Find mass from density and volume using the standard mass = density × volume formula.
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Mass is one of the most fundamental properties in physics and everyday life, yet it is routinely confused with weight. This comprehensive guide explains the distinction between mass and weight, covers all major mass units used in the UK and US, explains how to calculate mass from force or density, and addresses practical applications from shipping weight limits to atomic mass in chemistry.
Mass and weight are related but fundamentally different physical quantities:
In everyday language we use "weight" to mean mass (e.g., "I weigh 70 kg"), but strictly speaking, you weigh 686.7 Newtons on Earth's surface. When you step on a bathroom scale, it reads in kilograms or pounds — which are actually mass units, not weight units. The scale assumes Earth's gravity and calculates mass from the force you exert on it.
From Newton's Second Law, F = ma, which rearranged gives:
Mass (m) = Force (F) / Acceleration (a)
In SI units: kg = Newtons / (m/s2). This is the fundamental relationship. In everyday applications:
| Unit | Equivalent in kg | Common Use |
|---|---|---|
| Kilogram (kg) | 1 kg | SI base unit; universal scientific and commercial use |
| Gram (g) | 0.001 kg | Food, medicine, small items |
| Milligram (mg) | 0.000001 kg | Pharmaceuticals, precise chemistry |
| Pound (lb) | 0.4536 kg | US and UK informal body weight |
| Ounce (oz) | 0.02835 kg | US food, postal, jewellery |
| Stone (st) | 6.350 kg | UK body weight — 1 stone = 14 lbs |
| Short ton (US ton) | 907.2 kg | US commercial freight (2,000 lbs) |
| Long ton (UK ton) | 1,016 kg | UK shipping and naval (2,240 lbs) |
| Metric tonne | 1,000 kg | International commercial; EU standard |
The stone (1 stone = 14 pounds = 6.35 kg) is used almost exclusively in the United Kingdom for expressing human body weight. It is rarely used in the US or internationally. Key conversions:
UK NHS patient records, GP consultations, weight management programmes, and media reporting all routinely use stones and pounds. A typical healthy weight range for a 5'10" (178 cm) male is approximately 10–13 stone (63–83 kg). The stone unit is not officially part of the SI or imperial systems used commercially under UK Weights and Measures legislation — kilograms are the legal unit for commercial trade — but it remains deeply embedded in British culture for personal weight.
| Location | Gravity (m/s2) | Weight of 70 kg Person | Fraction of Earth Weight |
|---|---|---|---|
| Earth | 9.81 | 687 N (154 lbs) | 1.00 (reference) |
| Moon | 1.625 | 114 N (25.5 lbs) | 0.166 (1/6 Earth) |
| Mars | 3.72 | 260 N (58.5 lbs) | 0.379 (38% of Earth) |
| Jupiter | 24.79 | 1735 N (390 lbs) | 2.53 (2.5x Earth) |
| Orbit (ISS) | ~0 (free fall) | ~0 N (weightless) | ~0 (mass unchanged) |
Critically, mass remains 70 kg in all these locations. Only weight changes. Astronauts aboard the ISS are not massless — they are in continuous free fall around Earth, creating apparent weightlessness while retaining all their mass.
When you know an object's density and volume, you can calculate its mass:
Mass (m) = Density (rho) x Volume (V)
Common densities: water = 1,000 kg/m3 (1 g/cm3), steel = 7,850 kg/m3, aluminium = 2,700 kg/m3, oak wood = 700 kg/m3, air = 1.225 kg/m3.
Example: A steel cube 10 cm x 10 cm x 10 cm has volume = 0.001 m3. Mass = 7,850 x 0.001 = 7.85 kg. This formula is fundamental in engineering design, material purchasing (UK steel merchants and US metal suppliers price by weight), and shipping calculations.
Archimedes' Principle states that a floating or submerged object displaces a mass of fluid equal to its own mass (for floating objects) or equal to the object's volume times the fluid density (for submerged objects). This is why steel ships float despite steel being denser than water — the hollow hull displaces a volume of water whose mass exceeds the ship's mass. UK maritime regulations (MCA) and US Coast Guard regulations both use displaced tonnage for vessel classification.
In chemistry, mass is measured at the atomic scale in atomic mass units (amu or u), where 1 amu = 1.661 x 10-27 kg. The molar mass of a substance (in g/mol) numerically equals its relative atomic or molecular mass. For example, water (H2O) has molar mass 18.015 g/mol, meaning 18.015 grams of water contains 6.022 x 1023 molecules (Avogadro's number).
| Service | Max Weight | Notes |
|---|---|---|
| Royal Mail 1st/2nd class letter | 100 g | Standard UK letter rate |
| Royal Mail Large Letter | 750 g | Covers A4 envelopes and small books |
| Royal Mail Parcel | 20 kg | Standard tracked parcel service |
| USPS First-Class Mail | 3.5 oz (99 g) | Standard US letter rate |
| UPS / FedEx standard | 150 lbs (68 kg) | Per package limit for standard services |
| UK lorry maximum axle load | 44 tonnes (GVW) | UK roads standard HGV limit |
Mass is the amount of matter in an object, measured in kilograms, and is constant regardless of location. Weight is the gravitational force acting on that mass, measured in Newtons, and varies with gravity. A 10 kg object always has 10 kg of mass but weighs 98.1 N on Earth and only 16.3 N on the Moon.
A stone is a traditional British unit of mass equal to 14 pounds or approximately 6.35 kilograms. It is used almost exclusively in the UK for expressing human body weight. 10 stone = 140 lbs = 63.5 kg. The stone is not used commercially in the UK (kg is the legal unit) but remains widespread in everyday life.
Divide kilograms by 6.35 to get stone (integer part) and multiply the decimal remainder by 14 to get remaining pounds. For example, 75 kg / 6.35 = 11.81 stone = 11 stone and 0.81 x 14 = 11.3 pounds, so 75 kg = 11 stone 11 pounds approximately.
The Moon's gravity is approximately 1/6 of Earth's (1.625 m/s2 vs 9.81 m/s2). A person who weighs 70 kg (mass) on Earth would weigh approximately 11.7 kg-equivalent on the Moon (25.7 lbs), or exert about 114 Newtons of force. Their mass remains exactly 70 kg regardless of location.
Mass = Density x Volume. Ensure units are consistent: if density is in kg/m3 and volume is in m3, mass is in kg. If density is in g/cm3 and volume is in cm3, mass is in grams. For example, a 2 litre water bottle contains 2,000 cm3 x 1 g/cm3 = 2,000 g = 2 kg of water.
A US short ton = 2,000 lbs = 907.2 kg. A UK long ton = 2,240 lbs = 1,016 kg. A metric tonne = 1,000 kg = 2,204.6 lbs. In international trade and UK commercial contexts, the metric tonne is standard. In US industries like coal, grain, and construction, the short ton is typically used. The UK long ton is now rare commercially.
Atomic mass (or relative atomic mass) is the mass of an atom relative to 1/12 of the mass of a carbon-12 atom. It is expressed in atomic mass units (amu or u), where 1 amu = 1.661 x 10-27 kg. Carbon-12 has atomic mass 12.000; hydrogen 1.008; oxygen 15.999. Molar mass (g/mol) numerically equals atomic/molecular mass and is used for stoichiometric calculations in chemistry.
Royal Mail charges by size and weight. Letters up to 100 g qualify for standard 1st or 2nd class rates. Large letters up to 750 g have their own rate band. Parcels are priced up to 20 kg for Royal Mail Parcel services. Items above 20 kg must use specialist courier services. All weights are measured in grams and kilograms under UK Weights and Measures legislation.