Free · Material properties

Density from Volume & Known Mass

Find density from positive mass and volume, or derive a rectangular solid’s volume from its three dimensions, with reverse calculations and unit choices.

  • Formula & worked example
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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 mass of 12 kg occupying 6 m³ has density 2 kg/m³. A rectangular solid measuring 1 m by 2 m by 3 m has that 6 m³ volume.

ρ = m / V; rectangular volume V = length × width × height

Worked example

Enter these known values and leave the other values blank.

Material mass
12 kg
Rectangular length
100 cm
Rectangular width
200 cm
Rectangular height
300 cm
Occupied volume
6 m³
Mass density
2 kg/m³

Assumptions and limitations

  • Mass, volume, density and any supplied rectangular dimensions are positive. Mass is not weight force.
  • The product of three dimensions applies to a rectangular solid. For another shape, enter its independently determined volume.
  • The result is average density over the entered volume. Use an appropriate occupied or bulk volume for the quantity you intend.
  • Changing units preserves the physical mass and volume; area or length alone is insufficient to determine density.

Common questions

Can I enter a known volume directly?

Yes. Enter mass and volume and leave the rectangular dimensions blank when that geometric model does not apply.

Can the calculator recover mass?

Yes. Enter positive density and volume; their product gives mass.

References

The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference.

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