How big is a foot? In the United States, that depends on which of the two official foot measurements you are talking about. If it comes as a surprise that there are two feet, how about this: One of those feet is about to go away.
The first foot is the old U.S. survey foot from 1893. The second is the newer, shorter and slightly more exact international foot from 1959, used by nearly everybody except surveyors in some states. The two feet differ by about one hundredth of a foot (0.12672 inches) per mile — that’s two feet for every million feet — an amount so small that it only adds up for people who measure over long distances.
Surveyors are such people. For more than six decades, they have been toggling between the two units, depending on what they are measuring and where.
The toggling does not always work. Michael L. Dennis, an Arizona-based surveyor and geodesist with the National Geodetic Survey, has been cataloging mix-ups with the two feet for years and repairing errors. Last year, he had enough.
“I kept running into these problems with different versions of the foot, and I thought it was ridiculous that this thing had gone on this long,” he said. “So I had this secret desire to kill off the U.S. survey foot, and I’d been harboring that for years.”
Most states mandate the use of the old U.S. survey foot for their state coordinate systems, which allow surveyors to take into account Earth’s curvature in their measurements. A few states mandate the use of the new, international foot. A handful do not specify which of the two feet should be used. Arizona, for example, is an international-foot state, but when employees with the Federal Aviation Administration or the U.S. Army Corps of Engineers or the Park Service measure there, they use the U.S. survey foot.
“There’s a recipe for disaster right there, and I’m getting this all the time,” Dr. Dennis said.
While such differences might seem merely philosophical, they can have vital and costly consequences in the real world. In one case, in a certain city that Dr. Dennis declined to name, the construction of a downtown high-rise that sat in the approach path to an international airport was delayed while the building was redesigned to be one floor shorter.
Other problems crop up when surveyors measure from one state to the next, unaware that the two states use different feet. In some cases, large projects employ international surveying firms whose employees are unaware that America has two feet. Some surveying computer software will not recognize the existence of two feet and even hand calculators usually default to the international foot.
Occasionally, surveyors must use one foot for horizontal measurements and the other for elevations. That happened to Dr. Dennis on an engineering project in Arizona. But while the geospatial software was capable of acknowledging both feet, it would not allow for different feet in different directions. He resolved the problem by converting everything to international feet and massaging the vertical measurements, which ought to have been in U.S. survey feet.
“It’s bad enough that people are worried about getting sued over it or losing clients,” Dr. Dennis said.
And then there’s the problem of knowing which foot is which. Even the National Geodetic Survey gets muddled. In a video about how not to mix up the two feet, it mixed them up. It wrongly said that 2,000 meters was 6,561.67 international feet and 6,561.68 U.S. survey feet, reversing the correct conversions. The error went unnoticed for years until Dr. Dennis watched the video recently as he plotted to kill the old foot. He was mortified.
“This provides yet more evidence of the folly of maintaining two nearly identical versions of the same foot,” he wrote in an email.
Fed up, Dr. Dennis broached the subject of retiring, or deprecating, the old U.S. survey foot with his boss, Juliana P. Blackwell, the director of the National Geodetic Survey. The nation’s geodesists are already in the throes of recalibrating the coordinates of the National Spatial Reference System, which is needed to measure where the U.S. exists geographically. It seemed like a golden opportunity to ask those who measure the nation to shift to one foot instead of two, Ms. Blackwell said.
“It’s one of those things that’s been with you for so long you forget that there’s an opportunity here to make things more accurate,” she said.
So, last April, Dr. Dennis braced for the worst, traveled to Arlington, Va., and told a meeting of the nation’s surveyors that the old foot was on its way out, a casualty of modernity.
“The joke was, the people who knew I was doing this said I need to wear a bulletproof vest,” he said.
To his surprise, the directors of the National Society of Professional Surveyors were in favor of the shift to a single foot. Although the directors don’t have a role in the decision, they wanted to know how their members would react. A poll told them that most support the move. But others consider it akin to blasphemy.
“One thing is, let’s be honest, the actual name, the U.S. survey foot,” said Timothy W. Burch, the society’s president-elect, who is in favor of retiring the old foot. “For unfortunately a lot of Americans, especially in this day and age, anything that has to do with the U.S. and that naming quality being taken away, it’s like we’re under attack. So there is a portion of the country that’s like, No, this is ours, this is what we’re going to keep.”
It’s no surprise that some Americans are reluctant to do away with the old foot, said Robert P. Crease, a philosopher and historian of science at the State University of New York at Stony Brook and the author of “World in the Balance: The Historic Quest for an Absolute System of Measurement.”
“The way we measure shapes our imagination,” he said. “Changing the way that you measure requires changing the imagination, and that’s really difficult. It sounds like a neutral activity but it’s anything but.”
