The rectangular survey system is a way of describing land by placing it on a giant grid of squares measured from fixed lines. It is also called the government survey system or the Public Land Survey System (PLSS), and it covers most of the land in the United States west of the original colonies. If a legal description mentions a township, a range or a section, it is using the rectangular survey system.
It is one of the three methods of legal description you need for the real estate exam, along with metes and bounds and lot and block. It is also the one that produces the most math questions. This guide explains how the grid works, how to read a legal description, how to work out acreage, and the traps exam writers like to set. When you are done, practice with our free real estate practice exam.
Table of Contents
What Is the Rectangular Survey System?
The rectangular survey system divides land into squares using two kinds of reference lines. Lines that run north and south are called principal meridians. Lines that run east and west are called base lines. Each principal meridian crosses its base line at a starting point called the initial point, and every parcel in that survey area is described by how far it sits from those two lines.
Because the squares are a standard size, a short legal description can pin down a parcel precisely. “The NE 1/4 of Section 14, Township 2 North, Range 3 West” describes exactly one 160-acre piece of land, and anyone with a map of that survey area can find it.
The Bureau of Land Management, the federal agency that keeps the official survey records, maintains the rectangular survey system today through its cadastral survey program.
A Short History of the Rectangular Survey System
After the American Revolution, the new national government owned huge areas of land west of the original states. It needed a fair, simple way to measure that land so it could be sold to settlers and used to pay public debts. The colonies had relied on metes and bounds, which describes land by landmarks and directions. That worked for small, irregular farms, but it led to overlapping claims and constant boundary disputes.
The answer was the Land Ordinance of 1785. A committee led by Thomas Jefferson proposed dividing the land into a grid. Jefferson suggested squares 10 miles on a side, but the final ordinance settled on townships 6 miles square, divided into 36 sections of one square mile each. The ordinance also reserved section 16 of every township to support public schools.
Surveying began in 1785 in the Seven Ranges of eastern Ohio, starting at a spot now known as the Point of Beginning near East Liverpool, Ohio. Over the next two centuries, surveyors carried the rectangular survey system across the Midwest, the Great Plains and the West, and eventually into Alaska.
Where the Rectangular Survey System Is Used
The rectangular survey system is used in 30 states, often called the public land states. They are Alabama, Alaska, Arizona, Arkansas, California, Colorado, Florida, Idaho, Illinois, Indiana, Iowa, Kansas, Louisiana, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Mexico, North Dakota, Ohio, Oklahoma, Oregon, South Dakota, Utah, Washington, Wisconsin and Wyoming.
It is not used in the original 13 states, or in Maine, Vermont, Kentucky, Tennessee, West Virginia, Texas and Hawaii. Those states rely mainly on metes and bounds and on recorded plats. Texas never handed its public land to the federal government, so it developed its own survey system.
Even inside public land states, the rectangular survey system is not the only method in use. Irregular parcels are often described by metes and bounds measured from a section corner, and most subdivisions are described by lot and block on a recorded plat.
How the Rectangular Survey System Works
The rectangular survey system builds the grid in layers, from very large squares down to small parcels. Learn the layers in order and the rest of the topic gets much easier.
Principal Meridians and Base Lines
Each survey area starts with an initial point. A principal meridian runs north and south through that point, and a base line runs east and west through it. There are dozens of these pairs across the country, and each principal meridian has a name. For example, the Fifth Principal Meridian is the reference for surveys in Arkansas, Missouri, Iowa and North Dakota and for parts of Minnesota and South Dakota, while the Willamette Meridian covers Oregon and Washington, and the Mount Diablo Meridian covers most of California and all of Nevada.
A complete legal description names the principal meridian, because “Section 14, Township 2 North, Range 3 West” exists once in every survey area. The meridian tells you which grid you are on.
Guide Meridians, Standard Parallels and Checks
The earth is round, so lines running north and south slowly get closer together as they head toward the North Pole. To keep the squares as square as possible, surveyors add correction lines. Guide meridians are run every 24 miles east and west of the principal meridian. Standard parallels, also called correction lines, are run every 24 miles north and south of the base line.
