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 of length.

\(\ds \) \(\) \(\ds 1\) foot
\(\ds \) \(=\) \(\ds 12\) inches
\(\ds \) \(=\) \(\ds 30.48\) centimetres
\(\ds \) \(=\) \(\ds 0 \cdotp 3048\) metres


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:


Mil

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


Inch

\(\ds \) \(\) \(\ds 1\) inch
\(\ds \) \(=\) \(\ds 2 \cdotp 54\) centimetres
\(\ds \) \(=\) \(\ds 0 \cdotp 0254\) metres

This definition is exact, and is how the imperial unit of length is defined.


Foot

The foot is the FPS base unit of length.

\(\ds \) \(\) \(\ds 1\) foot
\(\ds \) \(=\) \(\ds 12\) inches
\(\ds \) \(=\) \(\ds 30.48\) centimetres
\(\ds \) \(=\) \(\ds 0 \cdotp 3048\) metres


Yard

\(\ds \) \(\) \(\ds 1\) yard
\(\ds \) \(=\) \(\ds 3\) feet
\(\ds \) \(=\) \(\ds 36\) inches
\(\ds \) \(=\) \(\ds 91 \cdot 44\) 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
\(\ds \) \(=\) \(\ds 502 \cdot 92\) 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
\(\ds \) \(=\) \(\ds 20 \cdotp 1168\) 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

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


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
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

\(\ds \) \(\) \(\ds 1\) fluid ounce
\(\ds \) \(=\) \(\ds \dfrac 1 {20}\) 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

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


Quart

\(\ds \) \(\) \(\ds 1\) quart
\(\ds \) \(=\) \(\ds 2\) pints
\(\ds \) \(=\) \(\ds 1 \cdotp 13652 25\) 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

\(\ds \) \(\) \(\ds 1\) gallon
\(\ds \) \(=\) \(\ds 2\) pottles
\(\ds \) \(=\) \(\ds 4 \cdotp 54609\) litres
\(\ds \) \(=\) \(\ds 4 \, 546 \cdotp 09\) millilitres


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

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


Ounce

$1$ ounce avoirdupois $= 16$ drams $= 437 \cdotp 5$ grains $= 28 \cdotp 34952 \, 3125$ grams.
\(\ds \) \(\) \(\ds 1\) ounce avoirdupois
\(\ds \) \(=\) \(\ds 16\) drams
\(\ds \) \(=\) \(\ds 437 \cdotp 5\) grains
\(\ds \) \(=\) \(\ds 28 \cdotp 34952 \, 3125\) grams

The gram equivalent is defined to be exact.


Pound

\(\ds \) \(\) \(\ds 1\) pound avoirdupois
\(\ds \) \(=\) \(\ds 16\) ounces avoirdupois
\(\ds \) \(=\) \(\ds 7 \, 000\) grains
\(\ds \) \(=\) \(\ds 453 \cdotp 59237\) grams

The gram equivalent is defined to be 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

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


Avoirdupois: Short Variants

Short Hundredweight

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


Short Ton

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


Apothecaries' Weights

Scruple

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


Drachm

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


Ounce

\(\ds \) \(\) \(\ds 1\) 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

\(\ds \) \(\) \(\ds 1\) 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

\(\ds \) \(\) \(\ds 1\) 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