Definition:Imperial

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Definition

The imperial system is a system of measurement based on traditional established folk measures, adopted by the British empire and used in Britain until the mid-20th century.

Its base units can be understood as being the FPS Base Units

Imperial / FPS Base Units

FPS base units
Name Unit symbol Dimension Symbol
foot $\mathrm {ft}$ Length $l$
pound $\mathrm {lb}$ Mass $m$
second $\mathrm s$ Time $t$


Foot

The foot is the FPS base unit and an imperial unit of length.

\(\ds \) \(\) \(\ds 1\) foot
\(\ds \) \(=\) \(\ds 12\) inches
\(\ds \) \(=\) \(\ds 30 \cdotp 48\) centimetres \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 0 \cdotp 3048\) metres \(\quad\) (exact)


Pound

The pound is the FPS unit of measurement of mass, which has a number of different standards.

The most common standard is for it to be defined in kilograms to be exactly $0.453 \, 592 \, 37 \ \mathrm{kg}$.


Second

The second is the SI base unit of time, and also therefore of the MKS system.

It is also the base unit of time for the FPS and CGS systems.


The second is defined as:

the duration of $9 \ 192 \ 631 \ 770$ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium $133$ atom at rest at $0 \ \mathrm K$.


Imperial Length Measure

The imperial units of length are as follows:


Microinch

The microinch is an imperial unit of length.

\(\ds \) \(\) \(\ds 1\) microinch
\(\ds \) \(=\) \(\ds 10^{-3}\) mil
\(\ds \) \(=\) \(\ds 10^{-6}\) inch
\(\ds \) \(=\) \(\ds 0 \cdotp 0254\) micrometre \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 2 \cdotp 54 \times 10^{-5}\) millimetres \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 2 \cdotp 54 \times 10^{-8}\) metres \(\quad\) (exact)


Mil

The mil is an imperial unit of length.

\(\ds \) \(\) \(\ds 1\) mil
\(\ds \) \(=\) \(\ds \dfrac 1 {1000}\) inch
\(\ds \) \(=\) \(\ds 1000\) microinches
\(\ds \) \(=\) \(\ds 25 \cdotp 4\) micrometres \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 0 \cdotp 0254\) millimetres \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 2 \cdotp 54 \times 10^{-5}\) metres \(\quad\) (exact)


Inch

The inch is an imperial and FPS unit of length.

\(\ds \) \(\) \(\ds 1\) inch
\(\ds \) \(=\) \(\ds \dfrac 1 {12}\) foot
\(\ds \) \(=\) \(\ds 2 \cdotp 54\) centimetres \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 0 \cdotp 0254\) metres \(\quad\) (exact)


Link

\(\ds \) \(\) \(\ds 1\) link
\(\ds \) \(=\) \(\ds 7 \cdotp 92\) inches
\(\ds \) \(=\) \(\ds \dfrac 1 {100}\) chains
\(\ds \) \(=\) \(\ds 201 \cdotp 168\) millimetres


Foot

The foot is the FPS base unit and an imperial unit of length.

\(\ds \) \(\) \(\ds 1\) foot
\(\ds \) \(=\) \(\ds 12\) inches
\(\ds \) \(=\) \(\ds 30 \cdotp 48\) centimetres \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 0 \cdotp 3048\) metres \(\quad\) (exact)


Yard

\(\ds \) \(\) \(\ds 1\) yard
\(\ds \) \(=\) \(\ds 3\) feet
\(\ds \) \(=\) \(\ds 36\) inches
\(\ds \) \(=\) \(\ds 91 \cdotp 44\) centimetres
\(\ds \) \(=\) \(\ds 0 \cdotp 9144\) metres


Rod, Pole or Perch

\(\ds \) \(\) \(\ds 1\) rod, pole or perch
\(\ds \) \(=\) \(\ds 5 \tfrac 1 2\) yards
\(\ds \) \(=\) \(\ds 16 \tfrac 1 2\) feet
\(\ds \) \(=\) \(\ds 198\) inches
\(\ds \) \(=\) \(\ds 502 \cdotp 92\) centimetres
\(\ds \) \(=\) \(\ds 5 \cdotp 0292\) metres


Chain

\(\ds \) \(\) \(\ds 1\) chain
\(\ds \) \(=\) \(\ds 4\) rods, poles or perches
\(\ds \) \(=\) \(\ds 22\) yards
\(\ds \) \(=\) \(\ds 66\) feet
\(\ds \) \(=\) \(\ds 792\) inches
\(\ds \) \(=\) \(\ds 100\) links
\(\ds \) \(=\) \(\ds 20 \cdotp 1168\) metres


