Free · Material properties

Cube Mass, Density, Volume and Diagonal Measurements

Relate a positive cube mass and density to its volume, edge, face diagonal and space diagonal while retaining every unit selector.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A cube with edge 2 m and density 3 kg/m³ has volume 8 m³ and mass 24 kg; its face and space diagonals are 2√2 m and 2√3 m.

m = ρV; V = a³; f = √2a; d = √3a

Worked example

Enter these known values and leave the other values blank.

Side (a)
2 m
Density
3 kg/m³
Cube mass
24 kg
Volume
8 m³
Cube diagonal (d)
3.464 m
Face diagonal (f)
2.83 m

Assumptions and limitations

  • All six quantities are positive. Density is the average mass per cube volume, and a, f and d refer to an ideal Euclidean cube. The field is mass in kg or other mass units, not force weight in newtons.
  • One edge, face diagonal, space diagonal or volume fixes cube geometry. Supply density to infer mass, or mass to infer average density. Mass plus density fixes volume and every geometric measure; geometry alone does not determine material density.
  • International mass/length definitions and exact liquid-volume/density conversions are retained through the selector corrections. The particle/atomic-mass selectors use 2022 CODATA central values and carry measurement uncertainty.
  • Earth and Sun selectors are fixed comparison conventions: 5.9722×10²⁴ kg and 1.989×10³⁰ kg respectively. They are not live measurements of astronomical bodies.
  • The original drawing is a static geometric reference. Homogeneous material is not required to define average density, but inferring mass from one supplied density assumes that value applies to the whole cube.

Common questions

Is the mass control gravitational weight?

No. It uses mass units such as kilograms, grams or pounds mass. Force weight would require gravity and force units, which are outside this workflow.

Which diagonal crosses the cube interior?

The space diagonal d connects opposite cube vertices and equals √3 times the edge. The face diagonal f lies within one square face and equals √2 times the edge.

Does edge length determine density?

No. Edge length fixes volume; a mass or independently known density is also needed for the material relationship.

References

Particle and atomic-mass comparison selectors use the 2022 CODATA central mass values in kilograms, replacing older rounded values. These measured constants carry uncertainty; exact arithmetic does not make their physical values exact. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor.

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