## The length of any object or the distance between two points can be measured in metric or imperial units.

### Metric System

The basic unit of length in the metric system is metre (m). Other units of measure can be derived by combining a prefix with the base unit, e.g. 1km (m combined with prefix k) meaning 1m multiplied by 1000 (=1000m) or 1cm (m combined with prefix c) meaning one-hundredth of 1m (0.01m).

#### Metric Units Table

Prefix | Meaning | Value |
---|---|---|

yotta (Y) | 10^{24} | 1 Ym = 1 000 000 000 000 000 000 000 000 m |

zetta (Z) | 10^{21} | 1 Zm = 1 000 000 000 000 000 000 000 m |

exa (E) | 10^{18} | 1 Em = 1 000 000 000 000 000 000 m |

peta (P) | 10^{15} | 1 Pm = 1 000 000 000 000 000 m |

tera (T) | 10^{12} | 1 Tm = 1 000 000 000 000 m |

giga (G) | 10^{9} | 1 Gm = 1 000 000 000 m |

mega (M) | 10^{6} | 1 Mm = 1 000 000 m |

kilo (k) | 10^{3} | 1 km = 1 000 m |

hecto (h) | 10^{2} | 1 hm = 100 m |

deka (da) | 10^{1} | 1 dam = 10 m |

1 m = 1 m | ||

deci (d) | 10^{-1} | 1 dm = 0.1 m |

centi (c) | 10^{-2} | 1 cm = 0.01 m |

milli (m) | 10^{-3} | 1 mm = 0.001 m |

micro (μ) | 10^{-6} | 1 μm = 0.000 001 m |

nano (n) | 10^{-9} | 1 nm = 0.000 000 001 m |

pico (p) | 10^{-12} | 1 pm = 0.000 000 000 001 m |

femto (f) | 10^{-15} | 1 fm = 0.000 000 000 000 001 m |

atto (a) | 10^{-18} | 1 am = 0.000 000 000 000 000 001 m |

zepto (z) | 10^{-21} | 1 zm = 0.000 000 000 000 000 000 001 m |

yocto (y) | 10^{-24} | 1 ym = 0.000 000 000 000 000 000 000 001 m |

#### Metric Unit Conversion

Follow steps below to calculate correct metric unit conversion, e.g. convert 1000000 cm to km.

###### Step 1:

Note the value with the original metric unit as a fraction, e.g.:

1000000 cm | = | 1000000 cm |

1 |

###### Step 2:

Look up the metric units table and find the cm to base unit ratio (1 cm = 0.01 m). Multiply the fraction noted in step 1 with the found ratio, also noted as fraction. Note the base unit value (0.01 m) as numerator and the original metric unit (1 cm) as denominator of the new fraction, e.g.:

1000000 cm | = | 1000000 cm | × | 0.01 m |

1 | 1 cm |

###### Step 3:

Look up the metric units table and find the km to base unit ratio (1 km = 1000 m). Multiply the fractions noted in step 2 with the found ratio, again noted as fraction. Note the required metric unit (1 km) as numerator and the base unit value (1000 m) as denominator of the new fraction, e.g.:

1000000 cm | = | 1000000 cm | × | 0.01 m | × | 1 km |

1 | 1 cm | 1000 m |

###### Step 4:

Almost done. Cross cancel metric units (cm and m) and calculate the required value, converted to the required metric unit value (km).

1000000 cm | = | 1000000 cm | × | 0.01 m | × | 1 km | = | 10 km |

1 | 1 cm | 1000 m |

See the Units of Measure: Length - Worksheet 1 for some worked problems.

### Imperial System

Imperial units of measurement are the units that were first defined in the British Weights and Measure Act of 1824, without a particular base unit. These units were in common usage in Ireland and the UK until the adoption of the metric system in the early 1970s. However, imperial units have continued to be in everyday use to varying degrees.

#### Imperial Units Table

Unit | Meaning | Value |
---|---|---|

mile (mi) | 8 furlongs | 1 mi = 5280 ft |

furlong (fur) | 10 chains | 1 fur = 660 ft |

chain (ch) | 22 yards | 1 ch = 66 ft |

yard (yd) | 3 feet | 1 yd = 3 ft |

foot (ft) | 1 ft = 1 ft | |

inch (in) | 1/12 foot | 1 in = 1 twelfth of a foot |

thou (th) | 1/12 000 foot | 1 th = twelve thousandths of a foot |

#### Imperial Unit Conversion

Follow steps below to calculate correct imperial unit conversion, e.g. convert 72000 in to mi.

