# Definition:Imperial

## 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

### 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

### 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

 $\displaystyle$  $\displaystyle 1$ 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.