Cube Density Calculator
This calculator finds the density of a cube, or works backwards to find its mass or side length, using the rule that density equals mass divided by volume. It helps identify what a solid object is made from, check whether it will float or sink, or verify a material against a known specification from basic measurements. Start by choosing what to solve for (density, mass, or side length), then pick your unit system: grams and centimetres for g/cm³, kilograms and metres for kg/m³, or kilograms and centimetres for kg/L. Enter the two known values and it instantly works out the third, plus the volume calculated too. Results appear as four tiles (density, volume, mass, and side length), a step-by-step breakdown showing the formula used and each intermediate figure, and a short verdict summarising the outcome. A material reference table lets you compare your result against water, aluminium, iron and steel, copper, lead, and gold, so you can see what your cube is likely made of and whether it would float. Under the hood, volume is the side length cubed (s³), so density equals mass divided by s³, and side length uses the cube root of volume. The tool assumes a solid, uniform cube with equal sides and no hollow sections; for rectangular shapes use the Rectangular Box Calculator, and treat results as an indicative check, not a lab measurement.
1. Solve For
2. Enter Known Values
Step-by-Step Breakdown
Material Reference
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:
For a cube, all three dimensions are equal, so the volume is simply the side length multiplied by itself three times:
Combining these gives the complete formula for the density of a cube:
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.
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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.