Quarter Sections and Aliquot Parts

A PLSS section is 640 acres — a full square mile. That is far more land than most transactions involve. To describe smaller parcels within a section, the PLSS uses a subdivision system based on halves and quarters, producing standardized parcels called aliquot parts. The most common are the quarter section (160 acres) and the quarter-quarter section (40 acres), but the system can divide land down to 2.5 acres or smaller.

If you have ever read a legal land description like NE¼ of the NW¼, Sec 14, T32N R21W, you have seen aliquot parts in action. This guide covers how the subdivision works, how to read the notation, and why it matters for anyone working with land in the 30 PLSS states.

The Quarter Section: 160 Acres

Each 640-acre section is divided into four quarter sections, each 160 acres (half a mile on each side). The quarters are named by compass direction:

┌─────────────────┬─────────────────┐
│                 │                 │
│       NW¼       │       NE¼       │
│   (160 acres)   │   (160 acres)   │
│                 │                 │
├─────────────────┼─────────────────┤
│                 │                 │
│       SW¼       │       SE¼       │
│   (160 acres)   │   (160 acres)   │
│                 │                 │
└─────────────────┴─────────────────┘

• NE¼ — Northeast Quarter (the upper-right quadrant)
• NW¼ — Northwest Quarter (the upper-left quadrant)
• SE¼ — Southeast Quarter (the lower-right quadrant)
• SW¼ — Southwest Quarter (the lower-left quadrant)

The 160-acre quarter section is historically significant. Under the Homestead Act of 1862, settlers could claim 160 acres of public land by living on it and improving it for five years. That is why 160 acres became the standard homestead size — it was literally one quarter of a section.

The Quarter-Quarter Section: 40 Acres

Each quarter section can be subdivided again into four quarter-quarter sections, each containing 40 acres (a quarter mile on each side). The naming follows the same compass convention, but now the description includes two levels:

              NW¼ of a Section
┌─────────────────┬─────────────────┐
│                 │                 │
│    NW¼ NW¼      │    NE¼ NW¼      │
│   (40 acres)    │   (40 acres)    │
│                 │                 │
├─────────────────┼─────────────────┤
│                 │                 │
│    SW¼ NW¼      │    SE¼ NW¼      │
│   (40 acres)    │   (40 acres)    │
│                 │                 │
└─────────────────┴─────────────────┘

The NE¼ NW¼ means the northeast quarter of the northwest quarter — a 40-acre parcel in the north-center area of the section. This notation is often written compactly as NENW.

A full section contains 16 quarter-quarter sections, each 40 acres:

┌────────┬────────┬────────┬────────┐
│ NWNW   │ NENW   │ NWNE   │ NENE   │
│ 40 ac  │ 40 ac  │ 40 ac  │ 40 ac  │
├────────┼────────┼────────┼────────┤
│ SWNW   │ SENW   │ SWNE   │ SENE   │
│ 40 ac  │ 40 ac  │ 40 ac  │ 40 ac  │
├────────┼────────┼────────┼────────┤
│ NWSW   │ NESW   │ NWSE   │ NESE   │
│ 40 ac  │ 40 ac  │ 40 ac  │ 40 ac  │
├────────┼────────┼────────┼────────┤
│ SWSW   │ SESW   │ SWSE   │ SESE   │
│ 40 ac  │ 40 ac  │ 40 ac  │ 40 ac  │
└────────┴────────┴────────┴────────┘

The 40-acre quarter-quarter section was the minimum parcel size sold by the General Land Office for much of the 19th century. It remains the most common subdivision level used in oil and gas leasing, timber sales, and rural real estate transactions today.

Going Smaller: Further Subdivisions

The aliquot system does not stop at 40 acres. Each quarter-quarter section can be halved or quartered again:

In practice, descriptions rarely go beyond the quarter-quarter level. When they do — for small rural parcels, well pad locations, or mineral tracts — the notation simply adds another level using the same compass abbreviations.

Half sections and half quarter sections are also valid aliquot parts:

• N½ — North Half (320 acres of a section, or 80 acres of a quarter section)
• S½ — South Half
• E½ — East Half
• W½ — West Half

For example, S½ NE¼ is the south half of the northeast quarter — an 80-acre parcel forming the southern strip of the NE¼.

Reading PLSS Descriptions: Smallest to Largest

The single most important rule for reading PLSS legal land descriptions is:

Read from the smallest subdivision to the largest.

The description is written with the smallest parcel first and the largest container last. This is the opposite of how you might naturally read it in English, but it follows a consistent pattern:

NE¼ NW¼ Sec 14, T32N R21W, 5th PM
 │    │    │      │          │
 │    │    │      │          └── Principal Meridian
 │    │    │      └── Township and Range
 │    │    └── Section number
 │    └── Quarter section (160 acres) ── the "container"
 └── Quarter of that quarter (40 acres) ── the specific parcel

To locate this parcel, you work from right to left:

1. Find the 5th Principal Meridian survey area
2. Within that area, find Township 32 North, Range 21 West
3. Within that township, find Section 14
4. Within Section 14, find the NW¼ (northwest quarter)
5. Within the NW¼, find the NE¼ (northeast quarter of that quarter)

That final parcel is 40 acres in the north-center part of Section 14.