###### Step 1:

Note the value with the original imperial unit as a fraction, e.g.:

72000 in | = | 72000 in |

1 |

###### Step 2:

Look up the imperial units table and find the inch to foot ratio (1 in = 1 twelfth of a foot ft). Multiply the fraction noted in step 1 with the found ratio, also noted as fraction. Note the foot unit value (1 twelfth of a foot) as numerator and the original imperial unit (1 in) as denominator of the new fraction, e.g.:

72000 in | = |
| × |
| |||||

1 | 1 in |

###### Step 3:

Look up the imperial units table and find the mile to foot ratio (1 mi = 5280 ft). Multiply the fractions noted in step 2 with the found ratio, again noted as fraction. Note the required imperial unit (1 mi) as numerator and the foot unit value (5280 ft) as denominator of the new fraction, e.g.:

72000 in | = |
| × |
| × |
| |||||||

1 | 1 in | 5280 ft |

###### Step 4:

Cross cancel imperial units (in and ft).

72000 in | = |
| × |
| × |
| |||||||

1 | 1 in | 5280 ft |

###### Step 5:

The inch to foot ratio (1 twelfth of a foot ft) creates a complex fraction. Simplify before calculating.

72000 in | = | 72000 | × | 1 | ÷ | 1 | × | 1 mi |

1 | 12 | 1 | 5280 |

Invert the third fraction and calculate the required value, converted to the required imperial unit value (mi).

72000 in | = | 72000 | × | 1 | × | 1 | × | 1 mi | = | 1.136 mi | = | 1 mi | + | 0.136 mi |

1 | 12 | 1 | 5280 |

###### Step 6:

Adapt above steps to convert the fractional part (0.136 mi) of the required imperial unit value to a smaller imperial unit value (fur).

72000 in | = | 1 mi | + | 0.136 mi | × | 5280 ft | × | 1 fur | = | 1 mi | + | 1.09 fur |

1 | 1 mi | 660 ft |

###### Step 7:

Continue to repeat above steps to convert any fractional part until the fractional part equals zero or can be rounded up/down to zero.

72000 in | = | 1 mi | + | 1 fur | + | 0.09 fur | × | 660 ft | × | 1 ch | = | 1 mi | + | 1 fur | + | 0.90 ch |

1 | 1 fur | 66 ft |

72000 in | = | 1 mi | + | 1 fur | + | 0 ch | + | 0.90 ch | × | 66 ft | × | 1 yd | = | 1 mi | + | 1 fur | + | 19.9 yd |

1 | 1 ch | 3 ft |

72000 in | = | 1 mi | + | 1 fur | + | 20 yd |

See the Units of Measure: Length - Worksheet 2 for some worked problems.

### Standard Conversion

The International Yard and Pound agreement defined 1 yard as exactly 0.9144 metre and 1 inch as exaclty 2.54 centimetre.

#### Metric to imperial Unit Conversion

Follow steps below to calculate correct metric to imperial unit conversion, e.g. convert 2032 cm to ch.

###### Step 1:

Note the value with the original metric unit as a fraction, e.g.:

2032 cm | = | 2032 cm |

1 |

###### Step 2:

Look up the metric units table and find the cm to base unit ratio (100 cm = 1 m). Multiply the fraction noted in step 1 with the found ratio, also noted as fraction. Note the base unit value (1 m) as numerator and the original metric unit value (100 cm) as denominator of the new fraction, e.g.:

2032 cm | = | 2032 cm | × | 1 m |

1 | 100 cm |

###### Step 3:

We know that 1 yard equals exactly 0.9144 metre (1 yd = 0.9144 m). Multiply the fractions noted in step 2 with this ratio, noted as fraction. Note the imperial yard unit value (1 yd) as numerator and the metric metre unit value (0.9144 m) as denominator of the new fraction, e.g.:

2032 cm | = | 2032 cm | × | 1 m | × | 1 yd |

1 | 100 cm | 0.9144 m |

###### Step 4:

Look up the imperial units table and find the yard to foot ratio (1 yd = 3 ft). We use this ratio as foot is the common unit listed in the imperial units table. Multiply the fractions noted in step 3 with the found ratio, again noted as fraction. Note the foot unit value (3 ft) as numerator and the yard unit value (1 yd) as denominator of the new fraction, e.g.:

2032 cm | = | 2032 cm | × | 1 m | × | 1 yd | × | 3 ft |

1 | 100 cm | 0.9144 m | 1 yd |

###### Step 5:

Step 4 converted to feet as feet is the common unit listed in the imperial units table. We use step 5 to convert to the required chains.

Look up the imperial units table and find the chain to foot ratio (1 ch = 66 ft). Multiply the fractions noted in step 4 with the found ratio, again noted as fraction. Note the required imperial unit (1 ch) as numerator and the foot unit value (66 ft) as denominator of the new fraction, e.g.:

2032 cm | = | 2032 cm | × | 1 m | × | 1 yd | × | 3 ft | × | 1 ch |

1 | 100 cm | 0.9144 m | 1 yd | 66 ft |

###### Step 6:

Cross cancel metric units (cm and m) and imperial units (yd and ft). Calculate the required value, converted to the required imperial unit value (ch).

