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.

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

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


Inch

\(\displaystyle \) \(\) \(\displaystyle 1\) inch
\(\displaystyle \) \(=\) \(\displaystyle 2 \cdotp 54\) centimetres
\(\displaystyle \) \(=\) \(\displaystyle 0 \cdotp 0254\) 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.

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


Yard

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


Rod, Pole or Perch

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


Chain

\(\displaystyle \) \(\) \(\displaystyle 1\) chain
\(\displaystyle \) \(=\) \(\displaystyle 4\) rods, poles or perches
\(\displaystyle \) \(=\) \(\displaystyle 22\) yards
\(\displaystyle \) \(=\) \(\displaystyle 66\) feet
\(\displaystyle \) \(=\) \(\displaystyle 20 \cdotp 1168\) metres


Furlong

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


International Mile

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


League

\(\displaystyle \) \(\) \(\displaystyle 1\) league
\(\displaystyle \) \(\) \(\displaystyle 3\) (international) miles
\(\displaystyle \) \(=\) \(\displaystyle 5280\) yards
\(\displaystyle \) \(\approx\) \(\displaystyle 2\) leuca
\(\displaystyle \) \(\approx\) \(\displaystyle 3000\) paces
\(\displaystyle \) \(=\) \(\displaystyle 4828 \cdotp 032\) 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.

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

The definition is exact.


Square Foot

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

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


Square Yard

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

\(\displaystyle \) \(\) \(\displaystyle 1\) square yard
\(\displaystyle \) \(=\) \(\displaystyle 9 = 3^2\) square feet
\(\displaystyle \) \(=\) \(\displaystyle 1296 = 36^2\) 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.

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


Square Chain

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

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


Rood

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


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


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


Square Mile

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

\(\displaystyle \) \(\) \(\displaystyle 1\) square mile
\(\displaystyle \) \(=\) \(\displaystyle 640\) 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

\(\displaystyle \) \(\) \(\displaystyle 1\) fluid ounce
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 1 {20}\) pint
\(\displaystyle \) \(=\) \(\displaystyle 28 \cdotp 41306 \, 25\) millilitres


Gill

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


Chopin

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


Pint

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


Quart

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


Pottle

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


Gallon

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


Peck

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


Demi-Bushel

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


Bushel

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


Kilderkin

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


Barrel

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


Hogshead

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


Pipe

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


Tun

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

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


Avoirdupois

Dram

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


Ounce

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

The gram equivalent is defined to be exact.


Pound

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

The gram equivalent is defined to be exact.


Stone

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

The gram equivalent is exact.


Quarter

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


Hundredweight

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


Ton

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


Avoirdupois: Short Variants

Short Hundredweight

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


Short Ton

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


Apothecaries' Weights

Scruple

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


Drachm

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


Ounce

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


Pound

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


Troy

Pennyweight

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


Ounce

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


Pound

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


Talent

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



Also known as

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


Also see


Sources