Physics

Convert between Feet and Meters



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• The Standard or International Foot •

All of the old British Imperial/US Customary units are now defined strictly in terms of SI ("metric") units.  In the USA, NIST (National Institute of Standards and Technology, formerly the National Bureau of Standards), an agency of the Department of Commerce, is responsible for maintaining standards of weights and measures; the conversion factors between legally defined customary units and standard SI units may be found on NIST's website.

Since the inch is exactly 25.4 mm (1 in ≡ 25.4 mm), and one foot is, by definition, twelve inches (1 ft  ≡ 12 in) , one foot is exactly 304.8 mm or 0.3048 m. (1 ft  ≡ 0.3048 m).

Taking the reciprocal of this, we find that there are approximately 3.2808 feet in the SI meter.  (1 m ≈ 3.2808 ft)

This is a non-terminating decimal fraction, with an infinite number of digits.  The exact conversion factor is 1/0.3048 feet/meter.  To convert a length in meters to units of feet, multiply by this conversion factor.  (Formally, all conversion factors equal 1:  1 ft / 0.3048 m ≡ 1.) 

For example, 100 m = 100 m · 1/0.3048 ft/m ≈ 328.08 ft.  The units "multiply" and "divide" as though they are numbers.

Similarly, by squaring the conversion factor, we find

1 ft²  ≡ 0.09290304 m², exactly, or 1 m² ≈ 10.76 ft²

and by multiplying again,

1 ft³  ≡ 0.028316846592 m³, exactly, or 1 m³ ≈ 35.31 ft³


• The Survey Foot or pre-1959 Foot •

The conversion factors above are suitable for most purposes, however, as also discussed by NIST in the NIST Guide to SI Units, the foot and derived units in geodetic surveys are based on an older definition of the foot now known as the "survey foot"; the modern foot is known more formally as the "international foot".  The "foot" referenced in Pre-1959 publications (and post-1959 laggards) is what is now known as the "survey foot".  The survey foot is related to the SI meter by 1 survey foot  ≡ 1200/3937 m exactly.  Thus

1 international ft ≡ 0.999 998 survey ft, exactly.

The symbols are distinguished by use of an italic or slanted typeface, the display of which is currently beyond Helium.com's technical capability; "ft" in italics is a survey foot, not an international foot.  The term "statute mile" refers to 5280 survey feet.  Since the chain, rod,  furlong, fathom, and acre are surveyors' measurements, they, too, are defined in terms of the survey foot, and not the international foot. The two parts in a million difference rarely makes any difference; the difference between either definition of the mile is a mere tenth of an inch, but for purposes of cartography and long-distance surveys with reference to the State Plane Coordinate System, the difference can be significant.


Source:

NIST Guide to SI Units

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ARTICLE SOURCES AND CITATIONS
  • InfoBoxCallToAction ActionArrowhttp://physics.nist.gov/Pubs/SP811/appenB8.html
  • InfoBoxCallToAction ActionArrowhttp://physics.nist.gov/Pubs/SP811/appenB.html#B.6
  • InfoBoxCallToAction ActionArrowhttp://www.nist.gov/physlab/pubs/sp811/index.cfm