2032 cm | = | 2032 cm | × | 1 m | × | 1 yd | × | 3 ft | × | 1 ch | = | 1.01 ch |

1 | 100 cm | 0.9144 m | 1 yd | 66 ft |

###### Step 7:

Calculating the required value in step 6 resulted in 1 ch and a fractional part of 0.01. We adapt the imperial unit conversion steps to convert this fractional part to smaller imperial units, repeating these steps until the fractional part equals zero or can be rounded up/down to zero.

2032 cm | = | 1 ch | + | 0.01 ch | × | 66 ft | × | 1 yd | = | 1 ch | + | 0.2 yd |

1 | 1 ch | 3 ft |

2032 cm | = | 1 ch | + | 0 yd | + | 0.2 yd | × | 3 ft | = | 1 ch | + | 0.6 ft |

1 | 1 yd |

2032 cm | = | 1 ch | + | 0 ft | + | 0.6 ft | × | 1 in | = | 1 ch | + | 0.6 | × | 1 in | × | 12 | = | 1 ch | + | 8 in |

1 |
| 1 | 1 | 1 |

#### Metric to Imperial Conversion Table

Metric | Imperial mile ^{*)} | Imperial yard ^{*)} | Imperial feet ^{*)} | Imperial inch ^{*)} |
---|---|---|---|---|

1 km | 0.621371192 mi | 1093.613298338 yd | 3280.839895013 ft | 39370.078740158 in |

1 m | 0.000621371 mi | 1.0936132983 yd | 3.280839895 ft | 39.370078740 in |

1 cm | 0.000006213 mi | 0.0109361329 yd | 0.032808398 ft | 0.393700787 in |

1 mm | 0.000000621 mi | 0.0010936132 yd | 0.003280839 ft | 0.039370078 in |

^{*)}Rounded to 9 decimal places.

#### Imperial to Metric Unit Conversion

Follow steps below to calculate correct imperial to metric unit conversion, e.g. convert 5 mi to km.

###### Step 1:

Note the value with the original imperial unit as a fraction, e.g.:

5 mi | = | 5 mi |

1 |

###### Step 2:

Look up the imperial units table and find the mi to foot unit ratio (1 mi = 5280 ft). Start by converting to feet as feet is the common unit listed in the imperial units table. Multiply the fraction noted in step 1 with the found ratio, also noted as fraction. Note the common imperial value (5280 ft) as numerator and the original imperial unit (1 mi) as denominator of the new fraction, e.g.:

5 mi | = | 5 mi | × | 5280 ft |

1 | 1 mi |

###### Step 3:

We know that 1 yard equals exactly 0.9144 metre (1 yd = 0.9144 m). Convert from ft to yd to use this ratio. Look up the imperial units table and find the yard to foot ratio (1 yd = 3 ft). Multiply the fractions noted in step 2 with the found ratio, again noted as fraction. Note the required imperial unit (1 yd) as numerator and the foot unit value (3 ft) as denominator of the new fraction, e.g.:

5 mi | = | 5 mi | × | 5280 ft | × | 1 yd |

1 | 1 mi | 3 ft |

Continue to add an additional fraction to convert from yd to m. Note the metric unit value (o.9144 m) as numerator and the imperial yard unit value (1 yd) as denominator of the new fraction, e.g.:

5 mi | = | 5 mi | × | 5280 ft | × | 1 yd | × | 0.9144 m |

1 | 1 mi | 3 ft | 1 yd |

###### Step 4:

Look up the metric units table and find the km to metric base unit ratio (1 km = 1000 m). Multiply the fractions noted in step 3 with the found ratio, again noted as fraction. Note the required metric unit (1 km) as numerator and the base unit value (1000 m) as denominator of the new fraction, e.g.:

5 mi | = | 5 mi | × | 5280 ft | × | 1 yd | × | 0.9144 m | × | 1 km |

1 | 1 mi | 3 ft | 1 yd | 1000 m |

###### Step 5:

Cross cancel imperial units (mi, ft and yd) and metric unit (m). Calculate the required value, converted to the required metric unit value (km).

5 mi | = | 5 mi | × | 5280 ft | × | 1 yd | × | 0.9144 m | × | 1 km | = | 8.04672 km |

1 | 1 mi | 3 ft | 1 yd | 1000 m |

#### Imperial to Metric Conversion Table

Imperial | Metric kilometre | Metric metre | Metric centimetre | Metric millimetre |
---|---|---|---|---|

1 mi | 1.609344 km | 1609.344 m | 160934.4 cm | 1609344 mm |

1 yd | 0.0009144 km | 0.9144 m | 91.44 cm | 914.4 mm |

1 ft | 0.0003048 km | 0.3048 m | 30.48 cm | 304.8 mm |

1 in | 0.0000254 km | 0.0254 m | 2.54 cm | 25.4 mm |