Common Mistake: Reading Order

A frequent error is reading the description left to right as if it were a street address. The description NE¼ NW¼ does NOT mean "northeast quarter, then northwest quarter." It means the northeast quarter of the northwest quarter — a single 40-acre parcel. The word "of" is implied between each level.

Written out in full, the example above would read: "The Northeast Quarter of the Northwest Quarter of Section 14, Township 32 North, Range 21 West of the 5th Principal Meridian."

Format Variations

Aliquot part descriptions appear in several formats across different industries and documents:

Formal deed language: The Northeast Quarter of the Northwest Quarter of Section Fourteen (14), Township Thirty-Two (32) North, Range Twenty-One (21) West of the 5th Principal Meridian

Standard abbreviated: NE¼ NW¼ Sec 14, T32N R21W, 5th PM

Compact (oil and gas): NENW 14-32N-21W

BLM notation: NE NW 14 32N 21W 5th PM

Unicode quarter symbol vs. fraction: NE¼ NW¼ (with ¼ symbol) and NE/4 NW/4 (with slash fraction) are both used. Many databases and older systems use the slash notation because the ¼ symbol was not available in ASCII.

All of these describe the same 40-acre parcel. The notation varies, but the system is consistent.

Half Sections and Irregular Descriptions

Not all aliquot parts are simple quarters. Legal descriptions frequently use halves and combinations:

The description E½ W½ is worth noting — it describes the eastern half of the western half of a section, which is a 160-acre strip running down the center of the section. While unusual, it is a valid aliquot part description that occasionally appears in older deeds and mineral leases.

Lots: When Aliquot Parts Do Not Apply

In fractional sections — sections along the north and west edges of a township, or sections bordering rivers, lakes, and state boundaries — the standard 160-acre and 40-acre subdivisions do not fit neatly. In these cases, the original survey divided the irregular area into numbered lots rather than standard quarter-quarter sections.

A lot-based description looks like this: Lot 3, Sec 4, T12N R5E. The lot number refers to a specific parcel shown on the original survey plat, typically between 20 and 50 acres but varying by the geometry of the fractional section.

When working with lots, you must consult the original BLM survey plat to determine the lot's exact location and acreage. Lots do not follow the compass-direction naming convention — they are simply numbered sequentially on the plat map.

Aliquot Parts in Real-World Applications

Understanding quarter sections and aliquot parts is not academic — these descriptions drive daily workflows across multiple industries:

Oil and Gas

Drilling permits, well spacing orders, and production reports all use aliquot part descriptions. In Oklahoma, a typical spacing unit might be described as "the NW¼ of Section 22, T9N R15W, Indian Meridian." Well locations within the spacing unit are described to the quarter-quarter level or smaller: "SENW Sec 22" places the well in the southeast 40 acres of the northwest quarter.

Real Estate and Title

Rural property deeds describe parcels using aliquot parts. A farm listed as "the NE¼ of Sec 8, T5N R3W" is a 160-acre property. A title examiner tracing ownership back to the original government patent will follow a chain of aliquot-part descriptions, sometimes spanning 150 years of conveyances.

Agriculture and Crop Insurance

Crop insurance filings identify fields by section, quarter, and quarter-quarter. An adjuster investigating a hail damage claim needs to locate the specific 40-acre or 160-acre parcel described in the policy. Knowing that "NESW Sec 20" is in the east-center area of the section saves time when the nearest street address is miles away.

Forestry and Timber

Timber sale contracts on public and private land describe harvest boundaries using aliquot parts. A sale might cover "the S½ NW¼ and the SW¼ NE¼ of Sec 15, T28N R12W" — two non-contiguous 80-acre and 40-acre parcels within the same section.

Emergency Services

In rural areas of Colorado, Montana, Wyoming, and other western states, emergency dispatchers sometimes use section-level descriptions to locate incidents. "Sec 14, T8N R4W" narrows the search to a specific square mile when no street address exists.

Visualizing the Full Hierarchy

To put it all together, here is how aliquot parts nest within the PLSS hierarchy:

T4N R5E (6th Principal Meridian)
  └── 36 sections, each 640 acres
       └── Sec 12
            ├── NE¼  (160 acres)
            │    ├── NE¼ NE¼  (40 acres)
            │    ├── NW¼ NE¼  (40 acres)
            │    ├── SE¼ NE¼  (40 acres)
            │    └── SW¼ NE¼  (40 acres)
            ├── NW¼  (160 acres)
            │    ├── NE¼ NW¼  (40 acres)
            │    └── ...
            ├── SE¼  (160 acres)
            │    └── ...
            └── SW¼  (160 acres)
                 └── ...

The complete description NE¼ NE¼ Sec 12, T4N R5E, 6th PM identifies one specific 40-acre parcel out of the hundreds of thousands in the 6th Principal Meridian survey area. That precision — built from nothing more than compass directions and nested rectangles — is why the PLSS has remained the standard for legal land descriptions for over 240 years.

Converting Aliquot Parts to GPS Coordinates

An aliquot part description tells you exactly where a parcel sits on the PLSS grid, but it does not give you a latitude and longitude you can enter into a GPS or mapping application. Converting from a PLSS description to GPS coordinates requires matching the description against official BLM survey data for the correct principal meridian, township and range, section, and quarter.

Township America handles this conversion across all 30 PLSS states and all 37 principal meridians. Enter a description at any level — from a full township down to a quarter-quarter section — and get the corresponding GPS coordinates.

Try the PLSS Converter →