Furlong

\(\ds \) \(\) \(\ds 1\) furlong
\(\ds \) \(=\) \(\ds 10\) chains
\(\ds \) \(=\) \(\ds 40\) rods, poles or perches
\(\ds \) \(=\) \(\ds 220\) yards
\(\ds \) \(=\) \(\ds 660\) feet
\(\ds \) \(=\) \(\ds 201 \cdotp 168\) metres


International Mile

The (international) mile is an imperial unit of length.

\(\ds \) \(\) \(\ds 1\) (international) mile
\(\ds \) \(=\) \(\ds 8\) furlongs
\(\ds \) \(=\) \(\ds 80\) chains
\(\ds \) \(=\) \(\ds 320\) rods, poles or perches
\(\ds \) \(=\) \(\ds 1760\) yards
\(\ds \) \(=\) \(\ds 5280\) feet
\(\ds \) \(=\) \(\ds 1609 \cdotp 344\) metres \(\quad\) (exact)


League

\(\ds \) \(\) \(\ds 1\) league
\(\ds \) \(\) \(\ds 3\) (international) miles
\(\ds \) \(=\) \(\ds 5280\) yards
\(\ds \) \(\approx\) \(\ds 2\) leuca
\(\ds \) \(\approx\) \(\ds 3000\) paces
\(\ds \) \(=\) \(\ds 4828 \cdotp 032\) metres (exactly)


Imperial Area Measure

The imperial units of area are based on a system of units in which each unit is the square of a corresponding imperial length unit.

The imperial units of area are as follows:


Square Inch

One square inch is equal to a square of side $1$ inch in length.

\(\ds \) \(\) \(\ds 1\) square inch
\(\ds \) \(=\) \(\ds 6 \cdotp 4516 = 2 \cdotp 54^2\) square centimetres

The definition is exact.


Square Foot

One square foot is equal to a square of side $1$ foot in length.

\(\ds \) \(\) \(\ds 1\) square foot
\(\ds \) \(=\) \(\ds 144 = 12^2\) square inches


Square Yard

One square yard is equal to a square of side $1$ yard in length.

\(\ds \) \(\) \(\ds 1\) square yard
\(\ds \) \(=\) \(\ds 9 = 3^2\) square feet
\(\ds \) \(=\) \(\ds 1296 = 36^2\) square inches


Square Rod, Pole or Perch

One square rod, pole or perch is equal to a square of side $1$ rod, pole or perch in length.

\(\ds \) \(\) \(\ds 1\) square rod, pole or perch
\(\ds \) \(=\) \(\ds 30 \dfrac 1 4 = \paren {5 \dfrac 1 2}^2\) square yards
\(\ds \) \(=\) \(\ds 272 \dfrac 1 4 = \paren {16 \dfrac 1 2}^2\) square feet


Square Chain

One square chain is equal to a square of side $1$ chain in length.

\(\ds \) \(\) \(\ds 1\) square chain
\(\ds \) \(=\) \(\ds 16 = 4^2\) square rods, poles or perches
\(\ds \) \(=\) \(\ds 484 = 22^2\) square yards


Rood

One rood is equal to an oblong measuring $1$ chain by $2 \frac 1 2$ chains.


\(\ds \) \(\) \(\ds 1\) rood
\(\ds \) \(=\) \(\ds 2 \tfrac 1 2\) square chains
\(\ds \) \(=\) \(\ds 40\) square rods, poles or perches
\(\ds \) \(=\) \(\ds 1210\) square yards
\(\ds \) \(=\) \(\ds 10 \, 890\) square feet
Rood.png


Acre

One acre is equal to an oblong measuring $1$ chain by $1$ furlong.

That is, measuring $4$ rods, poles or perches by $10$ chains.


\(\ds \) \(\) \(\ds 1\) acre
\(\ds \) \(=\) \(\ds 4\) roods
\(\ds \) \(=\) \(\ds 10\) square chains
\(\ds \) \(=\) \(\ds 160 = 4 \times 40\) square rods, poles or perches
\(\ds \) \(=\) \(\ds 4840 = 22 \times 220\) square yards
\(\ds \) \(\approx\) \(\ds 0 \cdotp 4\) hectares
Acre.png


Square Mile

One square mile is equal to a square whose side measures $1$ mile.

