Mass is the amount of matter in an object. It's an intrinsic property that doesn't change based on location.

SI Unit: Kilogram (kg) - was the only base SI unit defined by a physical artifact until the 2019 redefinition

Property: Scalar quantity, invariant across locations

A 70 kg person has 70 kg of mass on Earth, Moon, or in space

Weight is the force exerted on mass by gravity. It varies with gravitational field strength.

SI Unit: Newton (N) - force unit derived from mass × acceleration

Property: Vector quantity, varies with gravity (W = m × g)

A 70 kg person weighs 687 N on Earth but only 114 N on the Moon (1/6 gravity)

Early civilizations used seeds, grains, and body parts as weight standards. Barley grains were remarkably consistent and became the basis for many systems.

• Mesopotamian: Shekel (180 grains of barley) - oldest documented weight standard
• Egyptian: Deben (91 g) and qedet for gold, silver, and copper trade
• Roman: Libra (327 g) - origin of 'lb' symbol and pound name
• Biblical: Talent (60 minas = 34 kg) for temple treasury and trade
• Grain: A single grain of barley became the smallest unit across cultures

Kings and guilds established official weights to prevent fraud in trade. Royal standards were kept in capital cities and verified by authorities.

• Tower Pound (UK, 1066): 350 g for minting coins, kept in Tower of London
• Troy Pound (1400s): 373 g for precious metals, still used today for gold/silver
• Avoirdupois Pound (1300s): 454 g for general commerce, became modern pound
• Stone (14 lb): English body weight unit, still used in UK/Ireland
• Grain (64.8 mg): Only unit common to all three systems (troy, tower, avoirdupois)

French Revolution created the kilogram as part of a decimal system based on nature, not royal decree.

• 1795: Kilogram defined as mass of 1 liter (1 dm³) of water at 4°C
• 1799: Platinum 'Kilogramme des Archives' created as reference
• 1875: Treaty of the Meter - 17 nations agree to metric system
• 1879: International Committee approves 40 national prototype kilograms
• 1889: Platinum-iridium 'International Prototype Kilogram' (IPK) becomes world standard

For 130 years, the kilogram was the only SI unit defined by a physical object - a cylinder of platinum-iridium alloy kept in a vault near Paris.

• IPK nicknamed 'Le Grand K' - 39 mm tall, 39 mm diameter cylinder
• Stored under three bell jars in climate-controlled vault in Sèvres, France
• Only taken out 3-4 times per century for comparisons
• Problem: Lost ~50 micrograms over 100 years (drift from copies)
• Mystery: Unknown if IPK lost mass or copies gained it
• Risk: If damaged, the definition of kilogram would be lost forever

On May 20, 2019, the kilogram was redefined using Planck's constant, making it reproducible anywhere in the universe.

• New definition: h = 6.62607015 × 10⁻³⁴ J⋅s (Planck constant fixed exactly)
• Kibble balance (watt balance): Compares mechanical power to electrical power
• X-ray crystal density: Counts atoms in ultra-pure silicon sphere
• Result: Kilogram now based on fundamental constants, not an artifact
• Impact: Any lab with proper equipment can realize the kilogram
• Le Grand K retired: Now a museum piece, no longer the definition

The 2019 redefinition was the culmination of 140+ years of work and represents humanity's most precise measurement achievement.

• Pharmaceutical: More accurate drug dosing at microgram scales
• Nanotechnology: Precise measurements for quantum computing components
• Space: Universal standard for interplanetary science
• Commerce: Long-term stability for trade and manufacturing
• Science: All SI units now based on fundamental constants of nature

• 2.2 rule: 1 kg ≈ 2.2 lb (exactly 2.20462, but 2.2 is close enough)
• Pint's a pound: 1 US pint water ≈ 1 pound (at room temp)
• 28-gram rule: 1 oz ≈ 28 g (exactly 28.35, round to 28)
• Ounces to pounds: Divide by 16 (16 oz = 1 lb exactly)
• Stone rule: 1 stone = 14 pounds (UK body weight)
• Carat constant: 1 carat = 200 mg = 0.2 g exactly

Troy ounces are HEAVIER, but troy pounds are LIGHTER - this confuses everyone!

