ConverterHub

Cube Calculator

Find the volume and surface area of a cube.

How it is calculated

From the edge length s the tool gives three results: volume V = s³, total surface area A = 6 × s² (six equal square faces) and space diagonal d = s × √3, the straight line from one corner through the inside to the opposite corner. The tool has no unit setting and labels results as "units", "units²" and "units³": use any one length unit for the edge (cm, m, in) and the results are in that unit, squared or cubed. The edge must be greater than zero. Results are rounded to two decimals, and no conversion to litres or other volume units is applied; for cm edges, divide the volume by 1000 to get litres.

Worked example

A cube has an edge of 12.5 cm. Step 1: volume = 12.5³ = 12.5 × 12.5 × 12.5 = 1,953.125, shown as 1,953.13 units³ (cm³). Step 2: surface area = 6 × 12.5² = 6 × 156.25 = 937.50 units². Step 3: space diagonal = 12.5 × 1.7321 = 21.65 units. So the cube holds about 1.95 litres and a 21.65 cm rod fits corner to corner inside it.

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Common mistakes

  • Confusing the face diagonal (s × √2) with the space diagonal (s × √3); the space diagonal is the longer one.
  • Mixing units, for example an edge in millimetres and then reading the volume as cm³.
  • Forgetting that doubling the edge multiplies the volume by 8 and the surface area by 4, not by 2.
  • Entering the volume or the area into the edge field when you want to work backwards; the tool goes only from edge to results.
  • Using the surface area as the paint or wrap needed without allowing for overlap and waste.

About this calculator

This calculator finds a cube's volume, V = a³, surface area, SA = 6·a², and space diagonal, d = a·√3, all from its single edge length a. The surface area formula sums the six identical square faces, while the space diagonal — the straight line from one corner through the interior to the opposite corner — comes from applying the Pythagorean theorem twice, first across a face and then through the cube's depth.

Packaging and shipping teams use these formulas to determine box volume for freight pricing and how much material a cube-shaped carton requires, 3D-printing hobbyists use them to estimate material and print time for cube-shaped models, and engineers use the space diagonal when checking whether an object fits diagonally through an opening. Geometry students working through solid-shape problems and anyone sizing a cube-shaped storage container or aquarium use this calculator to get exact figures from one measurement.

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