Density of Regular Solids

General Chemistry • Matter Its Properties and Measurement

Written by STEM Calculators Team Published October 9, 2025 Updated February 24, 2026

Choose the body and what to solve for, then enter the required values. Use SI units: length in \(\mathrm{m}\), mass in \(\mathrm{kg}\); density will be in \(\mathrm{kg\cdot m^{-3}}\).

Regular body Solve for Mass \( m \) \([\mathrm{kg}]\) Density \( \rho \) \([\mathrm{kg\cdot m^{-3}}]\)

Length \( L \) \([\mathrm{m}]\)

Width \( W \) \([\mathrm{m}]\)

Height \( H \) \([\mathrm{m}]\)

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Density of Regular Bodies

Density relates mass and volume: \[ \rho = \frac{m}{V} \] with SI units \(\rho\) in \(\mathrm{kg\cdot m^{-3}}\), \(m\) in \(\mathrm{kg}\), and \(V\) in \(\mathrm{m^{3}}\). For regular (geometric) bodies, compute \(V\) from dimensions, then apply the definition to find the requested quantity.

Geometric volumes used by the calculator

Cuboid (rectangular box): \(\displaystyle V = L \cdot W \cdot H\).
Sphere: \(\displaystyle V = \frac{4}{3} \cdot \pi \cdot r^{3}\).
Cylinder: \(\displaystyle V = \pi \cdot r^{2} \cdot h\).

Solving paths

Find density \(\rho\). Measure mass \(m\) and dimensions, compute \(V\) from the chosen body, then \(\displaystyle \rho = \frac{m}{V}\).

Find mass \(m\). If \(\rho\) is known (material property) and dimensions are given, compute \(V\) and then \( \displaystyle m = \rho \cdot V\).

Find volume \(V\). Use the geometric formula directly from the dimensions of the selected body.

Units and common conversions

\[ 1\ \mathrm{g\cdot cm^{-3}} = 1000\ \mathrm{kg\cdot m^{-3}}, \quad 1\ \mathrm{cm^{3}} = 1\times 10^{-6}\ \mathrm{m^{3}} \]

Keep units consistent. Negative or zero dimensions are non-physical. Report results with a sensible number of significant figures.

Frequently Asked Questions

How do you calculate density for a regular solid?

Density is computed as rho = m / V. Measure mass m, compute volume V from the shape dimensions, then divide mass by volume.

What volume formulas are used for a cuboid, sphere, and cylinder?

Cuboid: V = L x W x H. Sphere: V = (4/3) x pi x r^3. Cylinder: V = pi x r^2 x h.

How do you find the mass if density and dimensions are known?

First compute the volume from the selected shape, then multiply by density: m = rho x V. This is useful when density is a known material property.

What units should be used in this density of regular solids calculator?

Use SI units: length in meters and mass in kilograms, which produces density in kg/m^3. A common conversion is 1 g/cm^3 = 1000 kg/m^3.

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