• Troy ounce: 31.1 g (heavier) - for gold, silver, precious metals
• Regular ounce: 28.3 g (lighter) - for food, postal, general use
• Troy pound: 373 g = 12 troy oz (lighter) - rarely used
• Regular pound: 454 g = 16 oz (heavier) - standard lb
• Memory trick: 'Troy ounces are Terrifically heavy, Troy pounds are Tiny'

• Each metric prefix is 1000×: mg → g → kg → tonne (÷1000 going up)
• Kilo = 1000: kilometer, kilogram, kilojoule all mean ×1000
• Milli = 1/1000: millimeter, milligram, milliliter all mean ÷1000
• Water rule: 1 liter water = 1 kg (at 4°C, exactly by original definition)
• Volume-mass link: 1 mL water = 1 g (density = 1 g/mL)
• Body weight: Average adult human ≈ 70 kg ≈ 150 lb

• Carat vs Karat: Carat (ct) = weight, Karat (kt) = gold purity (don't confuse!)
• Grain: Same in all systems (64.8 mg) - troy, avoirdupois, apothecary
• Point: 1/100 of a carat = 2 mg (for small diamonds)
• Pennyweight: 1/20 troy oz = 1.55 g (jewelry trade)
• Atomic mass unit (amu): 1/12 of carbon-12 atom ≈ 1.66 × 10⁻²⁷ kg
• Tola: 11.66 g (Indian gold standard, still widely used)

• US ton (2000 lb) ≠ UK ton (2240 lb) ≠ metric ton (1000 kg = 2205 lb)
• Troy oz (31.1 g) > regular oz (28.3 g) - gold is weighed differently!
• Dry vs wet measurements: Don't weigh flour in ounces meant for liquids
• Temperature matters: Water density changes with temperature (affects mL to g)
• Carat ≠ Karat: Weight vs purity (200 mg vs gold %, totally different)
• Stone is UK only: Don't use in US contexts (14 lb = 6.35 kg)

Base Unit: Kilogram (kg)

The kilogram was redefined in 2019 using Planck's constant, replacing the 130-year-old International Prototype Kilogram (Le Grand K). This ensures universal reproducibility.

Used globally in science, medicine, and 195+ countries for everyday commerce

• picogram

  DNA and protein analysis, single cell mass
• milligram

  Pharmaceuticals, vitamins, precise medical dosing
• gram

  Food ingredients, jewelry, small item measurements
• kilogram

  Human body weight, everyday objects, scientific standard
• metric ton

  Vehicles, cargo, industrial materials, large-scale commerce

Base Unit: Pound (lb)

Defined exactly as 0.45359237 kg since the 1959 international agreement. Despite being 'imperial', it's now defined using the metric system.

United States, some UK applications (body weight), aviation worldwide

• grain

  Gunpowder, bullets, arrows, precious metals, pharmaceuticals
• ounce

  Food portions, postal mail, small packages
• pound

  Body weight, food products, everyday items in US/UK
• stone

  Human body weight in UK and Ireland
• ton (US/short)

  US short ton (2000 lb): Vehicles, large cargo
• ton (UK/long)

  UK long ton (2240 lb): Industrial capacity

Precious Metals & Gems

Dating to medieval France, the troy system is the global standard for precious metals trading. Gold, silver, platinum, and palladium prices are quoted per troy ounce.

• Troy Ounce (oz t) - 31.1034768 g: Standard unit for gold/silver prices
• Troy Pound (lb t) - 12 oz t: Rarely used, mainly historical
• Pennyweight (dwt) - 1/20 oz t: Jewelry making, small precious metal amounts

A troy ounce is heavier than a regular ounce (31.1g vs 28.3g), but a troy pound is lighter than a regular pound (373g vs 454g)

Gemstones & Pearls

The carat system for gemstones was standardized internationally in 1907 at exactly 200 mg. Not to be confused with karat (gold purity).

