Density calculator
Enter two of density, mass and volume, get the third.
How do I calculate density?
Density = mass ÷ volume. 500 g in 250 cm³ is 2 g/cm³.
What is the density of water?
About 1 g/cm³ (1,000 kg/m³, 62.4 lb/ft³) — the kilogram was originally defined from a liter of water.
How do I find mass from density?
Mass = density × volume: half a cubic meter of steel at 7,850 kg/m³ weighs 3,925 kg.
How do I convert g/cm³ to kg/m³?
Multiply by 1,000: 2.7 g/cm³ (aluminum) is 2,700 kg/m³. To lb/ft³, multiply g/cm³ by 62.428.
Will it float?
An object floats in water if its average density is below about 1 g/cm³ — which is why a steel ship, full of air, floats while a steel bolt sinks.
What are the densities of common materials?
OpenStax University Physics (Volume 1, section 14.1) lists, in kg/m³: fresh water at 4.0 °C 1,000, at 20 °C 998.2, ice at 0 °C 917, aluminum 2,700, iron 7,860, gold 19,300 and air at 0 °C and 101.3 kPa 1.29. Divide by 1,000 for g/cm³, so iron is 7.86 g/cm³ and ice 0.917 g/cm³.
What is specific gravity?
The density of a material divided by the density of water at 4.0 °C, which is 1,000 kg/m³. It has no units: aluminum has a specific gravity of 2.7 (OpenStax, section 14.1). Anything below 1 floats in water and anything above 1 sinks, provided it is solid all the way through.
Does the density of water change with temperature?
Slightly. It is 1,000 kg/m³ at 4.0 °C, 999.8 at 0 °C and 998.2 at 20 °C (OpenStax Table 14.1), a spread of under 0.2%, so 1 g/cm³ is fine for everyday work. Gases are different: their density depends strongly on temperature and pressure.
The formula and what it assumes
Density is mass per unit volume, ρ = m ÷ V (OpenStax University Physics, Volume 1, Eq. 14.1). The SI unit is kg/m³, and 1 g/cm³ = 1,000 kg/m³. The calculator converts everything to kg and m³ first, so 1 lb/ft³ equals 16.018 kg/m³ (1 lb = 0.45359237 kg, 1 ft³ = 0.028316846592 m³). The result is an average over the whole object: a hollow part, a pore or a trapped air pocket lowers it, and the density of a real material also shifts with temperature and pressure.
Worked example: identify a metal bar
A bar measures 2 in × 2 in × 6 in, which is 24 in³ or 393.3 cm³, and weighs 2.34 lb, or 1.061 kg. Density = 1.061 kg ÷ 3.933 × 10⁻⁴ m³ = 2,699 kg/m³, which is 2.70 g/cm³ or 168.5 lb/ft³. That matches aluminum (2,700 kg/m³). Run the other way, half a cubic meter of a 2,700 kg/m³ material has a mass of 1,350 kg.
Common mistakes
Volume units cause most errors. There are 1,728 in³ in a ft³ (12³, not 12) and 1,000,000 cm³ in a m³, so 1 g/cm³ is 1,000 kg/m³ but 1 g/m³ is only 0.001 kg/m³. Mass is not weight: a weight in newtons must be divided by 9.80665 first (98.07 N is a mass of 10 kg). And an object that floats has an average density below water’s, which is not the density of its material: a steel ship floats because the air inside counts as part of its volume.
Sources: OpenStax University Physics, Volume 1, section 14.1 (density, Eq. 14.1; Table 14.1; specific gravity); NIST SP 811, Appendix B, for the pound, the cubic inch and the cubic foot. Related: buoyancy calculator, material weight calculator, metal weight calculator and pressure calculator.