Density Calculator

Using the density calculator

Pick what you want to find with the Calculate buttons: density, mass or volume. The form then shows the two other quantities, each with its own unit menu, so you can mix metric and US units freely, such as a mass in pounds and a volume in litres.

• Density: enter mass and volume. The result is shown in kg/m³, oz/in³, lb/ft³ and lb/yd³, plus g/litre (or kg/litre once the density reaches 1,000 kg/m³).
• Mass: enter density and volume. The result is given in kilograms and pounds, in grams and pounds for light objects under 1 kg, or in tonnes and tons from 1,000 kg upwards.
• Volume: enter density and mass. The result covers cm³, m³, in³, ft³ or yd³ and litres, with the set of units adjusting to the size of the answer.

All inputs must be greater than zero. A tonne is the metric ton of 1,000 kg, while a ton here is the US short ton of 2,000 lb (about 907.18 kg). Gallons and fluid ounces are US units.

The density formula

Density tells you how much mass is packed into a given volume. It is a property of a material, not of a particular object: a pebble and a boulder of the same granite have the same density.

ρ = m ÷ Vρ (rho) is density, m is mass and V is volume

m = ρ × V V = m ÷ ρ

In SI units density is measured in kilograms per cubic metre (kg/m³). Chemists and engineers often prefer g/cm³, which is equal to kg/L, and numerically 1 g/cm³ = 1,000 kg/m³. In US customary units density is usually quoted in lb/ft³ and sometimes in oz/in³ or lb/yd³.

Worked examples

Density from mass and volume. A sample weighs 250 g and fills 300 cm³. Convert to SI: 0.25 kg and 0.0003 m³. Then ρ = 0.25 ÷ 0.0003 = 833.33 kg/m³, which is 0.8333 g/cm³ or 52.02 lb/ft³. Because it is below 1,000 kg/m³, it is lighter than water and would float on it.

Mass from density and volume. A steel plate measures 20 cm × 10 cm × 5 cm. Its volume is 0.2 × 0.1 × 0.05 = 0.001 m³. Using 7,850 kg/m³ for steel, m = 7,850 × 0.001 = 7.85 kg, about 17.31 lb.

Volume from mass and density. How much space does 50 kg of petrol (gasoline, roughly 740 kg/m³) take up? V = 50 ÷ 740 = 0.06757 m³, which is 67.57 litres or about 17.85 US gallons.

Checking the water reference. 1 kg of water fills about 1 litre, so ρ = 1 kg ÷ 0.001 m³ = 1,000 kg/m³ = 62.43 lb/ft³. The calculator shows this as 1 kg/litre for the last row.

Typical densities of common materials

A body floats in a fluid when its average density is lower than the fluid's. Ice at 917 kg/m³ is about 8% less dense than fresh water, so roughly 92% of a block of ice floating in a glass sits below the surface (about 90% in sea water, where the fluid is denser). To work out the upward push on a submerged object, use the buoyant force calculator.

What affects density

• Temperature. Most materials expand when heated, so the same mass takes more volume and the density falls. Water is the famous exception near freezing: it is densest at about 4 °C.
• Pressure. Solids and liquids barely change, but gases compress strongly. For a gas you should state the pressure and temperature along with the density; the ideal gas law calculator links all of them.
• Mixtures and porosity. Wood, soil, concrete and foam have air spaces. The density you measure from outside dimensions is the bulk density, which is lower than the density of the solid material itself.
• Weight is not mass. Density uses mass. If you only know a weight in pounds or newtons, make sure it is converted to mass first.

To get the volume of a regular shape before you use it here, see the volume calculator or the tank volume calculator. For a quick weight of metal stock, the metal weight calculator applies the same formula with built-in densities.