\(\ds \) \(\) \(\ds 1\) square mile
\(\ds \) \(=\) \(\ds 640\) acres


Imperial Volume Measure

The imperial units of volume are based on a binary system, in which each unit is a factor of $2$ larger than the next smaller unit.

Fluid Ounce

The fluid ounce is an imperial unit of volume.

It is also part of the apothecaries' system of volume.

\(\ds \) \(\) \(\ds 1\) fluid ounce
\(\ds \) \(=\) \(\ds 8\) fluid drachms
\(\ds \) \(=\) \(\ds \dfrac 1 {20}\) (imperial) pint
\(\ds \) \(=\) \(\ds 28 \cdotp 41306 \, 25\) millilitres


Gill

\(\ds \) \(\) \(\ds 1\) gill
\(\ds \) \(=\) \(\ds 5\) fluid ounces
\(\ds \) \(=\) \(\ds 0 \cdotp 14206 \, 53125\) litres
\(\ds \) \(=\) \(\ds 142 \cdotp 06531 \, 25\) millilitres


Chopin

\(\ds \) \(\) \(\ds 1\) chopin
\(\ds \) \(=\) \(\ds 2\) gills
\(\ds \) \(=\) \(\ds 0 \cdotp 28413 \, 0625\) litres
\(\ds \) \(=\) \(\ds 284 \cdotp 13062 \, 5\) millilitres


Pint

The pint is an imperial unit of volume.

It is also part of the apothecaries' system of volume.

\(\ds \) \(\) \(\ds 1\) pint (imperial)
\(\ds \) \(=\) \(\ds 20\) fluid ounces
\(\ds \) \(=\) \(\ds 2\) chopins
\(\ds \) \(=\) \(\ds 0 \cdotp 5682 \, 6125\) litres
\(\ds \) \(=\) \(\ds 568 \cdotp 26125\) millilitres


Quart

\(\ds \) \(\) \(\ds 1\) quart (imperial)
\(\ds \) \(=\) \(\ds 2\) pints (imperial)
\(\ds \) \(=\) \(\ds 1 \cdotp 13652 25\) litres
\(\ds \) \(=\) \(\ds 1 \, 136 \cdotp 5225\) millilitres


Pottle

\(\ds \) \(\) \(\ds 1\) pottle
\(\ds \) \(=\) \(\ds 2\) quarts
\(\ds \) \(=\) \(\ds 2 \cdotp 273045\) litres
\(\ds \) \(=\) \(\ds 2 \, 273 \cdotp 045\) millilitres


Gallon

The (imperial) gallon is an imperial unit of volume.

It is defined as the volume of $10$ pounds of water under a specific set of conditions.

\(\ds \) \(\) \(\ds 1\) imperial gallon
\(\ds \) \(=\) \(\ds 2\) pottles
\(\ds \) \(=\) \(\ds 4\) quarts
\(\ds \) \(=\) \(\ds 277 \cdotp 4198\) cubic inches
\(\ds \) \(=\) \(\ds 0 \cdotp 1605\) cubic feet
\(\ds \) \(=\) \(\ds 4 \, 546 \cdotp 09\) millilitres
\(\ds \) \(=\) \(\ds 4 \cdotp 54609\) litres
\(\ds \) \(=\) \(\ds 4 \cdotp 54609 \times 10^{-3}\) cubic metres


Peck

\(\ds \) \(\) \(\ds 1\) peck
\(\ds \) \(=\) \(\ds 2\) (imperial) gallons
\(\ds \) \(=\) \(\ds 9 \cdotp 09218\) litres


Demi-Bushel

\(\ds \) \(\) \(\ds 1\) demi-bushel
\(\ds \) \(=\) \(\ds 2\) pecks
\(\ds \) \(=\) \(\ds 18 \cdotp 18436\) litres


Bushel

\(\ds \) \(\) \(\ds 1\) bushel
\(\ds \) \(=\) \(\ds 2\) demi-bushels
\(\ds \) \(=\) \(\ds 0 \cdotp 03636 \, 872\) cubic metres
\(\ds \) \(=\) \(\ds 36 \cdotp 36872\) litres


Kilderkin

\(\ds \) \(\) \(\ds 1\) kilderkin
\(\ds \) \(=\) \(\ds 2\) bushels
\(\ds \) \(=\) \(\ds 0 \cdotp 07273 \, 744\) cubic metres
\(\ds \) \(=\) \(\ds 72 \cdotp 73744\) litres


