How do you calculate the density of a cube?

Density equals mass divided by volume (density = mass / volume). For a cube, the volume is the side length cubed (volume = s x s x s = s3). So the full formula is: density = mass / s3. For example, a cube with a side of 5 cm and a mass of 337.5 g has a volume of 125 cm3 and a density of 337.5 / 125 = 2.7 g/cm3, which is close to the density of aluminium.

What units should I use for cube density?

The most common unit for density is grams per cubic centimetre (g/cm3), which is used for small objects. For larger engineering applications, kilograms per cubic metre (kg/m3) is standard. The two are related: 1 g/cm3 = 1000 kg/m3. Water has a density of 1 g/cm3 (1000 kg/m3), so materials with a density above 1 g/cm3 sink in water and those below float. Make sure your mass and side length use consistent units before dividing.

How do I find the side length of a cube if I know its density and mass?

Rearrange the density formula to find volume first: volume = mass / density. Since volume = s3 for a cube, the side length is the cube root of the volume: s = (mass / density)^(1/3). For example, if an aluminium cube (density 2.7 g/cm3) has a mass of 337.5 g, then volume = 337.5 / 2.7 = 125 cm3, and side = 125^(1/3) = 5 cm.

Cube Density Calculator

Calculate the density of a cube from its mass and side length, or solve for mass or side length when the other values are known. Density equals mass divided by volume, and for a cube the volume is the side length cubed.

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Standard formula Density = mass / volume; volume of a cube = side length cubed (s³).

1. Solve For

What do you want to calculate?

Units

2. Enter Known Values

Mass (g)

Please enter a positive number.

Side length (cm)

Please enter a positive number.

Density (g/cm³)

g/cm³

Please enter a positive number.

Results

Density
-
g/cm³

Volume

cm³

Mass

Side Length

Step-by-Step Breakdown

Formula used-

Side length-

Volume (s³)-

Mass-

Density-

Material Reference

Water1.00 g/cm³

Aluminium2.70 g/cm³

Iron / steel7.87 g/cm³

Copper8.96 g/cm³

Lead11.34 g/cm³

Gold19.32 g/cm³

Densities above 1 g/cm³ sink in water.

Result: Enter values above to see the result.

How to Calculate the Density of a Cube

Density is a measure of how much mass is packed into a given volume. For any object the formula is:

density = mass / volume

For a cube, all three dimensions are equal, so the volume is simply the side length multiplied by itself three times:

volume = s × s × s = s³

Combining these gives the complete formula for the density of a cube:

density = mass / s³

For example, a cube with a side length of 5 cm and a mass of 337.5 g has a volume of 5 × 5 × 5 = 125 cm³ and a density of 337.5 / 125 = 2.7 g/cm³. This is the density of aluminium, so the cube is made of aluminium.

Rearranging the Formula

The same formula can be rearranged to find mass or side length:

To find mass: mass = density × s³
To find side length: s = (mass / density)⅓ (the cube root of volume)

This calculator handles all three arrangements. Select what you want to solve for in the first section.

Units of Density

Unit	Common use	Equivalent
g/cm³ (grams per cubic centimetre)	Small objects, materials science	Same as g/mL
kg/m³ (kilograms per cubic metre)	Engineering, SI standard	1 g/cm³ = 1000 kg/m³
kg/L (kilograms per litre)	Liquids, food science	Same as g/cm³

Water has a density of exactly 1 g/cm³ at 4 degrees Celsius, which makes it a convenient reference. Any material with a density greater than 1 g/cm³ will sink in water; anything below 1 g/cm³ will float.

Worked Example

A solid metal cube has a side length of 5 cm and a mass of 337.5 g. What is its density?

Volume = 5³ = 5 × 5 × 5 = 125 cm³
Density = 337.5 g / 125 cm³ = 2.7 g/cm³
Comparing with the reference table, this is consistent with aluminium (2.70 g/cm³).

This matches the default output of the calculator above.

Related Calculators

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Density Calculator: general density calculator for any shape using mass and volume directly.
Rectangular Box (Cuboid) Calculator: volume, surface area, and space diagonal for a rectangular box.
Volume Calculator: calculate volume for spheres, cylinders, cones, and more.

Method: Standard density formula (density = mass / volume) with cube volume = s³. Side length from density and mass uses the cube root: s = (mass / density)⅓. All arithmetic is performed in the selected unit system with no rounding until display.

This calculator assumes a perfect cube where all sides are equal. For rectangular objects with different length, width, and height, use the Rectangular Box Calculator. Results are for a uniform, solid cube with no hollow sections.

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