What is the density formula?

Density = Mass / Volume (ρ = m/V). Units are typically kg/m³ (SI) or g/cm³ (CGS). Water has a density of 1000 kg/m³ (1 g/cm³) at 4°C — the standard reference.

What is specific gravity?

Specific gravity is the ratio of a substance's density to water's density. It's dimensionless. SG > 1 means the object sinks in water; SG < 1 means it floats. Gold has SG ≈ 19.32, ice ≈ 0.92, mercury ≈ 13.55.

How do I measure density of irregular objects?

Archimedes' method: weigh the object, then submerge it in water and measure displaced water volume. Density = mass / displaced volume. Works for any shape that doesn't absorb water and is denser than water. For floating objects, use a sinker.

Why does ice float on water?

Ice (917 kg/m³) is less dense than liquid water (1000 kg/m³). Water uniquely expands on freezing because hydrogen bonds form a hexagonal crystal that occupies more space than liquid water. About 92% of an iceberg is underwater; 8% above.

How does temperature affect density?

Most materials expand when heated, so density decreases with temperature. Gases change density dramatically (ideal gas: ρ ∝ 1/T at constant P). Liquids and solids change by ~0.01-0.1% per °C. Water is unusual: maximum density at 4°C.

What are typical material densities?

Air ~1.2 kg/m³, water 1000, ice 917, aluminum 2,700, steel 7,850, copper 8,960, lead 11,340, gold 19,320, platinum 21,450. The densest stable element is osmium (22,590 kg/m³). Neutron stars reach ~10¹⁷ kg/m³.

What's the difference between bulk and particle density?

Particle density is of the material itself; bulk density includes voids (air gaps in powders, gravel, foams). A pile of sand has bulk density ~1,500 kg/m³ but particle density ~2,650 kg/m³ (the silica grains themselves). Difference matters for shipping, mixing, and structural calculations.

How is density measured commercially?

For liquids: hydrometers (calibrated for SG, Brix, API gravity), pycnometers (precise mass/volume), digital density meters (oscillating U-tube). For solids: water displacement, gas pycnometers, calibrated dimension measurements. Industry standards (ASTM, ISO) define methods for each material class.

Density Calculator

Q: How do I measure density of irregular objects?

Archimedes' method: weigh the object, then submerge it in water and measure displaced water volume. Density = mass / displaced volume. Works for any shape that doesn't absorb water and is denser than water. For floating objects, use a sinker.

Q: Why does ice float on water?

Ice (917 kg/m³) is less dense than liquid water (1000 kg/m³). Water uniquely expands on freezing because hydrogen bonds form a hexagonal crystal that occupies more space than liquid water. About 92% of an iceberg is underwater; 8% above.

Q: What are typical material densities?

Air ~1.2 kg/m³, water 1000, ice 917, aluminum 2,700, steel 7,850, copper 8,960, lead 11,340, gold 19,320, platinum 21,450. The densest stable element is osmium (22,590 kg/m³). Neutron stars reach ~10¹⁷ kg/m³.

Q: What's the difference between bulk and particle density?

Particle density is of the material itself; bulk density includes voids (air gaps in powders, gravel, foams). A pile of sand has bulk density ~1,500 kg/m³ but particle density ~2,650 kg/m³ (the silica grains themselves). Difference matters for shipping, mixing, and structural calculations.

Q: How is density measured commercially?

For liquids: hydrometers (calibrated for SG, Brix, API gravity), pycnometers (precise mass/volume), digital density meters (oscillating U-tube). For solids: water displacement, gas pycnometers, calibrated dimension measurements. Industry standards (ASTM, ISO) define methods for each material class.

Solve for density, mass, or volume using the relationship Density = Mass / Volume. Supports multiple units and compares results to common materials like water, iron, and aluminum.

Density measures how much mass is packed into a given volume. It is one of the most useful single-number characterizations of a material, distinguishing aluminum (2,700 kg/m³) from steel (7,850 kg/m³) from lead (11,340 kg/m³) without further measurement. The formula ρ = m/V is among the simplest in physics but underlies vast practical work — from naval architecture to gemstone identification to space-mission payload planning.

The story of density's importance starts with Archimedes' "Eureka!" moment around 250 BC: he reportedly figured out the king's crown wasn't pure gold by measuring its volume by water displacement and comparing the resulting density to known pure gold. The same method is still used today by jewelers, forensic scientists, and material identification labs.

Densities span an enormous range — from ~10⁻²⁷ kg/m³ in intergalactic space to ~10¹⁷ kg/m³ in neutron stars (one teaspoon weighs a billion tons). Everyday materials cluster in a narrower band: gases around 1 kg/m³, liquids 800-2000 kg/m³, common metals 2000-10000 kg/m³. Water at 1000 kg/m³ is a natural reference point — densities relative to water are called specific gravities.

