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 Physics Formulae
Units of Measurements

MEASUREMENTS UNITS - MASS

Mass (kilogram): The kilogram is the unit of mass. It is equal to the mass of the International prototype of the kilogram (a platinum-iridium alloy cylinder) kept at BIPM, the International Bureau of Weights and Measures in Sèvres, Paris. It consists of an alloy of 90 % platinum 10 % iridium, and was made in 1879 by George Matthey, of Johnson Matthey, in the form of a cylinder, 39 mm high and 39 mm diameter. It is stored at atmospheric pressure in a specially designed triple bell-jar.

Mass is denoted by kg

For all practical purposes Conventional Mass is related to Mass via the following equation:

where:

• Mc is the conventional mass value
• M is the mass value
• is the density of the test weight material in kg·m-3

## Units of mass

There have historically been four different English systems of mass: Tower weight, Troy weight, avoirdupois weight, and apothecaries weight. Tower weight fell out of use (due to legal prohibition) centuries ago, and was never used in the United States. Troy weight is still used to weigh precious metals. Apothecaries weight, once used in pharmacy, has been largely replaced by metric measurements. Avoirdupois weight is the primary system of mass in the U.S. customary system.

The Avoirdupois units are legally defined as measures of mass, but the names of these units are sometimes applied to measures of force. For instance, in most contexts, the pound avoirdupois is used as a unit of mass, but in the realm of physics, the term "pound" can represent "pound-force" (a unit of force properly abbreviated as "lbf").

English Standards of weight

### Avoirdupois weight

 27.344 grains = 1 dram 16 drams = 437 ½ grains 16 ounces = 7000 grains 14 pounds = 1 stone 28 pounds = 1 quarter 4 quarters = 112 pounds 20 hundredweights = 2240 pounds 3 pennies = 5 halfpennies 4 grains = 1 carat 24 grains = 1 pennyweight 20 pennyweights = 480 grains 12 troy ounces = 5760 grains

The ton and hundredweight above are referred to as the short ton, and the short hundredweight, to distinguish them from the British Imperial ton and hundredweight, which are larger and hence are referred to as the long ton and long hundredweight. The long ton has limited use in the United States.

• 1 long hundredweight = 112 lb ≈ 50.802 kg
• 1 long ton = 20 long cwt = 2240 lb ≈ 1016.047 kg ≈ 1.016 t

### Apothecaries' weight

The grain has the same definition as for avoirdupois weight.

• 1 scruple (s ap) = 20 gr ≈ 1.296 g
• 1 dram apothecaries (dr ap) = 3 s ap ≈ 3.888 g
• 1 ounce apothecaries (oz ap) = 1 oz t = 8 dr ap = 480 gr ≈ 31.103 g
• 1 pound apothecaries (lb ap) = 1 lb t = 12 oz ap = 5760 gr ≈ 373.242 g

The pound and ounce apothecaries are identical to the pound and ounce troy.

### Troy weight

The grain has the same definition as for Avoirdupois weight.

• 1 pennyweight (dwt) = 24 gr ≈ 1.555 g
• 1 ounce troy (oz t) = 20 dwt = 480 gr ≈ 31.103 g
• 1 pound troy (lb t) = 12 oz t = 5760 gr ≈ 373.242 g

Metric Standards of weight

Weight

 1 grain (avoirdupois and troy) = 0.0648 grammes 1 pennyweight = 1.5552 grammes 1 dram (avoirdupois) = 1.772 grammes 1 ounce (16 drams) = 28.350 grammes 1 ounce (troy and apothecary) = 31.1035 grammes 1 pound (16 ounces) = 0.45359 kilogram 1 hundredweight = 112 pounds 1 British ton = 2240 pounds 1 American ton = 2000 pounds 1 milligram = 0.015 grain 1 gramme = 15.432 grains 1 kilogram = 2.20462 pounds 1 quintal = 100 kilograms 1 tone = 0.9842 British ton 1 gallon of water at 62˚F = 10 lb 1 cubic foot water at 60˚F = 62.37 lb 1 cubic inch water at 60˚F = 0.0361 lb 24 hours = 1440 min 12 hour = 720 1 metre = 3 ft 3 in.

Distinctive Masses of Certain Objects

 Object Mass (Kg) Electron 10-30 Proton 10-27 Uranium atom 10-25 Red blood cell 10-13 Dust Particles 10-9 Rain Drop 10-6 Mosquito 10-6 Grape 10-3 Human 102 Automobile 103 Boeing 747 air craft 106 Moon 1023 Earth 1025 Sun 1030 Milky Way galaxy 1041 Observable Universe 1055