thumb|Sectioning a [[survey township|township (36 sections).]]
thumb|right|Perfectly square 160-acre quarter sections of farmland cover central [[Indiana.]]
thumb|Satellite image of crops growing in southwest [[Kansas, mainly using center pivot irrigation. The primary grid pattern is of quarter sections ().]]
<!-- Deleted image removed: thumbnail|A brass disc in concrete marking a quarter section corner. -->
In U.S. land surveying under the Public Land Survey System (PLSS), a section is an area nominally , containing , with 36 sections making up one survey township on a rectangular grid.
Description
The legal description of a tract of land under the PLSS includes the name of the state, name of the county, township number, range number, section number, and portion of a section. Sections are customarily surveyed into smaller squares by repeated halving and quartering. A quarter section is and a "quarter-quarter section" is . In 1832 the smallest area of land that could be acquired was reduced to the quarter-quarter section, and this size parcel became entrenched in American mythology. After the Civil War, freedmen (freed slaves) were reckoned to be self-sufficient with "40 acres and a mule," though they never received it. In the 20th century real estate developers preferred working with parcels. The phrases "front 40" and "back 40," referring to farm fields, indicate the front and back quarter-quarter sections of land.
One of the reasons for creating sections of was the ease of dividing into halves and quarters while still maintaining a whole number of acres. A section can be halved seven times in this way, down to a parcel, or half of a quarter-quarter-quarter section—an easily surveyed 50-square-chain (2 ha) area. This system was of great practical value on the American frontier, where surveyors often had a shaky grasp of mathematics and were required to work quickly. The ordinance also specified that out of every township, the four lots, being numbered 8, 11, 26, 29, and out of every fractional part of a township, so many lots of the same numbers as shall be found thereon, for future sale.
On May 20, 1862, President Abraham Lincoln signed into law the Homestead Act, by which settlers could "claim" 160 acres (a quarter section) of public land. Claimants were required to "live on" and “improve” their plots by cultivating the land. After five years, the original filer of the claim was entitled to the property, free and clear, except for a small registration fee.
Roads and urban planning
Numbering within a township
thumb|Section map of [[Rock Creek Township, Saunders County, Nebraska (1907)]]
Every township is divided into 36 sections, each usually square. Sections are numbered boustrophedonically within townships
{| class="wikitable"
|-
|NW
| NE
|-
|SW
| SE
|}
Sections can be further broken up into blocks, or quarter-quarter sections. These add a second intercardinal direction label. For instance, the southeast quarter of the southwest quarter section mentioned above is labeled SE 1/4, SW 1/4:
{| class="wikitable"
|-
|NWNW
| NENW
| NWNE
| NENE
|-
|SWNW
| SENW
| SWNE
| SENE
|-
|NWSW
| NESW
| NWSE
| NESE
|-
|SWSW
| SESW
| SWSE
| SESE
|}
Measurement anomalies
The curvature of the Earth makes it impossible to superimpose a regular grid on its surface, as the meridians converge toward the North Pole. As the U.S. is in the Northern Hemisphere, if a section's or township's east and west sides lie along meridians, its north side is shorter than its south side. Because sections were surveyed from south and east to north and west, accumulated errors and distortions resulted in the north and west lines, and north and west sections diverged the most from the ideal shape and size.
The entire township grid shifts to account for the Earth's curvature. Where the grid is corrected, or where two grids based on different principal meridians meet, section shapes are irregular. Sections also differ from the PLSS ideal of one square mile for other reasons, including errors and sloppy work by surveyors, poor instrumentation, and difficult terrain. In addition, the primary survey tool was the magnetic compass, which is influenced by local irregularities. Once established, even an imperfect grid remains in force, mainly because the monuments of the original survey, when recovered, hold legal precedent over subsequent surveys.
Alternatives and legacy systems
The Public Land Survey System was not the first to define and implement a survey grid. Similar systems were established, often using terms like section and township but not necessarily in the same way. For example, the lands of the Holland Purchase in western New York were surveyed into a township grid before the PLSS was established. In colonial New England land was often divided into squares called towns or townships and further subdivided into parcels called lots or sections.