Density measures how much mass is packed into a volume. Like comparing feathers vs lead—same size, different weight. Key property for identifying materials.

• Density = mass ÷ volume (ρ = m/V)
• Higher density = heavier for same size
• Water: 1000 kg/m³ = 1 g/cm³
• Determines floating/sinking

Specific gravity = density relative to water. Dimensionless ratio. SG = 1 means same as water. SG < 1 floats, SG > 1 sinks.

• SG = ρ_material / ρ_water
• SG = 1: same as water
• SG < 1: floats (oil, wood)
• SG > 1: sinks (metals)

Density changes with temperature! Gases: very sensitive. Liquids: slight changes. Water max density at 4°C. Always specify conditions.

• Temperature ↑ → density ↓
• Water: max at 4°C (997 kg/m³)
• Gases sensitive to pressure/temp
• Standard: 20°C, 1 atm

kg/m³ is SI standard. g/cm³ very common (= SG for water). g/L for solutions. All related by powers of 10.

• 1 g/cm³ = 1000 kg/m³
• 1 g/mL = 1 g/cm³ = 1 kg/L
• 1 t/m³ = 1000 kg/m³
• g/L = kg/m³ (numerically)

lb/ft³ most common. lb/in³ for dense materials. lb/gal for liquids (US ≠ UK gallons!). pcf = lb/ft³ in construction.

• 1 lb/ft³ ≈ 16 kg/m³
• US gal ≠ UK gal (20% diff)
• lb/in³ for metals
• Water: 62.4 lb/ft³

API for petroleum. Brix for sugar. Plato for brewing. Baumé for chemicals. Non-linear conversions!

• API: petroleum (10-50°)
• Brix: sugar/wine (0-30°)
• Plato: beer (10-20°)
• Baumé: chemicals

ρ = m/V. Know any two, find third. m = ρV, V = m/ρ. Linear relationship.

• ρ = m / V
• m = ρ × V
• V = m / ρ
• Units must match

Archimedes: buoyant force = weight of displaced fluid. Float if ρ_obj < ρ_fluid. Explains icebergs, ships.

• Float if ρ_obj < ρ_fluid
• Buoyant force = ρ_fluid × V × g
• Submerged % = ρ_obj/ρ_fluid
• Ice floats: 917 < 1000 kg/m³

Density from atomic mass + packing. Osmium: densest (22,590 kg/m³). Hydrogen: lightest gas (0.09 kg/m³).

• Atomic mass matters
• Crystal packing
• Metals: high density
• Gases: low density

• Water is 1: g/cm³ = g/mL = kg/L = SG (all equal 1 for water)
• Multiply by 1000: g/cm³ × 1000 = kg/m³ (1 g/cm³ = 1000 kg/m³)
• Rule of 16: lb/ft³ × 16 ≈ kg/m³ (1 lb/ft³ ≈ 16.018 kg/m³)
• SG to kg/m³: Just multiply by 1000 (SG 0.8 = 800 kg/m³)
• Float test: SG < 1 floats, SG > 1 sinks, SG = 1 neutral buoyancy
• Ice rule: 917 kg/m³ = 0.917 SG → 91.7% submerged when floating

• g/cm³ ≠ g/m³! Factor of 1,000,000 difference. Always check your units!
• Temperature matters: Water is 1000 at 4°C, 997 at 20°C, 958 at 100°C
• US vs UK gallons: 20% difference affects lb/gal conversions (119.8 vs 99.8 kg/m³)
• SG is dimensionless: Don't add units. SG × 1000 = kg/m³ (then add units)
• API gravity is backwards: Higher API = lighter oil (opposite of density)
• Gas density changes with P&T: Must specify conditions or use ideal gas law

Material selection by density. Steel (7850) strong/heavy. Aluminum (2700) light. Concrete (2400) structures.

• Steel: 7850 kg/m³
• Aluminum: 2700 kg/m³
• Concrete: 2400 kg/m³
• Foam: 30-100 kg/m³

API gravity classifies oil. Specific gravity for quality. Density affects mixing, separation, pricing.

• API > 31.1: light crude
• API < 22.3: heavy crude
• Gasoline: ~720 kg/m³
• Diesel: ~832 kg/m³

Brix for sugar content. Plato for malt. SG for honey, syrups. Quality control, fermentation monitoring.

• Brix: juice, wine
• Plato: beer strength
• Honey: ~1400 kg/m³
• Milk: ~1030 kg/m³

g/cm³ × 1000 = kg/m³. lb/ft³ × 16 = kg/m³. SG × 1000 = kg/m³.

• 1 g/cm³ = 1000 kg/m³
• 1 lb/ft³ ≈ 16 kg/m³
• SG × 1000 = kg/m³
• 1 g/mL = 1 kg/L

m = ρ × V. Water: 2 m³ × 1000 = 2000 kg.

• m = ρ × V
• Water: 1 L = 1 kg
• Steel: 1 m³ = 7850 kg
• Check units

V = m / ρ. Gold 1 kg: V = 1/19320 = 51.8 cm³.

• V = m / ρ
• 1 kg gold = 51.8 cm³
• 1 kg Al = 370 cm³
• Dense = small

2m × 0.3m × 0.3m steel beam, ρ=7850. Weight?

V = 0.18 m³. m = 7850 × 0.18 = 1413 kg ≈ 1.4 tons.

Wood (600 kg/m³) in water. Float?

600 < 1000, floats! Submerged: 600/1000 = 60%.

