Density Calculator (ρ = m/V)
Calculate density, mass or volume using ρ = m/V. Enter any two of density, mass and volume to find the third. Includes specific gravity vs water.
How to use this tool
- Enter mass, volume and density (if known) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your density and the full breakdown beneath it.
Density is mass per unit volume: ρ = m/V. The SI unit is kg/m³. Specific gravity is the ratio of a substance's density to that of water (1000 kg/m³ at 4°C). Objects with SG < 1 float in water.
Formula
ρ = m ÷ V
Rearranged: m = ρ × V | V = m ÷ ρ
Specific gravity = ρ ÷ 1000 (relative to water at 1000 kg/m³)
Where ρ = density (kg/m³), m = mass (kg), V = volume (m³).
How it works
This calculator solves for whichever of density, mass, or volume is unknown, given the other two. It also expresses density as specific gravity — the ratio of the material's density to that of water (1000 kg/m³ at 4 °C). Specific gravity is dimensionless; values above 1 mean the substance sinks in water. The calculation assumes uniform density throughout the sample.
Worked example
- Given: mass m = 2 kg, volume V = 0.001 m³ (1 litre). Density is unknown.
- Apply: ρ = m ÷ V = 2 ÷ 0.001.
- Calculate: ρ = 2000 kg/m³.
- Specific gravity = 2000 ÷ 1000 = 2.0 (twice as dense as water).
Density = 2000 kg/m³; Specific gravity = 2.0
Common mistakes to avoid
- Confusing mass and weight -- entering a force value (Newtons) instead of mass (kg) in the mass field overstates density by 9.81x.
- Mixing volume units -- entering cm cubed instead of m cubed inflates density by 10 to the power of 6 (1 m cubed = 1000000 cm cubed).
- Assuming specific gravity equals density in kg/m cubed -- specific gravity is dimensionless and equals density divided by 1000 kg/m cubed (density of water).
Key terms
- Density (ρ)
- Mass per unit volume, measured in kg/m³. It quantifies how much matter is packed into a given space.
- Specific gravity
- The ratio of a substance's density to that of water (1000 kg/m³). A value greater than 1 means the substance is denser than water and will sink.
- Volume
- The three-dimensional space occupied by a substance, measured in m³ in SI units. 1 m³ = 1000 litres.
- Uniform density assumption
- This formula treats the sample as homogeneous — the same density throughout. Composite or heterogeneous materials have locally varying densities.
Frequently asked questions
- What is the density of common materials?
- Water: 1000 kg/m³, aluminium: ~2700, steel: ~7800–8000, gold: ~19,300, air: ~1.2 kg/m³ at sea level.
- How do I convert g/cm³ to kg/m³?
- Multiply by 1000. So 2.7 g/cm³ (aluminium) = 2700 kg/m³.