Density Calculator

Calculate density, mass, or volume using ρ = m / V

Density Calculator

Calculate density (rho = m / V)

Density

rho = mass / volume

Formula
rho = m / V

What Is Density?

Density is the amount of mass packed into a given volume — how "heavy" a material is for its size. Measured in kg/m³ or g/cm³, it determines whether an object floats or sinks, how materials behave under pressure, and how to compare different substances. Gold (19,300 kg/m³) is far denser than ice (917 kg/m³) or wood (~600 kg/m³). Every material has a characteristic density that reveals a lot about its atomic structure and composition.

This calculator solves for any of the three variables in ρ = m/V: density (ρ), mass (m), or volume (V). Enter two known values to find the third. It supports SI units (kg, m³, g, cm³) and displays specific gravity (density relative to water at 4°C), so you can immediately see whether an object will float or sink in fresh water.

How to Use the Density Calculator

  1. Select what you want to calculate — density, mass, or volume.
  2. Enter the two known values with their units.
  3. Click Calculate.
  4. Read the result, specific gravity, and whether the object floats in water.

Formulas & Reference

ρ = m / V (density = mass / volume) m = ρ × V (mass = density × volume) V = m / ρ (volume = mass / density) Specific gravity = ρ_object / ρ_water ρ_water = 1,000 kg/m³ = 1 g/cm³ Floats if specific gravity < 1 (ρ < water) Sinks if specific gravity > 1 (ρ > water) Common densities (kg/m³): Water: 1,000 Ice: 917 Air: 1.225 Wood: ~600 Aluminum: 2,700 Iron: 7,874 Gold: 19,300 Osmium: 22,590 (densest element)

Density is temperature-dependent — water is densest at 4°C (1,000 kg/m³) and less dense as ice (917 kg/m³). This explains why ice floats on water: freezing actually makes water expand slightly, reducing its density below that of liquid water.

Worked Examples

Gold Bar

A gold bar has a mass of 12.4 kg and a volume of 640 cm³. Density = 12,400 g / 640 cm³ = 19.375 g/cm³ — nearly identical to pure gold (19.32 g/cm³), confirming its authenticity.

One Liter of Ice

Ice has a density of 0.917 g/cm³. One liter (1,000 cm³) of ice therefore has a mass of 0.917 g/cm³ × 1,000 cm³ = 917 g — about 8.3% lighter than the same volume of liquid water (1,000 g).

Floating Wood Block

A block of wood has a mass of 500 g and occupies 1,000 cm³. Density = 500 g / 1,000 cm³ = 0.5 g/cm³. Specific gravity = 0.5, which is less than 1 — so the block floats and sits roughly half-submerged in water.

Frequently Asked Questions

Why does ice float on water?
Water is unusual: when it freezes, its molecules form a hexagonal lattice that takes up more space than liquid water. This makes ice (917 kg/m³) less dense than liquid water (1,000 kg/m³ at 4°C), so ice floats. This property is critical for aquatic life — frozen lakes insulate the liquid water below.
What does specific gravity mean?
Specific gravity is the ratio of a material's density to the density of water (1 g/cm³). It's dimensionless. A specific gravity less than 1 means the material floats; greater than 1 means it sinks. For example, ethanol has a specific gravity of ~0.789, and steel is about 7.85.
What is the densest material on Earth?
Osmium is the densest naturally occurring element at 22,590 kg/m³ — more than twice as dense as lead and about 17% denser than gold. Among man-made materials, some high-density alloys and depleted uranium (~19,100 kg/m³) are also extremely dense.
How is density used in engineering?
Engineers use density constantly: to calculate structural loads (mass from volume), to select lightweight materials (aerospace uses aluminum and carbon fiber for their low density-to-strength ratio), to design ships and submarines (buoyancy), and to specify fluid systems (pipeline flow depends on fluid density).
How do you measure density experimentally?
The most common method is to weigh an object (to get mass) and then find its volume. For regular shapes, calculate volume from dimensions. For irregular objects, use water displacement: submerge the object and measure how much water it displaces — that volume equals the object's volume. Density = mass / displaced volume.