Length

Length - imperial

The following table illustrates the conversion factors of common imperial (and U.S. customary) length measurement units. In the United States the "survey" definition of length is still used for the purposes of surveying land. According to the U.S. N.I.S.T. the original American defintion of the metre was exactly 39.37 inches as defined by the U.S. Metric Law of 1866. This defined the yard as being 3600/3937 metre (1 ft = 1200/3927 m, 1 in = 1/3937 m). In 1959 the U.S. standardized their yard to be equal to those used by other countries and thus it was defined as being exactly 0.9144 metre (1 ft = 0.3048 m, 1 in = 0.0254 m). The original definition of the foot (1200/3937 m) was retained as the "U.S. survey foot". The international or "statute" foot is thus 0.999 998 U.S. survey foot.

This table reflects the official defintion of the yard as being 0.9144 metre. All imperial and U.S. customary measurement units (length, area, volume, and mass) are internationally defined using metric units.

Note that the metric equivalents of imperial measures are exact conversions.

Table 1. Imperial length unit conversion factors.

LENGTHmilinchfootyardrodchainfurlongmileleaguemetric
mil125.4 µm
inch1 000125.4 mm
foot12130.48 cm
yard3630.9144 m91.44 cm
rod19816.55.515.0292 m
chain79266224120.1168 m
furlong7 92066022040101201.168 m
mile63 3605 2801 76032080811 609.344 m
league190 08015 8405 28096024024314 828.032 m

Length - metric

This second table illustrates the relationship between metric units of length. The metre is the base unit of length. All other length units are base-10 multiples or submultiples of the metre. The metre was originally defined as being 1/10 000 000 of the distance from the North Pole to the Equator along the line of longitude passing through Paris, France. The International Bureau for Weights and Measures (BIPM) is the agency responsible for maintaining international metric standards. Members are from 48 countries and including the United Kingdom, Canada, and the United States. The BIPM currently defines the metre as being the distance travelled by light in a vacuum in 1/299 792 458 of a second. The speed of light is a physical constant and using the speed of light to define the metre reflects the current technological level of precision required for scientific pursuits. While the defintion of the metre has changed the actual physical length of the metre has not changed since its creation in the late 1700s. This makes the metre a longer lived physical unit than the yard.

Note that the imperial equivalents listed for metric units are approximate.

Table 2. Relationship between metric units of length.

LENGTHnmµmmmcmdmmdamhmkmimperial
nm10.000 000 0010.004 mil
µm1 00010.000 0013.937 mil
mm1E+061 00010.0010.039 in
cm1E+0710 0001010.010.394 in
dm1E+08100 0001001010.13.937 in
m1E+091 000 0001 00010010139.37 in
dam1E+101E+0710 0001 00010010132.81 ft
hm1E+111E+08100 00010 0001 000100101328.1 ft
km1E+121E+091 000 000100 00010 0001 0001001013 280.8 ft
Mm1E+151E+121E+091E+081E+071 000 000100 00010 0001 000621.4 mi
Gm1E+181E+151E+121E+111E+101 000 000 000100 000 00010 000 0001 000 000621 371.2 mi

Notes

The numbers in the tables are written using the international standard method of grouping by using a space rather than a comma to group multiples of 1000.

Long numbers are written using standard scientific notation (E) as a means of saving space. For example, the number 1E+06 represents the number one-million (1 000 000, a 1 with 6 zeros following), the number 1E+09 represents the number one-billion (1 000 000 000, a 1 with 9 zeros following), and the number 1E+12 represents the number one-trillion (1 000 000 000 000, a 1 with 12 zeros following).



10 cm ruler

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