How to Read PLSS Aliquot Descriptions: A Field Guide for Survey Crews

The Public Land Survey System (PLSS) covers most of the United States west of Ohio, plus portions of Alabama, Mississippi, and Florida. It is the primary method for describing land parcels in survey work across those states, and aliquot part descriptions — the NE¼, the SW¼ of the NE¼, the N½ of the SE¼ — are how individual parcels within that grid are identified.

If you work in PLSS states and don't fully understand how these descriptions work, this guide will fix that. We'll start from the grid itself and work down to nested descriptions, acreage calculations, and common mistakes.

The PLSS Grid: Townships, Ranges, and Sections

Every PLSS description starts from a principal meridian — a specific north-south line established by federal survey. There are 37 principal meridians in the United States. Each one defines the reference point for a regional survey grid.

From the principal meridian and its associated baseline, the land is divided into a grid of townships:

• Each township is 6 miles × 6 miles (36 square miles)
• Township location is given as Township N/S (rows north or south of the baseline) and Range E/W (columns east or west of the principal meridian)
• Example: T3N, R7W — three rows north of the baseline, seven columns west of the principal meridian

Each township is divided into 36 sections, each 1 square mile = 640 acres. Sections are numbered 1–36 in a specific serpentine pattern: Section 1 is in the northeast corner, numbering goes west across the top row, then drops down one row and goes east, then west again, ending with Section 36 in the southeast corner.

A full land description looks like this: Section 14, Township 3 North, Range 7 West, 6th Principal Meridian. That's a specific 640-acre square — one of thousands in that particular township and range grid. The aliquot part description then identifies which portion of that section you're actually talking about.

What Is an Aliquot Part?

An aliquot part is a regular, proportional subdivision of a section. The PLSS was designed so that sections could be divided evenly in half or in quarters, repeatedly, to reach practical parcel sizes.

The two subdivision types are:

• Quarters (¼) — divide the section or parent parcel into four equal parts: NE¼, NW¼, SE¼, SW¼
• Halves (½) — divide the section or parent parcel into two equal parts: N½, S½, E½, W½

These can be applied repeatedly, at any depth. You can describe a quarter of a quarter of a quarter, or a half of a quarter, or a quarter of a half — each one is a valid aliquot part, and each one has a precise location and acreage.

How to Read the Description: Smallest to Largest

This is the part that trips up most people encountering PLSS descriptions for the first time. Aliquot descriptions are written and read from smallest subdivision to largest— the opposite of how you'd intuitively think about it.

Consider: “the SW¼ of the NE¼ of Section 14”

To locate this parcel, work right to left (largest to smallest):

1. Start with Section 14 — the full 640-acre section
2. Find the NE¼ — the northeast quarter of the section (160 acres, northeast corner)
3. Find the SW¼ of that — the southwest quarter of the NE¼ (40 acres)

The result is a 40-acre parcel in what is sometimes called the “center 40” of the section — the fourth that sits just off-center to the northeast.

The written order (SW¼ first, NE¼ second) tells you where you end up, not where to start. You always start from the largest unit — the section — and work inward following each modifier from right to left.

Acreage Calculation

Acreage follows directly from the description:

• Every ¼ subdivision divides acreage by 4
• Every ½ subdivision divides acreage by 2
• Start from 640 acres (full section) and apply each subdivision

In practice: count the ¼ modifiers and ½ modifiers in the description. Each ¼ divides by 4; each ½ divides by 2. Multiply all the divisors together and divide 640 by the result.

“The N½ of the SW¼ of the NE¼” has one NE¼ (÷4), one SW¼ (÷4), and one N½ (÷2): 640 ÷ 4 ÷ 4 ÷ 2 = 20 acres.