• Carat (ct) - 200 mg: Diamonds, rubies, sapphires, emeralds
• Point (pt) - 0.01 ct: Diamond sizing (a 50-point diamond = 0.5 carats)
• Pearl Grain - 50 mg: Traditional pearl measurement

The word 'carat' comes from carob seeds, which were used as counterweights in ancient times due to their uniform mass

Historical Pharmacy

Used for centuries in medicine and pharmacy until replaced by metric system in the 1960s-70s. Based on troy weights but with different divisions.

• Scruple - 20 grains: Smallest apothecary unit
• Dram (apothecary) - 3 scruples: Medicine compounding
• Ounce (apothecary) - 8 drams: Same as troy ounce (31.1g)

The word 'scruple' also means a moral concern, possibly because pharmacists had to carefully measure potentially dangerous substances

The International Prototype Kilogram (Le Grand K) lost approximately 50 micrograms over 100 years compared to its copies. Scientists never determined if the prototype lost mass or the copies gained it—this mystery helped drive the 2019 quantum redefinition.

Troy weights originated in Troyes, France, a major medieval trading city. A troy ounce (31.1g) is heavier than a regular ounce (28.3g), but a troy pound (373g) is lighter than a regular pound (454g) because troy uses 12 oz/lb while avoirdupois uses 16 oz/lb.

The grain (64.8 mg) is the ONLY unit that's exactly the same in troy, avoirdupois, and apothecary systems. It was originally based on a single grain of barley, making it one of humanity's oldest standardized measurements.

On the Moon, you'd weigh 1/6 of your Earth weight (the force would be less), but your mass would be identical. A 70 kg person weighs 687 N on Earth but only 114 N on the Moon—yet their mass is still 70 kg.

On May 20, 2019 (World Metrology Day), the kilogram was redefined using Planck's constant (h = 6.62607015 × 10⁻³⁴ J⋅s). This makes the kilogram reproducible anywhere in the universe, ending 130 years of dependence on a physical artifact.

The carat (200 mg) gets its name from carob seeds, which ancient merchants used as counterweights because of their remarkably uniform mass. The word 'carat' comes from Greek 'keration' (carob seed).

The stone (14 pounds = 6.35 kg) is still commonly used for body weight in the UK and Ireland. It dates to medieval England when merchants used standardized stones to weigh goods. A 'stone' was literally a stone kept for weighing!

The metric system was designed so 1 liter of water = 1 kilogram (at 4°C). This beautiful relationship means 1 milliliter of water = 1 gram, making conversions between volume and mass trivial for water-based calculations.

• Atomic Mass Unit (u/amu)

  1/12 the mass of a carbon-12 atom (1.66 × 10⁻²⁷ kg). Essential for chemistry, nuclear physics, and molecular biology.
• Dalton (Da)

  Same as amu. Kilodalton (kDa) used for proteins: insulin is 5.8 kDa, hemoglobin is 64.5 kDa.
• Particle Masses

  Electron: 9.109 × 10⁻³¹ kg | Proton: 1.673 × 10⁻²⁷ kg | Neutron: 1.675 × 10⁻²⁷ kg (CODATA 2018 values)

• Earth Mass (M⊕)

  5.972 × 10²⁴ kg - Used for comparing terrestrial exoplanets and moons
• Solar Mass (M☉)

  1.989 × 10³⁰ kg - Standard for stellar masses, black holes, and galactic measurements

The quantum of mass in quantum mechanics, derived from fundamental constants.