1 kg gold. ρ=19320. Volume?

V = 1/19320 = 51.8 cm³. Matchbox size!

22,590 kg/m³. A cubic foot = 1,410 lb! Beats iridium slightly. Rare, used in pen tips.

Ice 917 < water 1000. Almost unique! Lakes freeze top-down, saving aquatic life.

Densest at 4°C, not 0°C! Keeps lakes from freezing solid—4°C water sinks to bottom.

1-2 kg/m³. 'Frozen smoke'. Supports 2000× its weight. Mars rovers use it!

~4×10¹⁷ kg/m³. Teaspoon = 1 billion tons! Atoms collapse. Densest matter.

0.09 kg/m³. 14× lighter than air. Most abundant in universe despite low density.

The most famous 'Eureka!' moment in science occurred when Archimedes discovered the principle of buoyancy and density displacement while taking a bath in Syracuse, Sicily.

• King Hiero II suspected his goldsmith of cheating by mixing silver into a golden crown
• Archimedes needed to prove fraud without destroying the crown
• Noticing water displacement in his bath, he realized he could measure volume non-destructively
• Method: Measure crown's weight in air and in water; compare to pure gold sample
• Result: Crown had lower density than pure gold—fraud proven!
• Legacy: Archimedes' Principle became foundation of hydrostatics and density science

This 2,300-year-old discovery remains the basis for modern density measurements via water displacement and buoyancy methods.

Scientific revolution brought precision instruments and systematic density studies of materials, gases, and solutions.

• 1586: Galileo Galilei invents hydrostatic balance—first precision density instrument
• 1660s: Robert Boyle studies gas density and pressure relationships (Boyle's Law)
• 1768: Antoine Baumé develops hydrometer scales for chemical solutions—still used today
• 1787: Jacques Charles measures gas density vs temperature (Charles's Law)
• 1790s: Lavoisier establishes density as fundamental property in chemistry

These advances transformed density from curiosity to quantitative science, enabling chemistry, material science, and quality control.

Industries developed custom density scales for petroleum, food, beverages, and chemicals, each optimized for their specific needs.

• 1921: American Petroleum Institute creates API gravity scale—higher degrees = lighter, more valuable crude oil
• 1843: Adolf Brix perfects saccharometer for sugar solutions—°Brix still standard in food/beverage
• 1900s: Plato scale standardized for brewing—measures extract content in wort and beer
• 1768-present: Baumé scales (heavy & light) for acids, syrups, and industrial chemicals
• Twaddell scale for heavy industrial liquids—still used in electroplating

These non-linear scales persist because they're optimized for narrow ranges where precision matters most (e.g., API 10-50° covers most crude oils).

Atomic-scale understanding, new materials, and precision instruments revolutionized density measurement and materials engineering.

• 1967: X-ray crystallography confirms osmium densest element at 22,590 kg/m³ (beats iridium by 0.12%)
• 1980s-90s: Digital density meters achieve ±0.0001 g/cm³ precision for liquids
• 1990s: Aerogel developed—world's lightest solid at 1-2 kg/m³ (99.8% air)
• 2000s: Metallic glass alloys with unusual density-strength ratios
• 2019: SI redefinition ties kilogram to Planck constant—density now traceable to fundamental physics

20th-century astrophysics revealed density extremes beyond earthly imagination.

• Interstellar space: ~10⁻²¹ kg/m³—near-perfect vacuum with hydrogen atoms
• Earth's atmosphere at sea level: 1.225 kg/m³
• White dwarf stars: ~10⁹ kg/m³—teaspoon weighs several tons
• Neutron stars: ~4×10¹⁷ kg/m³—teaspoon equals ~1 billion tons
• Black hole singularity: Theoretically infinite density (physics breaks down)

Known densities span ~40 orders of magnitude—from the universe's voids to collapsed stellar cores.

Today, density measurement is indispensable across science, industry, and commerce.

• Petroleum: API gravity determines crude oil price (±1° API = millions in value)
• Food safety: Density checks detect adulteration in honey, olive oil, milk, juice
• Pharmaceuticals: Sub-milligram precision for drug formulation and quality control
• Materials engineering: Density optimization for aerospace (strong + light)
• Environmental: Measuring ocean/atmosphere density for climate models
• Space exploration: Characterizing asteroids, planets, exoplanet atmospheres

Density has units (kg/m³, g/cm³). SG is dimensionless ratio to water. SG=ρ/ρ_water. SG=1 means same as water. Multiply SG by 1000 to get kg/m³. SG useful for quick comparisons.

Water expands when freezing. Ice=917, water=1000 kg/m³. Ice 9% less dense. Lakes freeze top-down, leaving water below for life. If ice sank, lakes would freeze solid. Unique hydrogen bonding.

Higher temp → lower density (expansion). Gases very sensitive. Liquids ~0.02%/°C. Solids minimal. Exception: water densest at 4°C. Always specify temp for precision.

US=3.785L, UK=4.546L (20% larger). Affects lb/gal! 1 lb/US gal=119.8 kg/m³. 1 lb/UK gal=99.8 kg/m³. Always specify.

Very accurate if temp controlled. ±0.001 typical for liquids at constant temp. Solids ±0.01. Gases need pressure control. Standard: 20°C or 4°C for water reference.

Liquids: hydrometer, pycnometer, digital meter. Solids: Archimedes (water displacement), gas pycnometer. Precision: 0.0001 g/cm³ possible. Temperature control critical.