube formulas are:

  • Volume: V = a³
  • Surface area: SA = 6a² (six square faces, each with area a²)
  • Face diagonal: a√2 ≈ 1.4142 × a (the diagonal across one square face)
  • Space diagonal: a√3 ≈ 1.7321 × a (corner to opposite corner, through the cube's interior)

If you know the volume, surface area, or space diagonal instead of the edge length, the calculator solves that formula for a first — a = ∛V from volume, a = √(SA ÷ 6) from surface area, or a = d ÷ √3 from the space diagonal — then applies the formulas above to fill in the rest.

Common sources of error

  • Unit mismatch: the number you enter must match the unit selected — a volume of 125 with unit "cm" is treated as 125 cm³, not 125 in³.
  • Wrong "known" selection: if you enter a volume but leave the selector on "Edge length," the result describes a cube whose edge is that number, not whose volume is that number.
  • Rounding early: the calculator keeps full floating-point precision internally and only rounds the displayed result, so intermediate steps do not lose accuracy.

Checking your result

A quick sanity check: for an edge of 5, volume should be 5³ = 125, surface area 6 × 5² = 150, and the space diagonal about 8.66 (5 × 1.7321). If you double the edge length, volume grows eightfold (2³) and surface area grows fourfold (2²) — both increase faster than the edge itself, since they depend on higher powers of a.

Applications

Cube formulas come up in packaging and shipping (box volume and surface area for material estimates), construction and woodworking (cutting square stock, sizing cubic bins or tanks), physics and chemistry (unit cells, dice, cubic containers), and basic geometry education. Label your result with its unit and note which measurement you started from so the calculation can be reproduced.

Frequently Asked Questions

What is the formula for the volume of a cube?
The volume of a cube is V = a³, where a is the length of one edge. For example, a cube with a 5 cm edge has a volume of 5³ = 125 cubic centimeters.
What is the difference between a face diagonal and a space diagonal?
The face diagonal crosses one square face and equals a√2 (about 1.4142 × a). The space diagonal runs from one corner through the cube's interior to the opposite corner and equals a√3 (about 1.7321 × a) — always the longer of the two.
How do I find the edge length if I only know the volume or surface area?
Solve the formula for a. From volume, a = ∛V (the cube root of V). From surface area, a = √(SA ÷ 6). This calculator performs that step automatically when you choose "Volume" or "Surface area" as your known value.
How accurate are the results?
The calculator applies the exact geometric formulas for a perfect cube, so results are mathematically exact for whatever edge length is entered or derived. The accuracy of a real-world answer depends only on how precisely you measured the value you typed in.

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