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# Imperial System|Definition & Meaning

## Definition

The imperial system is a system of **units** and measures developed in **England**, although it has been replaced by the **metric** system in almost all countries. Except for the **volume** measurements (all imperial volume units are larger than their **US** counterparts), all other units are exactly the **same** as in the US standard units.

**Figure 1** shows all the **imperial** system units of length, mass, volume, and area.

## History

The imperial system of units, also known as the **British** imperial system, was adopted in **1824** in Great Britain. It was replaced by the **Metric** system in **1965**, which France introduced in the 1790s.

The imperial measurement system paved the way for the **United States**‘ standard measurement system. The prefix “**imp**” with the unit denotes the imperial unit, and “**US**” denotes the US standard unit.

Many **evolutions** took place in the imperial system in the Celtic, Roman, Anglo-Saxon, and Middle East **eras**.

The values of the **imperial** units such as gallon, foot, and pound varied with time, **trade**, place, and product specifications. The variations of the **gallon**, such as corn, ale, and wine, were abolished, and a single imperial gallon equal to ten **pounds** was introduced.

The **rod** and **chaldron** were also terminated.

The troy pound and the **yard** were the basic imperial units restricted to **weigh** metal, drugs, and jewels. The imperial pound and yard were equal to 0.45359237 **kilograms** and 0.9144 **meters**, respectively.

Imperial units are converted to **metric** units, which are used mostly in **mathematical** problems. The seven **base** units of the metric system are meters(m), kilograms(kg), seconds(s), Kelvins(K), candela(cd), mole(mol), and ampere(A).

The **imperial units** of length, area, weight, and volume are discussed below.

## Length

The measure of **distance** is known as the length. The unit of length is a **base** unit from which other units are derived in many unit measurement systems, including the **imperial** system. The System International unit of length is **meters**, denoted by “**m**.” The following imperial units are used to measure **length**.

### Inches

An inch, abbreviated as “**in**,” is the smallest unit of length. It is equal to **0.0254** meters. So:

1 inch = 0.0254 m

Dividing **0.0254** into both sides in the above equation gives:

1 m = 39.3701 inches

One **inch** is equal to the other **imperial** units of length as follows:

1 inch = 1/12 **feet**

1 inch = 1/36 **yards**

1 inch = 0.00126 **chains**

1 inch = 1/63,360 **miles**

### Feet

The unit of length **greater** than “inches” is “feet,” as one foot equals **twelve** inches as:

1 foot = 12 inches

It is abbreviated as “**ft**” and related to the other **imperial** units of length as:

1 foot = 1/3 **yards**

1 foot = 1/66 **chains**

1 foot = 1/660 **furlongs**

1 foot = 1/5280 **miles**

For example, the average length of a **truck** is approximately **20** feet. Also, one **meter** equals 3.28084 meters, so:

1 **foot** = 0.3048 meters

### Yards

Three **feet** make one yard; hence yard is a greater unit than the feet, so:

1 yard = 3 feet

It is abbreviated as “**yd**” and related to the other **imperial** units as:

1 yd = 36 **inches**

1 yd = 0.0455 **chain**

1 yd = 1/220 **furlongs**

1 yd = 1/1760 **miles**

For example, the length of a **mattress** is almost **3** yards. One yard is equal to the **metric** unit of length as:

1 yd = 0.9144 m

### Chains

One imperial **chain** is equal to 22 yards, so:

1 chain = 22 yards

Additionally, we have:

1 chain = 4 **rods**

1 chain = 66 **feet**

1 chain = 22 **yards**

1 chain = 1/10 **furlongs**

1 chain = 1/80 **miles**

In the metric system, one **chain** equals **20.1168 **meters.

### Furlongs

A furlong is used to measure **distance** in the **US** and imperial units. One furlong is equal to 10 imperial chains, so:

1 furlong = 10 **chains**

It is related to the other **imperial** units as:

1 furlong = 40 **rods**

1 furlong = 660 **feet**

1 furlong = 220 **yards**

1 furlong = 40 **rods**

1 furlong = 1/8 **mile**

In SI units, one furlong equals **201.168** meters.