A step back in time
The choice of units of measurement is also laden with history. As settlers began to colonize America, they brought with them measurements from their former countries. These included the English ell for cloth but also the far shorter Dutch ell, the Rhineland rod and the British chain and the Spanish vara for measuring land, the English flitch of bacon and hattock of grain, plus the German quentchen for gold.
By the time of Independence, 100,000 units of measurement were in use, Andro Linklater, a British historian, recounted in “Measuring America: How the United States Was Shaped By the Greatest Land Sale in History.” Opportunities for cheating were rife. Establishing common measurements, and therefore fair trade, became a political imperative.
The first message to Congress by President George Washington, in January 1790, contained a call to lawmakers about the importance of establishing a standard system of weights and measurements. Their solution was to adopt parts of the British imperial system, including the yard. In 1815, a brass yard bar made by the Edward Troughton, a London instrument maker, arrived in the U.S. to become the American standard yard.
By 1850, most states then in the union had received official copies of that yard and the other standards, a bid to make sure that every citizen and enterprise in the nation had equal access to the same units of measurement.
But imperial measurements, while standard, were also arbitrarily derived. The yard, for instance, evolved from the idea that “foure graines of barley make a finger, foure fingers a hande, foure handes a foote,” Mr. Linklater noted. During the reign of Elizabeth I, those 16 fingers per foot became 12 inches and were tripled to make the yard that Mr. Troughton fashioned into a bar for America.
Even as the U.S. government shipped imperial standards across the country, the move to metric was gaining appeal in America and elsewhere, driven by a hunger for ever greater precision and easier replicability. Decimalized metric standards, which were being developed by French scientists at the urging of its National Assembly during the French Revolution, are based on scientific findings rather than folksy norms, and these days units increasingly relate to each other. The meter was originally based on one ten-millionth the distance from the geographic North Pole to the Equator; it is now derived from the speed of light. Volume and mass, in turn, are based on the meter.
By 1866, Congress legalized the use of metric units across the U.S., setting the meter 39.37 inches long, and in 1875, America was among the original 17 signatories of the Treaty of the Metre, which aimed to establish metric standards across the world. America broke with the imperial system of measurement in 1893 and officially adopted metric standards under the order of Thomas Mendenhall, then the superintendent of the U.S. Coast and Geodetic Survey, the forerunner of the National Geodetic Survey.
That means imperial-sounding measurements are actually derived from metric units. So at that point, the foot became a fraction of a meter. The math works like this: 36 inches divided by 3 feet is a foot, or 12 inches. Divide that by the number of inches in a meter: 39.37. Move the decimal places for ease of calculation and you get one foot is 1200/3937 of a meter, a ratio whose run-on decimal places (0.3048006096….) make it slightly imprecise because the measurement will always need to be rounded.
But the 20th century demanded greater exactitude, for the sake of accuracy as well as for international trade in machine-tooled industrial components.
“We believe that there is romance in precision measurement, and that ability to extend the absolute accuracy of measurement by one decimal place frequently demands as much in ingenuity, perseverance and analytical competence as does the discovery of a new principle or effect in science,” Allen V. Astin, then the director of the National Bureau of Standards, said in a speech to the American Physical Society in 1953.
In 1959, the U.S. redefined the foot to align with international standards, making it exactly 0.3048 of a meter, a difference of two parts per million from the old foot. The new foot became known as the international foot.
The government allowed geodesists and surveyors to keep using the foot of 1893, which became known as the U.S. survey foot, in deference to the historical measurements they relied on, with the understanding that they would eventually embrace the new foot.
One foot forward
Whether they embrace the new one or not, the old foot will be obsolete as of Jan. 1, 2023, according to the National Institute of Standards and Technology, the agency within the Department of Commerce with the authority to fix weights and measures for the U.S.
“At that point, we will discourage everyone from using the U.S. survey foot,” said Elizabeth Benham, the institute’s metric program coordinator.
The switch to a single foot, which will be known as either the international foot or simply the foot, is too subtle to require surveyors to purchase new yardsticks or measuring tapes, but it is part of an intellectual retooling among those who, as Mr. Linklater wrote, practice the “masochistic science” of land measurement.
Once, surveyors depended on handwritten deeds or plaques with century-old notes to describe plots of land, said Mr. Burch of the National Society of Professional Surveyors. Later, when Mr. Burch learned the profession from his father in the 1980s, each job felt like its own world, he said.
Today, thanks to global navigational satellite systems such as GPS, every measurement is part of a master global coordinate system. The way Mr. Burch sees it, moving to a single American foot is a small step in the long march toward standardization and precision.
“It’s funny how protective people have gotten over this change,” Mr. Burch said. “It’s just not taking into account that science and technology has allowed us to get that much smarter about this big blue marble we live on.”
As for Dr. Dennis, his successful campaign to get rid of the old foot leaves him feeling that he has made an important contribution to America’s future.