How this calculator works
A cube has three equal perpendicular edges. The face diagonal crosses a square face; the body diagonal joins opposite corners through the interior. Pythagoras converts either diagonal to an edge, and cubing the edge gives volume. Density mode divides the measured mass by that volume. Size mode reverses the relation and reports both diagonals. Use consistent outside measurements for a bulk density; a hollow or porous cube produces an average including its empty space. Small edge errors are magnified because volume depends on the cube of edge length.
Formula
V = a³; rho = m/a³; a = cube root(m/rho); face diagonal = a sqrt(2); body diagonal = a sqrt(3).
Worked example
A 2 cm cube has volume 8 cm³. If its mass is 64 g, its density is 8 g/cm³ or 8000 kg/m³. The same cube has a face diagonal of 2.82843 cm and a body diagonal of 3.46410 cm.
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Frequently asked questions
Which diagonal should I choose?
Choose face for a line on one square face. Choose body for a line passing through the cube between opposite corners.
Can I use a rectangular block?
Use the general density calculator with its rectangular-dimensions mode. This page assumes equal edge lengths.
Does a hollow cube give material density?
Using outside volume gives bulk density. To find wall-material density, use the actual solid material volume instead.