### Miles

A mile is the **largest** imperial unit of length used to measure **long** distances. A mile consists of **1760** yards. Also, it is related to the other imperial units as:

1 mile = 63,360 **inches**

1 mile = 5280 **feet**

1 mile = 1760 **yards**

1 mile = 80 **chains**

1 mile = 8 **furlongs**

Also, in SI units, one mile equals **1,609.344** meters.

## Mass

Most people use the term “**weight**” for “**mass**” because the scales which measure mass are called “**weighing scales**,” but both are two different quantities.

Mass is the amount of **matter** composed within an object. The metric unit of mass is the **kilogram **(kg). Weight is defined as the mass of an object due to **gravitational** pull. It is the force experienced by the object due to gravitational acceleration.

The **imperial** units in which weight or what should be called **mass** is measured are as follows:

### Grains

The **grain** is the **smallest** imperial unit of mass. One milligram consists of **0.0154** grains.

### Ounces

One ounce consists of **437.5** grains. An ounce abbreviated as “**oz**” is different from a fluid ounce. It is related to the other **imperial** units as follows:

1 oz = 1/16 **pound**

1 oz = 1/224 **stone**

1 oz = 1/1792 **hundredweight**

1 oz = 1/35,840 **imp ton**

### Pounds

A pound abbreviated as “**lb**” is also known as pound-mass. Sixteen **ounces** make one pound, so:

1 lb = 16 oz

A pound is used to measure the **weight** of a person, object, etc. It is related to the other **imperial** units as:

1 **lb** = 7000 grains

1 **lb** = 1/14 stone

1 **lb** = 1/112 hundredweight

1 **lb** = 1/2240 imp ton

### Stones

Fourteen **pounds** makes one imperial stone, so:

1 **stone** = 14 pounds

It is related to the other **imperial** units as:

1 stone = 98,000 **grains**

1 stone = 224 **ounces**

1 stone = 1/8 **hundredweight**

1 stone = 1/160 **imp ton**

### Hundredweights

Eight **stones** make one hundredweight. A hundredweight is abbreviated as “**cwt**” and is related to the other **imperial** units of mass as:

1 cwt = 7,84,000 **grains**

1 cwt = 1792 **oz**

1 cwt = 112 **lb**

1 cwt = 8 **stones**

1 cwt = 1/20 **imp ton**

### Imperial Tons

One imperial ton, abbreviated as “**imp t**,” is **greater** than one **US** ton, which is why the imperial ton is sometimes referred to as the **long ton **(UK) and the US ton as the short ton. The imp ton is related to the other **imperial** units as follows:

1 imp ton = 35,840 **oz**

1 imp ton = 2240 **lb**

1 imp ton = 160 **stones**

1 imp ton = 20 **hundredweights**

**Figure 2** shows the imperial unit conversions for **length** and **mass**.

## Area

A plane region’s area is the measurement of the **size** of a region on the **plane** surface. The SI unit of area is **meter squared**(m^{2}). For example, the area of a **circle** is πr^{2}. The following units of area are used in the **imperial** system.

### Square Inches

One square inch is equal to **6.4516** cm^{2}. A **square inch** is abbreviated as in^{2} or “sq inch.” Also:

0.155 in^{2} = 100 mm^{2} = 1 cm^{2}

### Square Feet

One square foot equals 0.0929 m^{2}. A **square foot** is abbreviated as ft^{2} or “sq foot.” Also:

1 ft^{2} = 144 in^{2}

### Square Yards

One **square yard** equals 0.8361 m^{2}. It is abbreviated as yd^{2} or “sq yd.” Also:

1 yd^{2} = 9 ft^{2}

1 yd^{2} = 1296 in^{2}

To convert **square meters** into square yards:

1 sq meter = 1.1960 yd^{2} = 10,000 cm^{2}

### Acres

One **acre** is equal to **43,560** square feet, which is used to measure the area of** land**. It can also be written as:

Area = 208.71 feet × 208.71 feet = 43,560 square feet

This area of land is a square as the **length** and **width** are the same, i.e., **208.71** feet. Also:

1 acre = 4,840 square yards

In **metric** meters, one acre equals **4046.86** square meters. Also:

1 acre = 0.4047 hectares

One **acre** is also equal to four **roods**, and one rood is equal to 40 **perches**.

