US survey foot vs international foot

Two different feet have been in lawful use in the United States, and they differ by two parts per million. On a tape length the difference is invisible. On a State Plane coordinate it is feet. Every year, projects are built on coordinates that were converted with the wrong one, and the symptom is always the same: everything is internally consistent, everything checks against itself, and the whole job sits several feet from where it belongs.

The distinction is not a historical curiosity that has been tidied away. Legacy data will outlive all of us, and a survey foot coordinate does not announce itself. A dataset in feet is ambiguous unless something external tells you which foot, and a converter that silently assumes one corrupts every coordinate it touches by an amount too small to notice and too large to accept.

This page covers the two definitions, the exact ratio between them, where they came from, the deprecation of the US survey foot, why coordinates in State Plane feet are overwhelmingly in survey feet, how far apart the two feet get at realistic magnitudes, how to work out which foot a dataset uses, and what to do when you cannot.

The two definitions

International foot

Exactly 0.3048 meters. Defined by the International Yard and Pound Agreement of 1959, which fixed the yard at exactly 0.9144 meters. This is the foot used everywhere in the world that uses a foot at all, and it is the foot meant by an unqualified reference to the foot outside a surveying context.

US survey foot

Exactly 1200/3937 meters, which is 0.30480060960121920… meters. It is exact as a fraction and non-terminating as a decimal. It descends from the Mendenhall Order of 1893, which defined the United States yard as 3600/3937 meters, and it was retained for surveying and mapping when the international foot was adopted in 1959.

Because the survey foot is defined through 3937, the meter-to-foot direction is the tidy one: one meter is exactly 39.37 US survey inches, so one meter is 3.28083333… US survey feet. In international feet the same meter is 3.280839895013… feet. That difference in the seventh significant figure is the whole problem.

The exact ratio

Divide one definition by the other and the ratio is 1.000002 to seven significant figures. Carried further it is 1.000002000004000008…, a recurring pattern that falls out of the arithmetic of 1200/1199.9976. For every practical purpose the useful statement is the simple one: the US survey foot is longer than the international foot by exactly two parts per million.

Two parts per million is a strange size of error. It is far below the precision of any single field measurement, which is why it never shows up in a check on a distance. It is far above the precision at which State Plane coordinates are published and used, which is why it shows up immediately in position. The error scales with the magnitude of the number, not with the accuracy of the work, and that is the property that makes it dangerous: a survey good to a hundredth of a foot can be misplaced by four feet without a single bad observation.

How far apart the two feet get

The divergence is a straight multiplication: the difference is the figure itself times 0.000002. The table below is that product at magnitudes a surveyor actually encounters, from a tape length to a State Plane northing.

Areas diverge twice as fast

An area is a length squared, so the ratio between areas computed in the two feet is 1.000002 squared, which is 1.000004000004 — a difference of four parts per million rather than two. The acre is unaffected as a definition, because 43,560 square feet is exact regardless of which foot is squared; what changes is the physical size of the square foot, and therefore of the acre.

Where the two feet came from

In 1893 the Office of Weights and Measures, under the Mendenhall Order, abandoned physical prototype standards for the yard and pound and redefined them in terms of the meter. The United States yard became 3600/3937 meters, which makes the foot 1200/3937 meters. Every public land survey, every early triangulation network and every State Plane zone that followed was computed on that foot.

In 1959 the English-speaking countries harmonised their units. The International Yard and Pound Agreement set the yard at exactly 0.9144 meters, shortening the United States yard by two parts per million. Recognising that changing the foot underneath a century of geodetic and cadastral data would be worse than living with two feet, the United States exempted surveying: the older foot was retained for that purpose and given the name US survey foot, while the new one became the international foot.

The deprecation

In 2019 the National Institute of Standards and Technology and the National Geodetic Survey jointly announced that the US survey foot would be deprecated, and that it should not be used for new work after 31 December 2022. From that date the international foot is the foot of the United States for all purposes, and the modernised National Spatial Reference System is defined in meters, with foot conversions to be made using the international foot.

Deprecation is not deletion. It governs what you should use going forward; it says nothing about how to read what already exists. Every coordinate published in the previous century remains in survey feet, and a deed, a plat or a control sheet does not become international-foot data because the definition moved. Treating a legacy value as though the deprecation retroactively reinterpreted it is the single most common way the announcement gets misapplied.