This calculator solves the basic relationship in any direction: given two of (mass, volume, density), find the third. Common applications: shipping calculations, material identification, fluid mechanics (buoyancy), chemistry (concentration), aerospace (payload), and any field where mass-volume relationships matter.

Inputs

Solve For

Mass (kg)

Volume (m³)

Density (kg/m³)

Results

Density

1000.00 kg/m³

Mass

5.000 kg

Specific Gravity

1.000

Density Results

Parameter	Value
Density	1000.0000 kg/m³
Density (g/cm³)	1.0000 g/cm³
Density (lb/ft³)	62.4280 lb/ft³
Mass	5.0000 kg
Volume	0.005000 m³
Volume (liters)	5.0000 L
Specific Gravity	1.0000
Floats in Water?	No (sinks in water)
Formula	ρ = m / V

Last updated: May 29, 2026

Formula

**Density:** ρ = m / V Where: - ρ = density (kg/m³ in SI, g/cm³ in CGS) - m = mass (kg) - V = volume (m³) **Rearranged:** - Mass: m = ρ × V - Volume: V = m / ρ **Unit conversions:** | From | To | Factor | |---|---|---| | g/cm³ | kg/m³ | × 1,000 | | kg/L | kg/m³ | × 1,000 | | lb/ft³ | kg/m³ | × 16.018 | | lb/in³ | kg/m³ | × 27,680 | | oz/in³ | g/cm³ | × 1.730 | 1 g/cm³ = 1,000 kg/m³ = 1 kg/L. Water at 4°C ≈ this exactly. **Worked example: density of an unknown metal** A piece of metal weighs 156 g and displaces 20 cm³ of water. ρ = 156 / 20 = 7.8 g/cm³ = 7,800 kg/m³ This matches steel (7,850 kg/m³) very well — likely steel or iron alloy. **Specific gravity:** SG = ρ_substance / ρ_water Water reference: 1,000 kg/m³ (1 g/cm³). SG is dimensionless. - SG < 1: floats on water (oil, ice, wood). - SG > 1: sinks (most metals, rocks). - SG = 1: hovers (gasoline at hot temps, certain plastics). **Common material densities (kg/m³):** | Material | Density | |---|---| | Hydrogen (STP) | 0.0899 | | Helium (STP) | 0.179 | | Air (sea level) | 1.225 | | Cork | 240 | | Pine wood | 350-500 | | Oak wood | 600-900 | | Ice | 917 | | Olive oil | 920 | | Water (4°C) | 1,000 | | Seawater | 1,025 | | Glycerin | 1,260 | | Bone | 1,700-2,000 | | Glass | 2,500 | | Aluminum | 2,700 | | Concrete | 2,400 | | Diamond | 3,520 | | Iron | 7,870 | | Steel | 7,850 | | Copper | 8,960 | | Silver | 10,490 | | Lead | 11,340 | | Mercury | 13,546 | | Tungsten | 19,250 | | Gold | 19,320 | | Platinum | 21,450 | | Osmium (densest metal) | 22,590 | | Sun average | 1,408 | | Neutron star | ~10¹⁷ | **Density vs temperature:** Most materials expand when heated, so density decreases with temperature. ρ(T) ≈ ρ₀ / (1 + β × ΔT) Where β = volumetric expansion coefficient. Water is unusual: maximum density at 4°C (1000.00 kg/m³). Above and below 4°C, density decreases — that's why ice floats and lake bottoms stay liquid in winter. **Density vs pressure (gases):** Ideal gas: ρ = P × M / (R × T) Where M = molar mass (kg/mol), R = 8.314 J/(mol·K). Liquids/solids: nearly incompressible, density barely changes with pressure. **Volume measurement by displacement:** For irregular objects: 1. Fill a graduated container with water to known level. 2. Submerge object completely. 3. Read new water level. 4. Volume = level rise. This is Archimedes' method for identifying materials. **Bulk vs particle density:** - **Particle density**: of the material itself (e.g., concrete grain). - **Bulk density**: includes voids (e.g., loose gravel includes air gaps). Bulk density < particle density. For powders: bulk = (1 − porosity) × particle.

How to use this calculator

Choose what to solve for: density, mass, or volume.
Enter the two known values with correct units.
Calculator returns the unknown.
Compare result to known material densities to identify or verify.
For irregular objects, measure volume by water displacement.
Note: for gases, density varies strongly with temperature and pressure.

Worked examples

Identifying a metal cube

**Scenario:** A 5 cm × 5 cm × 5 cm cube weighs 1,346 g. What metal is it? **Calculation:** Volume = 125 cm³. Density = 1,346 / 125 = 10.77 g/cm³. **Result:** Closest match: silver (10.49 g/cm³) or lead (11.34 g/cm³). The 10.77 value is between but closer to silver. Confirm by chemical test or specific gravity in different fluids.