2.176434 × 10⁻⁸ kg ≈ 21.76 micrograms - about the mass of a flea egg (CODATA 2018)

Mesopotamian shekel (180 grains of barley) becomes first documented standardized weight

Egyptian deben (91g) used for precious metals and copper trade

Biblical talent (34 kg) and shekel (11.4g) established for temple and commerce

Greek mina (431g) and talent (25.8 kg) standardized across city-states

Roman libra (327g) created—origin of 'lb' abbreviation and modern pound

Tower Pound (350g) established in England for minting coins

Avoirdupois system emerges for general commerce (modern pound = 454g)

Troy system standardized for precious metals (troy oz = 31.1g)

French Revolution creates kilogram as mass of 1 liter of water at 4°C

'Kilogramme des Archives' (platinum cylinder) created as first physical standard

Treaty of the Metre signed by 17 nations, establishing international metric system

International Prototype Kilogram (IPK / Le Grand K) becomes world standard

International yard and pound agreement: 1 lb defined exactly as 0.45359237 kg

UK adopts metric system officially (though stones persist for body weight)

BIPM decides to redefine kilogram using fundamental constants

Kilogram redefined using Planck constant—'Le Grand K' retired after 130 years

All SI units now based on fundamental constants of nature—no physical artifacts

• Catty/Jin (斤) - 604.79 g: China, Taiwan, Hong Kong, SE Asia markets
• Kin (斤) - 600 g: Japan, metric-aligned catty equivalent
• Tahil/Tael (両) - 37.8 g: Hong Kong gold trading, traditional medicine
• Picul/Dan (担) - 60.5 kg: Agricultural produce, bulk goods
• Viss (ပိဿ) - 1.63 kg: Myanmar markets and trade

• Tola (तोला) - 11.66 g: Gold jewelry, traditional medicine, still widely used
• Seer (सेर) - 1.2 kg: Regional markets, varies by location
• Maund (मन) - 37.32 kg: Agricultural produce, wholesale trade

The tola remains the standard for gold trading in India, Pakistan, Nepal, and Bangladesh

• Livre - 489.5 g: French pound (pre-metric)
• Pfund - 500 g: German pound (now metric-aligned)
• Pud (пуд) - 16.38 kg: Russian traditional weight
• Funt (фунт) - 409.5 g: Russian pound

• Arroba (@) - 11.5 kg: Spain, Latin America (wine, oil, grain)
• Libra - 460 g: Spanish/Portuguese pound
• Quintal - 46 kg: Bulk agricultural goods, 4 arrobas

• Gerah (גרה) - 0.57 g: Smallest unit, 1/20 shekel
• Bekah (בקע) - 5.7 g: Half shekel, temple tax
• Shekel (שקל) - 11.4 g: Ancient currency and weight standard

The shekel of the sanctuary was a precise weight standard maintained by temple authorities for religious offerings and commercial fairness

• Mina (μνᾶ) - 431 g: Trade and commerce weight, 100 drachmas
• Talent (τάλαντον) - 25.8 kg: Large transactions, tribute, 60 minas

A talent represented approximately the mass of water required to fill an amphora (26 liters)

• As - 327 mg: Bronze coin, smallest practical weight
• Uncia - 27.2 g: 1/12 libra, origin of 'ounce' and 'inch'
• Libra - 327 g: Roman pound, origin of 'lb' abbreviation

The libra was divided into 12 unciae, establishing the duodecimal (base-12) tradition seen in pounds/ounces and feet/inches

Recipe precision varies by region: US uses cups/pounds, Europe uses grams, professional kitchens use grams/ounces for consistency.

• Baking: 1% error in yeast can ruin bread (grams essential)
• Portion control: 4 oz (113g) meat, 2 oz (57g) cheese portions
• Molecular gastronomy: Milligram precision for gelling agents

Medical dosing demands extreme precision. Milligram errors can be lethal; microgram precision saves lives.

• Tablets: Aspirin 325 mg, Vitamin D 1000 IU (25 µg)
• Injections: Insulin measured in units, epinephrine 0.3-0.5 mg doses
• Pediatric: Dosing by kg body weight (e.g., 10 mg/kg)

Weight determines shipping costs, vehicle capacity, and customs duties. Dimensional weight (volumetric) often applies.

