Density Calculator

Density tells you how tightly mass is packed into space. Two things the same size can weigh very differently: a 100 cm³ block of aluminium weighs about 270 g, the same block of pine about 50 g. Divide mass by volume and you get a number that belongs to the material, not to the size of the piece.

The formula

density ρ = mass m ÷ volume V
mass m = density ρ × volume V
volume V = mass m ÷ density ρ
specific gravity = density ÷ density of water (1,000 kg/m³)
cube V = side³ · box V = length × width × height
cylinder V = π × (diameter ÷ 2)² × height
sphere V = π × diameter³ ÷ 6
volume by displacement = water level after − water level before
it floats if its density is less than the water's; share under the surface = its density ÷ water density

Worked example

Density (the default): 270 g with a volume of 100 cm³. Mass: 270 g = 0.27 kg. Volume: 100 cm³ = 0.0001 m³. Density: 0.27 ÷ 0.0001 = 2,700 kg/m³, which is 270 ÷ 100 = 2.7 g/cm³. In US units: 2,700 ÷ 16.018 = 168.6 lb/ft³. Specific gravity: 2,700 ÷ 1,000 = 2.7, more than 1, so it sinks. The closest listed material is aluminium (about 2,700 kg/m³).

Mass: 1 US gallon of petrol at about 740 kg/m³. 1 US gal = 0.003785411784 m³, and 740 × 0.003785411784 = 2.801 kg (6.176 lb).

Volume: 1 kg of copper at about 8,960 kg/m³. 1 ÷ 8,960 = 0.0001116 m³ = 111.6 cm³.

Mass of a steel cylinder: 5 cm across and 10 cm tall. Radius 2.5 cm = 0.025 m, height 0.1 m. Volume: π × 0.025² × 0.1 = 0.00019635 m³ (196.35 cm³). Mass: 7,850 × 0.00019635 = 1.541 kg.

Mass of a gold ball: 2 cm across. Volume: π × 2³ ÷ 6 = 4.189 cm³. Mass: 4.189 × 19.3 g/cm³ = 80.84 g.

Water rise (Archimedes): a 100 g ring raises the water in a jug from 200 mL to 205.2 mL. Volume: 205.2 − 200 = 5.2 mL = 5.2 cm³. Density: 100 ÷ 5.2 = 19.23 g/cm³, close to gold (about 19.3). This is the test Archimedes is said to have used on a king’s crown.

Floating: ice at about 917 kg/m³ has a specific gravity of 0.917, so it floats with 917 ÷ 1,000 = 91.7% under fresh water, and 917 ÷ 1,025 = 89.5% under sea water.

Typical densities (approximate)

These are rounded, typical values. Real samples change with temperature, grade, alloy, moisture and air gaps (wood and concrete vary a lot). Water is about 1,000 kg/m³ near 4 °C and about 998 kg/m³ at 20 °C. Air is about 1.225 kg/m³ at sea level and 15 °C. For exact work, use the figure on the material’s data sheet: you can type it into the density box.

Notes

• 1 g/cm³ = 1 g/mL = 1 kg/L = 1,000 kg/m³ = 62.43 lb/ft³ = 8.345 lb per US gallon.
• Unit definitions used: 1 lb = 0.45359237 kg, 1 oz = 1/16 lb, 1 in = 2.54 cm, 1 US gallon = 231 in³ (3.785 L), 1 UK gallon = 4.54609 L, 1 US fl oz = 1/128 US gallon.
• For a hollow object or one with holes (a boat, a bottle, a sponge), the result is its average density, which decides whether it floats.
• In the water-rise method the object must be fully under water and must not soak up water. Use a narrow jug for small objects so the rise is easy to read.
• Specific gravity here is compared with water at 1,000 kg/m³. Some industries compare with water at 15.6 °C (60 °F, about 999 kg/m³), which changes the answer by about 0.1%.