Calculate density from mass and volume for science, engineering, and lab work.
This tool provides estimates for informational purposes only. It is not a substitute for professional advice. Individual results vary based on your inputs and assumptions, so review important decisions with a qualified professional.
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Density is one of the most fundamental physical properties in science and engineering, connecting mass and volume in a way that predicts how substances behave — whether an object floats or sinks, how heavy a container of material will be, and how concentrated a solution is. This guide covers the density formula, SI and US units, the density of common materials, specific gravity, Archimedes' principle and buoyancy, how temperature affects density, and the difference between mass density and population density.
Density is defined as mass per unit volume:
ρ = m ÷ V
Where:
Rearranged: m = ρ × V and V = m ÷ ρ
These three forms allow you to find any one variable if you know the other two.
| From | To kg/m³ | Multiply by |
|---|---|---|
| g/cm³ | kg/m³ | 1,000 |
| lb/ft³ | kg/m³ | 16.0185 |
| lb/gal (US) | kg/m³ | 119.826 |
| oz/in³ | kg/m³ | 1,729.99 |
| Material | Density (kg/m³) | Density (g/cm³) | Density (lb/ft³) |
|---|---|---|---|
| Water (4°C) | 1,000 | 1.000 | 62.43 |
| Seawater | 1,025 | 1.025 | 63.99 |
| Ice | 917 | 0.917 | 57.24 |
| Aluminium | 2,700 | 2.70 | 168.6 |
| Iron | 7,874 | 7.874 | 491.5 |
| Steel | 7,850–7,900 | 7.85–7.9 | 490–493 |
| Copper | 8,960 | 8.96 | 559.4 |
| Gold | 19,320 | 19.32 | 1,206 |
| Lead | 11,340 | 11.34 | 708.0 |
| Wood (oak) | 600–900 | 0.6–0.9 | 37.5–56.2 |
| Concrete | 2,300–2,500 | 2.3–2.5 | 143.6–156.1 |
| Air (at sea level, 15°C) | 1.225 | 0.001225 | 0.0765 |
| Petrol/Gasoline | 720–775 | 0.72–0.775 | 44.9–48.4 |
Specific gravity (SG) is the ratio of a material's density to the density of a reference substance — usually water at 4°C (1,000 kg/m³). Specific gravity is dimensionless (no units) and numerically equals the density in g/cm³ for liquids and solids.
SG = ρ (material) ÷ ρ (water)
Examples:
Any material with SG less than 1.0 floats in fresh water. Any material with SG less than 1.025 floats in seawater.
Archimedes' principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced:
Buoyant force = ρ (fluid) × V (displaced) × g
Where g = 9.81 m/s² (gravitational acceleration).
An object floats when its average density is less than the fluid density. A steel ship floats because its average density (including the hollow air-filled hull) is less than water, even though steel itself has SG ≈ 7.85.
Density decreases as temperature increases for most substances, because thermal energy causes atoms and molecules to vibrate more, expanding the volume while mass stays constant. Water is a famous exception: its density increases from 0°C to 4°C, reaching maximum density at 4°C (1,000 kg/m³), then decreases above 4°C. This unusual behaviour means ice floats, lakes freeze from the top down, and aquatic life survives in cold climates.
For gases, the ideal gas law governs density changes with temperature and pressure: ρ = (P × M) ÷ (R × T), where P = pressure, M = molar mass, R = universal gas constant, T = absolute temperature in Kelvin.
For regularly shaped objects, density = mass ÷ (length × width × height). For irregular objects, the volume is measured by water displacement (Archimedes' method):
In the US, volume is typically measured in mL or fl oz in lab settings. In the UK, lab volumes are always in mL or cm³. Both use grams for mass in lab density measurements, regardless of national measurement system conventions.
Density is not just a physical chemistry concept — it also describes how crowded a geographic area is. Population density is expressed as people per unit area:
| Region | People per sq mile (US) | People per sq km (UK) |
|---|---|---|
| USA (national) | 94 per sq mile | 36 per km² |
| UK (national) | 692 per sq mile | 267 per km² |
| New York City | 28,317 per sq mile | 10,933 per km² |
| London | 14,200 per sq mile | 5,484 per km² |
The UK is far more densely populated than the US on a per-square-mile basis, largely because the US has vast areas of very low-density plains, desert, and forest. England alone has a population density of about 430 per km², comparable to the denser parts of Germany or the Netherlands.
The density formula is ρ = m ÷ V, where ρ (rho) is density, m is mass, and V is volume. Rearranged: mass = density × volume, and volume = mass ÷ density. These three forms allow you to calculate any one of the three variables given the other two.
The density of water at 4°C (its maximum density) is exactly 1,000 kg/m³ = 1.000 g/cm³ = 1.000 g/mL. At room temperature (20°C), water density is approximately 998 kg/m³. At 100°C (boiling), it is approximately 958 kg/m³. The slight decrease from 4°C to 20°C is small enough that 1.000 g/cm³ is used for most practical calculations.
Specific gravity is the ratio of a substance's density to the density of water at 4°C. SG = ρ (substance) ÷ ρ (water) = ρ (g/cm³). It is dimensionless. Materials with SG less than 1.0 float in water; those above 1.0 sink. Gold has SG ≈ 19.3, meaning it is 19.3 times denser than water.
Ice has a lower density than liquid water. Water has its maximum density at 4°C (1,000 kg/m³). As it freezes to ice at 0°C, its crystal structure causes it to expand slightly, reducing density to approximately 917 kg/m³ (SG = 0.917). This is why ice floats — it is less dense than liquid water. Almost all other substances are denser as solids than as liquids.
Use water displacement (Archimedes' method): fill a graduated cylinder with water (record volume V₁), submerge the object (record new volume V₂). Volume of object = V₂ − V₁. Weigh the object to get its mass. Density = mass ÷ (V₂ − V₁). Both the US and UK use mL or cm³ as standard lab volume units for this measurement.
In the US, common density units include lb/ft³ (pounds per cubic foot) for solid materials and construction, lb/gal (pounds per US gallon) for liquids, and g/cm³ for scientific and lab work. The SI unit kg/m³ is used in engineering and international contexts. To convert lb/ft³ to kg/m³, multiply by 16.0185.
For most liquids and solids, density decreases as temperature increases (thermal expansion). Water is a notable exception, reaching maximum density at 4°C. For ideal gases, density is proportional to pressure and inversely proportional to temperature (in Kelvin). Doubling the absolute temperature (at constant pressure) halves the gas density.
Density (ρ) describes the mass per unit volume of a substance in pure form or mixed state. Concentration describes how much of a specific component (solute) is dissolved in a solution. A solution's density and concentration are related but distinct: a 1 M NaCl solution is slightly denser than pure water (density ≈ 1,040 kg/m³) because the dissolved salt adds mass without proportionally increasing volume.
Disclaimer: Density values given are at standard conditions (typically 20°C, 1 atm) unless stated otherwise. Actual densities vary with temperature, pressure, and purity. For engineering applications, always use material-specific data sheets.