Barrel

\(\ds \) \(\) \(\ds 1\) barrel
\(\ds \) \(=\) \(\ds 2\) kilderkins
\(\ds \) \(=\) \(\ds 0 \cdotp 14547 \, 488\) cubic metres
\(\ds \) \(=\) \(\ds 145 \cdotp 47488\) litres


Hogshead

\(\ds \) \(\) \(\ds 1\) hogshead
\(\ds \) \(=\) \(\ds 2\) barrels
\(\ds \) \(=\) \(\ds 0 \cdotp 29094 \, 976\) cubic metres
\(\ds \) \(=\) \(\ds 290 \cdotp 94976\) litres


Pipe

\(\ds \) \(\) \(\ds 1\) pipe
\(\ds \) \(=\) \(\ds 2\) hogsheads
\(\ds \) \(=\) \(\ds 0 \cdotp 58189 \, 952\) cubic metres
\(\ds \) \(=\) \(\ds 581 \cdotp 89952\) litres


Tun

\(\ds \) \(\) \(\ds 1\) tun
\(\ds \) \(=\) \(\ds 2\) pipes
\(\ds \) \(=\) \(\ds 1 \cdotp 16379 \, 904\) cubic metres
\(\ds \) \(=\) \(\ds 1 \, 163 \cdotp 79904\) litres


Imperial Mass Measure

There are three imperial systems of measurement of mass:


Grain

The grain is the imperial unit of mass which is used as the basis of all three of the imperial weight systems.

\(\ds \) \(\) \(\ds 1\) grain
\(\ds \) \(=\) \(\ds \dfrac 1 {437 \cdot 5}\) ounce avoirdupois
\(\ds \) \(\approx\) \(\ds 64 \cdotp 8\) milligrams


Avoirdupois

Dram

The dram is an avoirdupois unit of mass.

\(\ds \) \(\) \(\ds 1\) dram
\(\ds \) \(=\) \(\ds 27 \cdotp 34375\) grains
\(\ds \) \(=\) \(\ds \dfrac 1 {16}\) ounce avoirdupois
\(\ds \) \(\approx\) \(\ds 1 \cdotp 77\) grams


Ounce

\(\ds \) \(\) \(\ds 1\) ounce avoirdupois
\(\ds \) \(=\) \(\ds 16\) drams
\(\ds \) \(=\) \(\ds 437 \cdotp 5\) grains
\(\ds \) \(=\) \(\ds 28 \cdotp 34952 \, 3125\) grams
\(\ds \) \(=\) \(\ds 0 \cdotp 02834 \, 95231 \, 25\) kilograms

The gram / kilogram equivalent is defined to be exact.


Pound

The pound is an avoirdupois unit of mass.

It is defined as being exactly $453 \cdotp 59237$ grams.

\(\ds \) \(\) \(\ds 1\) pound avoirdupois
\(\ds \) \(=\) \(\ds 16\) ounces avoirdupois
\(\ds \) \(=\) \(\ds 7 \, 000\) grains
\(\ds \) \(=\) \(\ds 453 \cdotp 59237\) grams \(\quad\) (exact)
\(\ds \) \(=\) \(\ds 0 \cdotp 45359237\) kilograms \(\quad\) (exact)


Stone

\(\ds \) \(\) \(\ds 1\) stone
\(\ds \) \(=\) \(\ds 14\) pounds avoirdupois
\(\ds \) \(=\) \(\ds 224\) ounces avoirdupois
\(\ds \) \(\approx\) \(\ds 6 \, 350 \cdotp 29318\) grams

The gram equivalent is exact.


Quarter

\(\ds \) \(\) \(\ds 1\) quarter
\(\ds \) \(=\) \(\ds 2\) stone
\(\ds \) \(=\) \(\ds 28\) pounds avoirdupois
\(\ds \) \(\approx\) \(\ds 12 \cdotp 7\) kilograms


Hundredweight

\(\ds \) \(\) \(\ds 1\) hundredweight
\(\ds \) \(=\) \(\ds 4\) quarters
\(\ds \) \(=\) \(\ds 8\) stone
\(\ds \) \(=\) \(\ds 112\) pounds avoirdupois
\(\ds \) \(\approx\) \(\ds 50 \cdotp 8\) kilograms


Ton

The ton is an avoirdupois unit of mass.

