Guide · 6 min read

PLSS for beginners

Townships, ranges, sections and aliquot parts: how the rectangular system was laid out, how to read a description, and why sections are rarely 640 acres.

Updated

The Public Land Survey System is the rectangular framework under which most land west of the original colonies was surveyed and disposed of. It is not a grid laid over existing parcels; it is the survey that created them. That distinction governs everything else, because a boundary established by an original government survey is where that survey put it, not where a perfect rectangle would have been.

For a technician the system matters in two ways. Descriptions arrive written in its language and have to be read correctly, and retracement depends on knowing what the original surveyors were instructed to do and what they actually did. The vocabulary is an afternoon's work; the evidence takes considerably longer.

Principal meridians and base lines

Each PLSS survey area is referenced to an initial point, through which a principal meridian was run north and south and a base line east and west. There are dozens across the country, each covering a region, and a description is ambiguous without naming the one it belongs to.

From that origin the land was divided into townships six miles square. A township is identified by how far it lies north or south of the base line and how far east or west of the principal meridian: T2N R3W means the second township north of the base line in the third range west of the principal meridian.

Township
Nominally a six-mile square containing thirty-six sections, and also the north-south coordinate in the township-and-range reference. The word does both jobs, so T2N is the tier number while the township is the block of land it identifies.
Range
The east-west coordinate of a township, counted east or west from the principal meridian. Ranges are columns of townships; townships in the tier sense are rows.

Sections and their numbering

Each township is divided into thirty-six sections, nominally one mile square and containing 640 acres. The numbering runs in a boustrophedon pattern: section 1 in the northeast corner, west along the north tier to section 6, down to section 7, east to section 12, down again, and so on, with section 36 ending in the southeast corner.

Nominal PLSS dimensions
UnitNominal sizeNominal area
Township6 miles square, 480 chains23,040 acres
Section1 mile square, 80 chains640 acres
Quarter section40 chains square160 acres
Quarter-quarter section20 chains square40 acres
Sixteenth of a quarter10 chains square10 acres

Aliquot parts and how to read a description

Land within a section is described by repeated halving and quartering, called aliquot parts. The description reads from the smallest part outward, so each term qualifies the one after it.

The NE 1/4 of the SW 1/4 of Section 14, T2N R3W of a named principal meridian, means: take Section 14, take its southwest quarter, and within that take the northeast quarter. The result is nominally 40 acres. Read it right to left to locate the parcel, then left to right to state its size: each quartering divides the area by four, and each halving by two.

Reading aliquot descriptions
DescriptionNominal areaReading
NE 1/4160 acresThe northeast quarter of the section
NE 1/4 SW 1/440 acresThe northeast quarter of the southwest quarter
S 1/2 NE 1/480 acresThe south half of the northeast quarter
N 1/2 SE 1/4 NW 1/420 acresThe north half of the southeast quarter of the northwest quarter

Every area in that table is nominal. An aliquot part is defined by geometry - by the corners the original survey set and the midpoints between them - not by acreage, so the deed conveys the part regardless of what it measures. Where a stated acreage conflicts with the aliquot call, the aliquot call ordinarily prevails.

Why sections are not 640 acres

Two things prevent the rectangular ideal. Meridians converge toward the pole, so ranges cannot stay six miles apart as they run north; and the surveys were run on the ground with chains, over rough country, with the accumulated error that implies.

Convergence was handled by resetting the framework periodically. Standard parallels, also called correction lines, were run east and west at intervals, and guide meridians north from them, so convergence accumulated only over a limited distance before the grid was re-established. Where a range line meets a standard parallel from the south it sets a closing corner, which generally does not coincide with the standard corner set from the north - the double corners that confuse people expecting a clean grid.

Excess and deficiency within a township were placed deliberately. The instructions put the irregular measure into the north and west tiers of sections so the interior sections could be regular. That is why fractional lots appear along the north and west edges of a township.

Government lots

Where a part of a section cannot be described as an aliquot part, it is numbered as a government lot. Lots arise in the north and west tiers where excess and deficiency were absorbed, and wherever a section is broken by a navigable water body, a reservation, an earlier grant or a state line.

Corners and the evidence they represent

The system is built on physical corners, and the corners rather than the geometry define the boundaries. The categories worth knowing are few.

  • Section corners, at the intersections of section lines, and quarter corners at the midpoints of section lines. Together they frame every section and control the subdivision of it.
  • Meander corners, set where a survey line meets a navigable water body, from which the meander line was run. The meander line describes the shoreline; it is generally not the boundary, which is the water itself.
  • Witness corners, set on line at a measured distance from a true corner that could not be monumented where it fell - in a stream, on a cliff, in a road.
  • Closing corners, set where a line closes onto a previously established line such as a standard parallel, as distinct from the standard corner set when that line was originally run.

The controlling principle in retracement is that an original corner, if its position can be established by acceptable evidence, is where the boundary is - whatever the measurements say. A lost corner, one whose position cannot be recovered from any evidence, is restored by proportionate measurement from the nearest existing corners. An obliterated corner, whose monument is gone but whose position can be established from testimony, marks, fences or records, is not lost and is not proportioned.

Subdividing a section

Quarter-quarter corners were not set by the original surveys. The interior of a section is subdivided by the retracing surveyor according to rules that are geometric rather than arithmetic: the center quarter corner lies at the intersection of the straight lines joining opposite quarter corners, not at the computed center of the section.

Where to go next

The authoritative source is the Bureau of Land Management Manual of Surveying Instructions, which is in the public domain and freely available. It governs retracement of PLSS boundaries on federal land, and it is far more readable than its length suggests.

Questions

How do I read an aliquot description?

Right to left to find the land, left to right to find the size. The NE 1/4 of the SW 1/4 of Section 14 means: go to Section 14, then its southwest quarter, then the northeast quarter of that. Each quartering divides the nominal area by four and each halving by two, so the result is nominally 40 acres.

Why is a section rarely exactly 640 acres?

Two reasons. Meridians converge toward the pole, so ranges cannot stay six miles apart as the surveys run north, and the original surveys were run on the ground with chains over rough country. The instructions deliberately placed the resulting excess and deficiency in the north and west tiers of sections, which is why fractional lots cluster there.

Is a government lot just an irregular leftover?

No. A government lot is a fully defined parcel whose boundaries were run and whose corners were set by the original survey. It conveys exactly what the plat shows. Treating a lot as an approximation of the nearest quarter-quarter section is a common and consequential mistake.

Where is the center of a section?

At the intersection of the straight lines joining opposite quarter corners, not at the computed geometric center of the section. Quarter-quarter corners were never set by the original surveys, so the interior of a section is subdivided by the retracing surveyor according to that rule.

What does T2N R3W actually mean?

The second tier of townships north of the base line, in the third range of townships west of the principal meridian, of a named principal meridian. The name of the meridian is part of the description: there are dozens of initial points across the country, and T2N R3W exists in every one of them.

Sources

  • BLM Manual of Surveying Instructions (2009) - Public domain and authoritative. The rectangular system, the numbering and layout rules, government lots, and the restoration of lost or obliterated corners.
  • BLM General Land Office records - Public domain. Original township plats and field notes, searchable by township, range and meridian - the primary evidence for any retracement.

Work it out

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