• Air freight: Charged per kg, exact weight critical for fuel calculations
• Postal: USPS ounces, Europe grams, international kg
• Container shipping: Metric tons (1000 kg) for cargo capacity

Troy ounces for metals, carats for stones. Precise weighing determines thousands of dollars in value.

• Gold: Traded per troy ounce (oz t), purity in karats (not carats)
• Diamonds: Priced exponentially by carat weight (1 ct vs 2 ct)
• Pearls: Measured in grains (50 mg) or momme (3.75 g) in Japan

Analytical chemistry requires milligram to microgram precision. Balances calibrated to 0.0001 g.

• Chemical analysis: Milligram samples, purity 99.99%
• Biology: Microgram DNA/protein samples, nanogram sensitivity
• Metrology: Primary standards maintained at national labs (±0.000001 g)

From raw materials to finished products, weight determines shipping costs, vehicle selection, and handling requirements.

• Trucking: US 80,000 lb limit, Europe 40,000 kg (44 tons)
• Aviation: Passenger + baggage weight affects fuel calculations
• Manufacturing: Component weights for structural engineering

Weight measurements critical for crop yields, livestock management, commodity trading, and food distribution.

• Crop trading: Bushel weights (wheat 60 lb, corn 56 lb, soybeans 60 lb)
• Livestock: Animal weights determine market value and medication dosing
• Fertilizer: Application rates in kg/hectare or lb/acre

Body weight tracking, equipment standards, and competitive weight classes require precise measurement.

• Weight classes: Boxing/MMA in pounds (US) or kilograms (international)
• Body composition: Tracking muscle/fat mass changes to 0.1 kg precision
• Equipment: Barbell plates standardized (20 kg/45 lb, 10 kg/25 lb)

• Know your precision: Cooking tolerates 5% error, pharmaceuticals need 0.1%
• Understand context: Body weight in stones (UK) or pounds (US) vs kg (scientific)
• Use appropriate units: Carats for gems, troy oz for gold, regular oz for food
• Check regional standards: US ton (2000 lb) vs UK ton (2240 lb) vs metric ton (1000 kg)
• Verify medication dosing: Always double-check mg vs μg (1000x difference!)
• Account for density: 1 lb feathers = 1 lb lead in mass, not volume

• Confusing troy ounce (31.1g) with regular ounce (28.3g) - 10% error
• Using wrong ton: Shipping to UK with US tons (10% underweight)
• Mixing carat (200mg gem weight) with karat (gold purity) - completely different!
• Decimal errors: 1.5 kg ≠ 1 lb 5 oz (it's 3 lb 4.9 oz)
• Assuming pound = 500g (it's 453.59g, 10% error)
• Forgetting stones are 14 lb, not 10 lb (UK body weight)

Mass is the amount of matter (kg); weight is the force of gravity on that mass (newtons). Scales typically report mass units by calibrating for Earth’s gravity.

A regular ounce is 28.349523125 g (1/16 lb). A troy ounce used for precious metals is 31.1034768 g. Never mix them.

No. US (short) ton = 2000 lb (907.18474 kg). UK (long) ton = 2240 lb (1016.0469 kg). Metric ton (tonne, t) = 1000 kg.

Carat (ct) is a mass unit for gemstones (200 mg). Karat (K) measures gold purity (24K = pure gold).

Always confirm the unit symbol. 1 mg = 1000 µg. In medicine, micrograms are sometimes written as mcg to reduce misreading risk.

They measure force and display mass by assuming standard gravity (≈9.80665 m/s²). On the Moon, the same scale would show a different value unless recalibrated.

Tradition and international standards: precious metals trade uses troy ounces; gemstones use carats for finer resolution.

International freight typically quotes kilograms or metric tons. Check if dimensional weight rules apply for parcels.