ACT Math For Dummies
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The rectangular survey system, often referred to as the government survey system, is based on a system of lines that form rectangles and squares throughout the United States.

The first sets of lines respectively are called principal meridians, which run north and south, and baselines, which run east and west. The principal meridians and baselines are based respectively on lines of longitude and latitude.

You’re likely to see at least a few questions on the real estate license exams on calculating the area of part of a section, and you’ll also see questions about terminology and some of the measurements that the rectangular survey system uses.

You may even see a question or two about the numbering system used for sections. Because the rectangular or government survey system was instituted when the United States was a new country, it was used to describe most of the land west of the original 13 colonies, so most of you are likely to see some questions about this system.

Longitude and latitude are imaginary lines that divide the earth through the north and south poles (longitude) and run parallel with the equator (latitude). Principal meridians, baselines, and where they intersect (cross each other) are used as the basis for formulating property descriptions in this system. They are the starting points for describing a property’s boundaries. The following is a list of helpful terms:

  • Quadrangles: The basic squares of land of the rectangular survey system, quadrangles (also government checks, or just checks) are 24 miles square (that means each side is 24 miles long) and are delineated by a principal meridian and a baseline. Quadrangles have an area of 576 square miles, more or less, and are divided into 16 townships.
  • Townships: The divisions of a quadrangle, townships, are six miles square (six miles on each side) and are delineated by township lines. Townships have an area of 36 square miles, more or less, and are each further divided into 36 sections.
  • Sections: The divisions of a township, sections, are one mile square and have an area of one square mile, or 640 acres. Sections can be divided in several ways, but basically for purposes of the United States Geological Survey (USGS), they are divided in quarter sections.
  • Quarter sections: The divisions of a section, quarter sections, are formed by dividing a section into fourths that are delineated by their direction from the center of the section (northwest—NW, northeast—NE, southeast—SE, and southwest—SW). Quarter sections have an area of 160 acres.
  • Half sections: Half section is a description of any two abutting quarter sections within a section, usually accompanied by a directional notation indicating the half of the section in which the two quarter sections are located. Half sections have an area of 320 acres. So, there can be the north, south, east, or west half section.
Because of the curvature of the earth, the lines in the government survey system are only theoretically straight. Imagine trying to draw straight lines on a rubber ball. Although the lines start out the same distance apart, they get closer together as you get near one or the other end of the ball.

Correction lines and guide meridians were established to correct this problem in the government survey system. Correction lines occur at every fourth township line or every 24 miles north and south of the baseline. The guide meridians occur every 24 miles east and west of the principal meridian. An area bounded on two sides by guide meridians and on the other two sides by correction lines is called a government check, check, or quadrangle, which is 24 miles square, meaning each of its boundaries is 24 miles long. A government check represents an area that measures 576 square miles.

Remember that although these correction lines and guide meridians are the way the government deals with the issue of the earth’s curvature, it isn’t the way the government survey system describes land. In reality, because of this earth curvature issue, many sections and townships vary from their exact area measurements. A system of fractional sections and government lots are parts of standard practice to account for these discrepancies.

So how does the system describe land? Using principal meridians and baselines as points of reference, land areas are divided by two kinds of lines, township lines and range lines. Township lines, which run east and west, parallel to baselines, are horizontal parallel lines that form township tiers.

Think about two lines running from left to right across this page about an inch apart. The range lines run north and south parallel to the principal meridians. These range lines form ranges. Think about two more lines running up and down the page on top of the first two lines, also about an inch apart. You got it: Tic tac toe. Where the two range lines and two township lines intersect, they form a township.

Now, the way it really works is for this page to be filled with the lines going up and down and right to left so that you have many townships. The township is the basic unit of measurement in the rectangular survey system. The area created by the intersection of a township line and a range line is a township. The townships are consecutively numbered by their location within the intersection of multiple range lines and township lines. The boundary of each township is 6 miles long, so a township contains 36 square miles and is described as being 6 miles square. These townships are not the same as political subdivisions.

Each township is further divided into 36 sections of one square mile each, or 640 acres, by horizontal and vertical section lines. Sections also are numbered consecutively. Section 1 within any township is always located at the upper right or northeast corner of the township. The numbering then moves from right to left across that first upper tier. The numbering continues directly beneath the sixth section, except that it progresses from left to right on the second tier. The numbering changes directions in the third tier from right to left. In other words, after section number 6, it drops down to 7 on the next tier then goes left to right to number 12. Then the numbering drops down to 13 and goes right to left again and so forth:

townships Townships are divided into 36 sections numbered consecutively.

Each section of 640 acres can be divided into halves and quarters called, get this, half sections and quarter sections. These divisions mean just that. For instance, a quarter section always contains 160 acres, or a fourth of the total 640 acres in a section. Specific directional references are needed in the actual description to locate a particular piece of property, but for finding out how large a particular piece of property is, only the fractions matter.

real estate sections Sections can be divided in a variety of ways, including quarters and smaller sections.

Each half or quarter section can be further subdivided into halves and quarters. So, you can refer to the south (S) 1/2 of the northwest (NW) 1/4 of a section in a township, for example. (The figure below shows a variety of divisions in a quarter section.)

Figuring out the size of a piece of property, which sometimes is called a parcel, is simple, if you keep in mind that you’re always dealing with a section of 640 acres. Putting the above description into words is half of a quarter section. Doing the math, it’s 1/2 × 1/4 × 640 = 80 acres.

quarter section A quarter section can be split into smaller parts.

A full rectangular survey system property description might read:

The SW 1/4 of the NE 1/4 of the NW 1/4 of Section 6, Township 4 South, Range 5, East of the Third Principal Meridian. (This description refers to a 10-acre parcel of land.)
The description probably would include the state and county in which the property is located and use abbreviations. So, in the example above, Township 4 South would be T4S. Whenever properties have irregular boundaries, the land may be further described using one of the two other systems described in this section.

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