Shipping calculation

**Scenario:** A pallet of bricks: 200 bricks each 0.0023 m³ at density 2,000 kg/m³. Total mass? **Calculation:** Volume = 200 × 0.0023 = 0.46 m³. Mass = 2,000 × 0.46 = 920 kg. **Result:** ~920 kg pallet. Truck capacity ~25 tonnes → can carry ~27 pallets. Stacking height and stability matter too.

Aluminum vs steel weight savings

**Scenario:** An automotive part has volume 500 cm³. Compare aluminum vs steel. **Calculation:** Aluminum: 0.0005 × 2,700 = 1.35 kg. Steel: 0.0005 × 7,850 = 3.93 kg. **Result:** Aluminum saves 2.58 kg (66%) — big advantage in cars, aircraft, and bicycles. Why steel is still used: aluminum has 1/3 the stiffness and lower fatigue strength, so part design must compensate.

When to use this calculator

**Use density calculations for:**

- **Material identification**: distinguish metals, minerals, polymers. - **Shipping/logistics**: mass and volume planning. - **Buoyancy problems**: float vs sink predictions. - **Quality control**: detect porosity or contamination. - **Gemology**: refractive index combined with density identifies stones. - **Fluid mechanics**: pressure, flow rates. - **Chemistry**: concentration and stoichiometry. - **Aerospace**: weight optimization. - **Forensic science**: composition analysis.

**Measurement methods:**

- **Regular shapes**: measure dimensions, calculate V = l × w × h or πr²h. - **Irregular objects**: water displacement (Archimedes method). - **Liquids**: hydrometer (float depth indicates density). - **Gases**: pycnometer or calculation from P, V, T. - **Powders**: tap density vs bulk density vs particle density.

**Hydrometer reading:**

A hydrometer floats deeper in less dense fluid. Common scales: - **Brix**: sugar content (wine, beer, juice). - **API gravity**: petroleum (lower API = denser oil). - **Specific gravity**: relative to water.

**Density-based separation:**

- **Cream separator**: cream (lighter) rises. - **Mining**: heavy minerals settle (gold panning). - **Centrifugation**: blood components separate by density. - **Plastic recycling**: floats sort polymers by density.

**Engineering and architecture:**

Concrete density: 2,400 kg/m³ → a 10 m × 10 m × 0.2 m slab = 48 tonnes. Steel rebar density 7,850 kg/m³ → calculating tonnage from drawings. Wood beams: density determines load capacity and span.

**Common applications:**

- **Hot air balloons**: hot air ρ < cold air ρ → buoyancy. - **Submarines**: ballast tanks adjust ρ_average around 1000 kg/m³. - **Oil rigs and tanker design**: hull volume calculations. - **Petroleum products**: API gravity grades crude oil. - **Biology**: cell flotation density (cesium chloride gradients). - **Geology**: identify minerals by density and crystal structure.

**Density of mixtures:**

Two liquids mixed: ρ_mix = (m₁ + m₂) / (V₁ + V₂)

If volumes are additive (ideal mixing): ρ_mix = (V₁ × ρ₁ + V₂ × ρ₂) / (V₁ + V₂)

Real mixtures (water + alcohol) show slight volume contraction → ρ slightly higher than ideal.

**Software:**

- **CAD packages** (SolidWorks, Fusion 360): compute mass from CAD geometry + material density. - **CRC Handbook of Chemistry and Physics**: reference densities for thousands of materials. - **MatWeb**: online material property database.

**Pitfalls:**

- **Mixing units**: g/cm³ vs kg/m³ (factor 1000). - **Volume measurement errors**: water displacement on porous materials gives wrong V. - **Temperature dependence**: precise work needs T noted. - **Air buoyancy**: precise weighings need air buoyancy correction (~0.1%). - **Specific gravity vs density**: SG is dimensionless ratio. - **Bulk vs particle density**: powders, granules, foams. - **Gas vs liquid**: gas density changes ~1000× with pressure; liquid density barely changes.

Common mistakes to avoid

Mixing units (g/cm³ vs kg/m³ vs lb/ft³).
Confusing density with specific gravity (SG is dimensionless ratio).
Measuring volume of a porous object as if solid (air gaps inflate V).
Forgetting temperature dependence (especially for gases and water near 4°C).
Reading hydrometer at the wrong meniscus level.
Confusing mass and weight (lb can mean either pound-mass or pound-force).
Treating bulk density as particle density for powders.
Ignoring volume contraction when mixing miscible liquids (e.g., water + ethanol).

Frequently Asked Questions

Sources & further reading

SponsoredShop Top Deals on AmazonSupport CalcMountain — browse top-rated products at no extra cost to you.