The 24-mile by 24-mile squares formed by these lines are called checks or quadrangles. Each check holds 16 townships.
Townships and Ranges
Inside each check, surveyors run lines every 6 miles. Lines running east and west, parallel to the base line, are township lines. They create rows called tiers. Lines running north and south, parallel to the principal meridian, are range lines. They create columns called ranges.
Tiers are numbered north or south of the base line: Township 1 North, Township 2 North, and so on. Ranges are numbered east or west of the principal meridian: Range 1 East, Range 2 East, and so on. Where a tier and a range cross, you get a township, a square roughly 6 miles on each side.
For example, the township in the first tier north of the base line and the first range east of the principal meridian is Township 1 North, Range 1 East, written T1N, R1E. The township in the fourth tier south and the third range west is Township 4 South, Range 3 West, or T4S, R3W.
Sections
Each township contains 36 square miles, so it is divided into 36 sections. A section is one square mile, 5,280 feet on each side, and contains 640 acres. A full township therefore contains 23,040 acres.
Sections are numbered in a back-and-forth pattern. Section 1 is in the northeast corner. The numbers run west across the top row to section 6, drop down to section 7, run east to section 12, and keep snaking back and forth until section 36 lands in the southeast corner.
Because the earth’s curve and small survey errors have to go somewhere, the rectangular survey system pushes them into the north and west edges of each township. Sections along the north row and west column may be larger or smaller than 640 acres, and odd-shaped pieces along those edges or along lakes and rivers are called government lots.
Subdividing a Section
A whole section is too large for most purposes, so sections are divided into halves and quarters, and those are divided again. The names follow compass directions:
- A quarter section, such as the NE 1/4, contains 160 acres.
- A half section, such as the N 1/2, contains 320 acres.
- A quarter of a quarter section, such as the NE 1/4 of the NE 1/4, contains 40 acres and is 1,320 feet, or a quarter mile, on each side.
- A quarter of that, such as the NE 1/4 of the NE 1/4 of the NE 1/4, contains 10 acres.
Two numbers do most of the work on the exam: a section contains 640 acres, and an acre contains 43,560 square feet. Memorize both, along with 5,280 feet in a mile.
How to Read a Rectangular Survey System Legal Description
A rectangular survey system description lists the smallest piece first and the largest area last. Here is a typical one:
The NE 1/4 of the SW 1/4 of Section 14, T2N, R3W, Fifth Principal Meridian.
The easiest way to read it is backward, from the end to the start:
- Fifth Principal Meridian: the survey area, which tells you the grid.
- R3W: the third range west of that meridian.
- T2N: the second tier north of the base line.
- Section 14: the section inside that township.
- SW 1/4: the southwest quarter of section 14, 160 acres.
- NE 1/4: the northeast quarter of that southwest quarter, 40 acres.
Reading backward keeps you from getting lost, because each step narrows down the area you found in the step before.
Rectangular Survey System Acreage Math
To find the size of a parcel, start with 640 acres and divide by the denominator of each fraction in the description. Ignore the directions; they tell you where the parcel is, not how big it is.
- The SW 1/4 of Section 9: 640 ÷ 4 = 160 acres.
- The S 1/2 of the NW 1/4 of Section 10: 640 ÷ 4 ÷ 2 = 80 acres.
- The NE 1/4 of the SW 1/4 of Section 14: 640 ÷ 4 ÷ 4 = 40 acres.
- The N 1/2 of the SE 1/4 of the NE 1/4 of Section 22: 640 ÷ 4 ÷ 4 ÷ 2 = 20 acres.
Watch for the word “and.” It means two separate parcels, so you add them. The NW 1/4 and the N 1/2 of the SW 1/4 of Section 5 is 160 + 80 = 240 acres. The word “of” means you keep dividing within the same parcel.
