Units of length
Units of length are measurement standards used to quantify distance, which has been essential for human activities since the time of early hunter-gatherers. Historically, many initial units were derived from human anatomy, such as the foot, which remains a fundamental unit in the American customary system. This system, also known as the American system, features units like inches, yards, and miles, with a foot measuring approximately 0.3048 meters. In contrast, the metric system, or Système International d’Unitès (SI), utilizes the meter as its base unit, with additional subdivisions including centimeters, millimeters, and kilometers. While the American system is predominantly used in the United States, the metric system is the global standard in most other countries and is preferred in scientific contexts.
Length measurements vary widely, with units like the light-year and parsec used for astronomical distances, while smaller measurements can be expressed in micrometers and nanometers. Specialized fields may still employ units from historical systems, such as furlongs in horse racing or fathoms in marine contexts. Understanding these units is crucial for various practical applications, making the study of length systems a fundamental aspect of science, engineering, and daily life.
Units of length
SUMMARY: Numerous units of length exist and are used according to the distance measured.
Measuring length or distance has been necessary as far back as the oldest hunter-gatherer peoples in order to perform necessary tasks, such as traveling and finding or hunting food. Many of the first units of length were derived from bodily measurements. Modern units of length can broadly be divided into two categories: the United States customary system and the Système International d’Unitès (SI), or International System of Units. The US customary system is more commonly known as the “American system.” The SI is more commonly known as the “metric system.” The basic unit of length in the American system is the foot, while the basic unit of length in the metric system is the meter. The American system is used more often in the United States, while the metric system is common in most other countries. Scientific journals almost always report measurements in metric units. The exact values of length measurements depend on the units chosen, but certain constants (like π) that are fundamental to related measurements (like circumference) are unitless.
American System
The American system of lengths is similar to the British imperial system from which the American system takes its historical roots. The basic unit of measurement is the foot (ft), which originally was set to be the length of an adult man’s foot. Each foot is approximately 0.3048 meters. Smaller distances in the American system are typically measured in inches (in) or, less commonly, in mils. There are 12 inches in a foot and 1,000 mils in an inch. Rather than mils, it is much more common to use fractions of an inch to obtain additional accuracy in the American system. Longer distances in the American system are usually measured in yards (yd) or miles (mi). There are three feet in a yard and 1,760 yards in a mile (5,280 feet in a mile).
Metric System
The meter was established in France as one ten-millionth of the distance from the Earth’s equator to the North Pole along the meridian passing through Paris. However, in 1983, it was defined as 1/299,792,458 of the distance traveled by light in a second in a vacuum. In 2019, the SI revised the definition of several units of measurement, including length, as the definition of the second was changed to be more accurate. However, this change only impacted the unit of measurement for scientific purposes. Individuals who use meters in everyday life were not impacted. Smaller units of length in the metric system are often measured in centimeters (cm), millimeters (mm), micrometers (μm, also known as the micron), and nanometers (nm). There are 100 centimeters in a meter and 1000 millimeters in a meter. Similarly, there are 1 million micrometers in a meter and 1 billion nanometers in a meter. Longer distances are usually measured in kilometers (km). There are 1000 meters in a kilometer, which are sometimes referred to as “klicks” in the military. The fermi (fm) and the angstrom (Å) are also units of length in the metric system, though they are not officially part of the international system. There are 10-15 fermi in a meter and 10 trillion angstroms in a meter. Because of their small length, the fermi and the angstrom are best suited for very small distances. Less common units of length in the metric system include the decimeter (one-tenth of a meter), picometer (10-12 meters), decameter (10 meters), megameter (1 million meters), gigameter (1 billion meters), and petameter (1015 meters).
Atomic and Astronomic Measurements
Atomic measurements are also given in terms of either Planck length or the Bohr radius. The Planck length is defined in terms of Planck’s constant, the gravitational constant, and the speed of light in a vacuum. The result is that the Planck length is based entirely on universal constants rather than human constructs, such as the second. A Planck length is approximately 1.616255×10-35 meters. The Bohr radius is defined as the expected distance between the nucleus of a hydrogen atom and its electron in the Bohr model of the atom. The Bohr radius is approximately 5.29177×10-11 meters.
Astronomical distances are typically given in terms of light-years, astronomical units, or parsecs. The light-year is defined as the distance light travels in a vacuum in a Julian year (365.25 days). The light year is approximately 9,460,730,472,580×1012 kilometers or 5,878,630,000,000x1012 miles. Distances such as the light-second, the light-minute, and the light-month are defined analogously to the light-year. The astronomical unit is defined as the average distance between the Earth and the sun, approximately 149,597,871 kilometers or 92,955,807 miles. The parsec is defined in terms of the astronomical unit and an angle with measure one arc second. The imaginary right triangle that defines the parsec has one angle with measure one arc second. The opposite side of the triangle from this angle has length equal to one astronomical unit. The length of the adjacent side to this angle is defined as a parsec and can be derived using basic trigonometry. There are approximately 3.26156 light-years in a parsec.
Other Measurements
There are a number of units of length that are based on the American system and still in use in certain professions in the twenty-first century. A furlong is often used in horse racing and is defined as one-eighth of a mile (220 yds). The hand is a unit of length used to describe the height of a horse and is equivalent to four inches. Rods (5.5 yds or 16.5 ft), sometimes called a pole or perch, and chains (22 yds or 66 ft) are often used in surveying. A fathom is often used to measure the depth of water and is equal to 6 feet. A nautical mile is approximately equal to one minute of latitude. Thus, there are 1852 meters or 6076.12 feet in a nautical mile. Fathoms and nautical miles are often used by mariners.
There are also a number of archaic units of length that may be familiar to the reader, most significantly the cubit (1.5 ft) and the league. The dimensions of Noah’s Ark, as well as other biblical artifacts, are given in cubits. The league has several different values, however, the most common is the distance that a person can walk in an hour (approximately 3 miles). The league was featured in the title of Jules Verne’s Twenty Thousand Leagues Under the Sea (1870).
Bibliography
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Hopkins, Robert A. The International (SI) System and How It Works. AMJ Publishing, 1975.
Liflander, Pamela. Measurements & Conversions. Running Press, 2003.
Wildi, Theodore. Metric Units and Conversion Charts. Wiley-IEEE Press, 1995.
Young, Hugh D., et al. University Physics With Modern Physics. 15th ed., Pearson, 2020.