Why State Plane coordinates in feet are usually US survey feet

The State Plane Coordinate System was defined in the 1930s on the foot then in use, and its zone constants — false eastings, false northings, central meridian scale factors — were published accordingly. When the system was readjusted onto NAD83 the defining parameters were expressed in meters, and states that wanted coordinates in feet legislated a conversion. The overwhelming majority legislated the US survey foot, because that was the foot every existing monument coordinate was already in and because switching would have shifted every published value.

A small number of jurisdictions adopted the international foot instead, so the assumption is strong rather than universal. If you work in one place, find out once which foot your state defines and write it down. If you work across state lines, check every time; the boundary between the two conventions is a state line, not a project line.

The tell is often in the zone constants themselves. A false easting of 600,000 meters converts to exactly 1,968,500.00 US survey feet — a round number, because 600,000 divided by 1200/3937 is exactly 500 times 3937. The same 600,000 meters in international feet is 1,968,503.937, which is not round at all. Constants that come out clean in one foot and ragged in the other are telling you which foot the published table was built on.

How to tell which foot a dataset uses

The question is never answered by looking at the numbers alone, because both interpretations produce plausible coordinates. It is answered by finding the statement of provenance, and failing that, by testing against something you already trust.

1. Read the metadata properly. A coordinate reference system identifier that names the unit is definitive: a well-known-text definition or an EPSG code distinguishes a survey-foot zone from an international-foot zone as different systems with different identifiers. A layer labelled only feet is not metadata, it is a guess someone else made.
2. Read the survey itself. Plats, control sheets, project datum notes and closure reports frequently state the unit explicitly, and a note in the surveyor's own hand outranks anything a file header says.
3. Check the age and lineage. Anything derived from NAD27, or from NAD83 State Plane before the early 2020s, is almost certainly in survey feet. Anything produced from the modernised reference system, or exported from a metric workflow after 2022, is more likely international.
4. Test against known control. Take a monument whose published metric coordinate you trust, convert it both ways, and compare with the dataset. At State Plane magnitudes the two candidates are several feet apart, so the answer is unambiguous the moment you have one good check point. This is the only test that settles the question by evidence rather than inference.
5. Ask the originator. It is the cheapest step and it is the one most often skipped.

What to do when you cannot tell

Sometimes there is no metadata, no control within reach, and no one left to ask. That situation has a correct answer, and it is not to pick the likelier foot and move on quietly.

• State the assumption in writing, on the deliverable, in the same place you would state the datum and the epoch. An assumption that is recorded can be revisited; one that is not becomes an undocumented error in someone else's project.
• Quantify the exposure. Multiply the largest coordinate in the dataset by 0.000002 and you have the worst-case displacement. If it is a hundredth of a foot, say so and stop worrying. If it is four feet, it belongs in the transmittal letter.
• Prefer the survey foot for legacy State Plane data in feet, because that is where the evidence points, and say that is what you did and why.
• Keep the original values. Store the source coordinates untransformed alongside the converted ones. If the assumption turns out to be wrong, the fix is a re-conversion rather than a re-survey.
• Never mix. A single dataset must be in one foot throughout. Combining survey-foot control with international-foot mapping produces a discrepancy that grows across the site and defeats every internal check, because internally each half is perfectly consistent.
• When you have the choice, work in meters. The meter is unambiguous, both feet are defined from it exactly, and converting to feet once at the point of delivery removes the problem from every intermediate step.

Practical rules to work by

• Below ten thousand feet, the two feet are interchangeable for any field purpose. Do not spend time on it.
• Above a hundred thousand feet, they are never interchangeable. Establish which one applies before computing anything.
• Distances are safe; coordinates are not. The ambiguity scales with the magnitude of the number, and a coordinate is a large number by construction.
• The acre and the 43,560 relationship are exact in both feet, so an acreage disagreement is never explained by the foot.
• New work uses the international foot or meters. Legacy State Plane work in feet is survey feet until proven otherwise.
• The unit belongs in the coordinate system name, not in a column header. Feet is not a coordinate system; US survey feet in a named zone on a named datum at a named epoch is.

The whole subject is two parts per million wide, which is exactly why it survives. It is too small to be caught by the checks surveyors run instinctively and too large to be absorbed by the tolerances they work to. The defence is documentary rather than computational: know which foot, write it down, and never let a dataset leave your hands with the unit unstated.