Price questions add one more step. If a 40-acre parcel sells for $3,500 per acre, the price is 40 × $3,500 = $140,000. If the question gives a price per square foot instead, convert acres to square feet first using 43,560. Our real estate math guide has more problems like these.
Rectangular Survey System vs Metes and Bounds vs Lot and Block
You need to know all three methods of legal description and when each one is used.
- Metes and bounds describes a parcel by its boundaries: a point of beginning, then directions and distances around the edge, ending back at the point of beginning. It is the oldest method and the main one in the original states. Cornell Law School has a short definition of metes and bounds.
- The rectangular survey system describes a parcel by its place on the grid of townships, ranges and sections. It is used in the 30 public land states and works best for large, square tracts.
- Lot and block, also called the recorded plat method, describes a parcel by its lot and block number on a subdivision map filed in the public records. It is the usual method for homes in subdivisions in every state.
A single property can be described by more than one method. A subdivision plat is often tied to a section corner from the rectangular survey system, and a metes and bounds description in a public land state may begin at a section corner.
Common Exam Traps
Exam writers tend to test the same handful of mistakes. Watch for these:
- Mixing up townships and ranges. Township tiers run east and west and are counted north or south. Ranges run north and south and are counted east or west.
- Forgetting where section 1 starts. It is always the northeast corner, and section 36 is always the southeast corner.
- Adding when you should divide. “Of” means divide again. Only “and” means add.
- Confusing the size of a township and a section. A township is 36 square miles; a section is 1 square mile, or 640 acres.
- Thinking every state uses the grid. The original colonies and Texas do not use the rectangular survey system.
Our guide to the physical characteristics of land is a good companion read, because the exam often pairs it with legal descriptions.
Rectangular Survey System Practice Questions
Try each question before you read the answer below it.
1. How many acres are in the NW 1/4 of the SE 1/4 of a section?
Answer: 40 acres. 640 ÷ 4 ÷ 4 = 40.
2. How many sections are in a township, and which corner is section 1 in?
Answer: 36 sections. Section 1 is in the northeast corner.
3. What is the legal shorthand for the township in the second tier south of the base line and the fifth range east of the principal meridian?
Answer: T2S, R5E.
4. How many acres are in the S 1/2 of the NE 1/4 and the NW 1/4 of a section?
Answer: 240 acres. The S 1/2 of the NE 1/4 is 80 acres, and the NW 1/4 is 160 acres, so 80 + 160 = 240.
5. A 10-acre parcel described under the rectangular survey system sells for $2.50 per square foot. What is the price?
Answer: $1,089,000. 10 acres × 43,560 square feet = 435,600 square feet, and 435,600 × $2.50 = $1,089,000.
6. Which states do not use the rectangular survey system?
Answer: The original 13 states, along with Maine, Vermont, Kentucky, Tennessee, West Virginia, Texas and Hawaii.
Frequently Asked Questions
Is the rectangular survey system the same as the government survey system?
Yes. The rectangular survey system, the government survey system and the Public Land Survey System (PLSS) are three names for the same method.
How big is a township in the rectangular survey system?
A township is 6 miles by 6 miles, or 36 square miles. It contains 36 sections and 23,040 acres.
How many acres are in a section?
A section contains 640 acres and measures one mile, or 5,280 feet, on each side.
Why are some sections not exactly 640 acres?
Because the earth is curved and older surveys were not perfect. The rectangular survey system places those errors in the sections along the north and west edges of each township, and odd pieces become government lots.
Key Takeaways
- The rectangular survey system describes land on a grid measured from principal meridians and base lines.
- Guide meridians and standard parallels every 24 miles correct for the earth’s curve.
- A township is 6 miles square, holds 36 sections and contains 23,040 acres.
- A section is 1 square mile and contains 640 acres; section 1 is in the northeast corner.
- Read legal descriptions backward and divide 640 by each fraction to find acreage.
Ready to test yourself? Take a free, timed practice exam and see how many legal description questions you get right. Your progress is saved in your browser, so you can pick up where you left off.