\(\ds \) \(\) \(\ds 1\) ton
\(\ds \) \(=\) \(\ds 20\) hundredweight
\(\ds \) \(=\) \(\ds 80\) quarters
\(\ds \) \(=\) \(\ds 160\) stone
\(\ds \) \(=\) \(\ds 2240\) pounds avoirdupois
\(\ds \) \(\approx\) \(\ds 1016\) kilograms
\(\ds \) \(\approx\) \(\ds 1 \cdotp 016\) tonnes


Avoirdupois: Short Variants

Short Hundredweight

\(\ds \) \(\) \(\ds 1\) short hundredweight
\(\ds \) \(=\) \(\ds 100\) pounds avoirdupois
\(\ds \) \(\approx\) \(\ds 45 \cdotp 359\) kilograms


Quarter

\(\ds \) \(\) \(\ds 1\) quarter
\(\ds \) \(=\) \(\ds 5\) short hundredweight
\(\ds \) \(=\) \(\ds 500\) pounds avoirdupois
\(\ds \) \(\approx\) \(\ds 181 \cdotp 44\) kilograms


Short Ton

\(\ds \) \(\) \(\ds 1\) short ton
\(\ds \) \(=\) \(\ds 4\) quarters
\(\ds \) \(=\) \(\ds 20\) short hundredweight
\(\ds \) \(=\) \(\ds 2000\) pounds avoirdupois
\(\ds \) \(\approx\) \(\ds 907 \cdot 2\) kilograms


Apothecaries' Weights

Scruple

The scruple is an apothecaries' unit of mass.

\(\ds \) \(\) \(\ds 1\) scruple
\(\ds \) \(=\) \(\ds 20\) grains
\(\ds \) \(=\) \(\ds 1 \cdotp 3\) grams


Drachm

The drachm is an apothecaries' unit of mass.

\(\ds \) \(\) \(\ds 1\) drachm
\(\ds \) \(=\) \(\ds 3\) scruples
\(\ds \) \(=\) \(\ds 60\) grains
\(\ds \) \(=\) \(\ds 3 \cdotp 89\) grams


Ounce

The apothecaries' ounce is an apothecaries' unit of mass.

\(\ds \) \(\) \(\ds 1\) apothecaries' ounce
\(\ds \) \(=\) \(\ds 8\) drachms
\(\ds \) \(=\) \(\ds 24\) scruples
\(\ds \) \(=\) \(\ds 480\) grains
\(\ds \) \(=\) \(\ds 1\) troy ounce
\(\ds \) \(=\) \(\ds 31 \cdotp 1\) grams


Pound

The apothecaries' pound is an apothecaries' unit of mass.

\(\ds \) \(\) \(\ds 1\) apothecaries' pound
\(\ds \) \(=\) \(\ds 12\) apothecaries' ounces
\(\ds \) \(=\) \(\ds 5 \, 760\) grains
\(\ds \) \(=\) \(\ds 373 \cdotp 24\) grams
\(\ds \) \(=\) \(\ds 1\) troy pound


Troy

Pennyweight

The pennyweight is a troy unit of mass.

\(\ds \) \(\) \(\ds 1\) pennyweight
\(\ds \) \(=\) \(\ds 24\) grains
\(\ds \) \(\approx\) \(\ds 1 \cdotp 56\) grams


Ounce

\(\ds \) \(\) \(\ds 1\) troy ounce
\(\ds \) \(=\) \(\ds 20\) pennyweight
\(\ds \) \(=\) \(\ds 480\) grains
\(\ds \) \(=\) \(\ds 1\) apothecaries' ounce
\(\ds \) \(\approx\) \(\ds 31 \cdotp 1\) grams


Pound

\(\ds \) \(\) \(\ds 1\) troy pound
\(\ds \) \(=\) \(\ds 12\) troy ounces
\(\ds \) \(=\) \(\ds 5 \, 760\) grains
\(\ds \) \(=\) \(\ds 1\) apothecaries' pound
\(\ds \) \(\approx\) \(\ds 373 \cdotp 24\) grams


Talent

\(\ds \) \(\) \(\ds 1\) talent
\(\ds \) \(=\) \(\ds 75\) troy pounds
\(\ds \) \(=\) \(\ds 900\) troy ounces



Also known as

The imperial or FPS system of measurement is also referred to as the British system.


Also see


Sources