### Hectare

One hectare(**ha**) is equal to **10,000** square meters. Also:

1 ha = 2.4711 acres

### Square Miles

One square mile consists of **640** acres. It is abbreviated as “ **sq mile**” or mile^{2}. Also:

1 sq mile = 2.59 km^{2}

One square mile is also equal to **258.999** hectares. Also:

1 sq mile = 100 hectares = 0.3861 sq mile

## Volume

A **liquid** has a definite **volume** but no fixed shape. The metric unit of volume is **cubic meters** which are equal to one **kiloliter**. The following **imperial** units are used to measure the volume of a liquid.

### Teaspoon

A teaspoon is the **smallest** unit to measure the volume of a liquid. One imperial teaspoon is equal to** five** milliliters.

### Tablespoon

One tablespoon is equal to half of a **fluid ounce** and also equal to **14.79** milliliters.

### Fluid Ounces

An imperial fluid ounce is **4.08%** smaller than a **US** fluid ounce. So:

1 **imp fl oz** = 0.960799 US fl oz

We also have:

1 US fl oz = 1.0408 imp fl oz

One imperial fluid ounce equals **28.4131** milliliters.

### Cups

One imperial cup equals **284.131** milliliters. Also:

1 imp cup = 9.60 imp fl oz

### Pints

One imperial pint equals **2.4** imperial cups. Also:

1 **imp pint** = 20 fl oz

One imperial pint also equals **568.261** milliliters.

### Quarts

**Two** imperial **pints** make one imperial quart. Also:

1 imp quart = 40 imp fl oz

One quart equals **946.36** ml. Four imp **cups** also make one imp quart.

### Gallons

One imperial **gallon** equals four imperial **quarts**. Also:

1 imp gallon = 8 imp pints

1 imp gallon = 16 imp cups

1 imp gallon = 160 imp fl oz

**Figure 3** shows the imperial unit conversions for **volume**.

## Pressure

Pressure is defined as the **force** per unit **area**. The imperial unit of pressure is pounds per square Inch(**PSI**).

## Temperature

**Fahrenheit** is the imperial unit of temperature, and its **SI** unit is Kelvin.

## Solved Examples of Unit Conversions in the Imperial System

### Example 1 – Imperial Unit Conversion for Length

Convert **20** furlongs into feet.

### Solution

As 1 furlong = 660 feet, so we have:

20 furlongs = 20 ✕ 660 feet = **13,200 feet**

Therefore, **20 furlongs** equals 13,200 feet.

### Example 2 – Imperial Unit Conversion for Area

The **land** has an area of **14,520** square yards. What is this area in **acres**?

### Solution

As 1 acre = 4840 square yards. Since 1 sq yd = 1/4840 acre, then:

14,520 sq yd = 14,520/4,840 acre

Hence:

14,520 sq yd = **3 acres**

Therefore, the **area** of the land is 3 acres.

### Example 3 – Imperial Unit Conversion for Mass

Convert **25** stones into **pounds**. Also, convert the answer into **ounces**.

### Solution

As 1 stone = 14 pounds, we have:

25 stones = 25 ✕ 14 = **350 pounds**

To convert 350 pounds in ounces:

1 lb = 16 oz

350 lb = 350 ✕ 16 oz = **5600 ounces**

### Example 4 – Imperial Unit Conversion for Volume

Convert **30** quarts into imperial fluid ounces.

### Solution

As 1 imp quart = 40 imp fl oz, we can say:

30 imp quarts = 30 ✕ 40 imp fl oz = **1200 imp fl oz**

Hence, **30** imperial quarts are equal to **1200** imperial fluid ounces.

*All the images are created using GeoGebra.*