Working with Halves

Half-section descriptions are common and sometimes cause confusion because they span the full width or height of the section (or parent parcel):

• N½ of Section 14 — the top half of the section, 320 acres, runs the full east-west width
• E½ of Section 14 — the right half, 320 acres, runs the full north-south height
• N½ of the NE¼ — a strip 160 chains wide and 40 chains tall, 80 acres, in the northeast corner
• E½ of the NW¼ — a strip in the center-north of the section, 80 acres

Half descriptions often appear in deeds that divided rectangular tracts without creating odd irregular boundaries. They create rectangular parcels aligned to section lines, which makes surveys straightforward.

Multiple Parts in One Description

Many deeds describe parcels made up of multiple aliquot parts combined. These are written as a list:

The NE¼ and the N½ of the SE¼ of Section 14, T3N, R7W, 6th P.M.

This describes two separate but adjacent parcels: the NE¼ (160 acres) and the N½ of the SE¼ (80 acres), totaling 240 acres. The word “and” connects separate parts; each part is read and located independently using the same right-to-left method.

In deed work, this combination form is very common when a property spans multiple aliquot parts that don't combine cleanly into a single description.

Lot Numbers and Irregular Sections

Standard aliquot parts assume regular 640-acre sections with straight survey lines. In practice, many sections along township boundaries, state lines, bodies of water, or early survey closure lines are irregular sections— they don't have exact dimensions.

In these cases, the Bureau of Land Management (BLM) assigns lot numbers (Lot 1, Lot 2, etc.) to irregular fractional pieces. These lots appear in the same position as aliquot descriptions:

Lot 3 and the SW¼ of Section 6, T3N, R7W

Lot acreage is notcomputed from the subdivision formula — it is listed in the original township plat and must be looked up from the BLM General Land Office (GLO) records. Each lot has a specific acreage from the original survey, and it may differ significantly from the “expected” aliquot acreage.

Sections along the north and west edges of a township are most commonly irregular, since those are where closure is taken. If your work involves the exterior sections of a township (Sections 1–7 along the north, or Sections 6, 7, 18, 19, 30, 31 along the west), check the GLO records before assuming standard acreage.

Common Mistakes

Reading left to right instead of right to left

The most common error. “The SW¼ of the NE¼” is not the NE corner of the SW quarter — it is the SW corner of the NE quarter. Always identify the section first, then work from the rightmost aliquot descriptor inward.

Confusing halves and quarters

N½ and NE¼ are very different parcels. N½ is 320 acres and spans the full width of the section. NE¼ is 160 acres in the corner. In handwritten field notes and old deeds, the fraction can be hard to read — double-check when the acreage doesn't add up.

Assuming standard acreage for all sections

In regular interior sections, the subdivision formula works exactly. But sections along township boundaries, near water, or at state lines are frequently irregular. Lot numbers are the signal that a section may not be standard — look up GLO acreage rather than computing it.

Misidentifying the principal meridian

A description that says “T3N, R7W” without specifying the principal meridian is ambiguous — T3N R7W of the 6th PM is a completely different piece of ground than T3N R7W of the Cimarron Meridian. Full descriptions always name the meridian. When working from incomplete descriptions, verify the meridian from the context of surrounding parcels or the county records.

Visualizing Before You Go to the Field

Before fieldwork in a sectionalized area, it's worth sketching the aliquot parts to confirm you understand exactly which portion of the section you're working with. A rough section sketch takes 30 seconds and prevents the kind of errors that send crews to the wrong field or the wrong corner.

The SlateTablet Aliquot Part Calculatorlets you build and visualize any PLSS description interactively — click on the section diagram to select quarters and halves, nest them to any depth, and see the acreage instantly. You can also paste a description directly and plot it. It's free and works in any browser.

Quick Reference

• 1 section = 640 acres = 1 square mile
• ¼ subdivision = divide by 4 (NE¼, NW¼, SE¼, SW¼)
• ½ subdivision = divide by 2 (N½, S½, E½, W½)
• Read right to left — the last item in the description is the largest unit
• Lot numbers = irregular sections — look up acreage from GLO records
• Township = 6×6 miles = 36 sections; sections number 1–36 starting NE corner, snaking west then east