- Official section
- National I.B and XI.E: Legal Descriptions and Land Measurement
- Broker weight
- A supporting calculation across ownership, legal descriptions, and real estate math
- Expected scored items
- The current PSI outline expressly tests government survey descriptions and structure and land measurement
Land description and measurement guide
Section and township area from 640 acres
Most section math begins with one number: 640. Apply every stated half or quarter to that base, and keep the answer nominal unless actual surveyed acreage is supplied. Township questions add one more number: 36 sections. The arithmetic is short, but the description still has to identify the correct section, township, range, and meridian. Write the fractions as a multiplication chain before touching the calculator. That one line separates the amount of land from its location and prevents a three-level description from losing one of its divisions.
Last updated: August 1, 2026
What calculation do you need to make?
Short answer: A standard PLSS section is nominally one square mile or 640 acres. A standard survey township is nominally six miles square, contains 36 sections, covers 36 square miles, and contains 23,040 acres. A half section is 320 acres, a quarter section is 160 acres, a half of a quarter is 80 acres, a quarter-quarter is 40 acres, and half of a quarter-quarter is 20 acres. For any nested aliquot description, begin with the stated section acreage and multiply every fraction. A standard quarter section is nominally one-half mile by one-half mile, while a quarter-quarter is nominally one-quarter mile, or 1,320 feet, on each side. Those dimensions assume an ideal square and should not override actual survey calls. Township identifies north or south position from a base line; range identifies east or west position from a principal meridian. Section numbers follow a serpentine pattern from 1 in the northeast to 36 in the southeast. Actual sections, lots, and townships can be irregular, so a supplied survey area controls over nominal exam conversions.
This page teaches nominal exam math and recognition of PLSS descriptions. It does not create, retrace, interpret, or certify a legal boundary. Original monuments, field notes, plats, patents, resurveys, controlling calls, government lots, water boundaries, correction lines, and applicable law can control actual location and acreage. A deed may use an aliquot description, a government lot, metes and bounds, or a combination, and its acreage recital may not be the controlling boundary call. Map layers and online section lines may be useful references without being the controlling legal survey record. Illinois civil townships and PLSS survey townships can differ even when their names or locations seem similar. Boundary and legal-description work belongs to qualified professionals. Sources were checked through August 1, 2026.
How do you calculate section and township acreage?
- Identify whether the problem gives a standard nominal section, an actual surveyed acreage, or a numbered government lot.
- For a standard section, write 640 acres; for a standard township, write 36 sections times 640 acres.
- Translate each half or quarter in the parcel description into one-half or one-fourth.
- Multiply the starting acreage by every stated fraction without skipping nested subdivisions on exam day.
- Read right to left when locating the successive aliquot parts inside the section.
- Convert square miles, acres, and square feet only after deciding which area unit the question requests, and carry the nominal qualifier into the converted answer.
- Use actual supplied acreage for irregular sections or lots instead of forcing the nominal conversion.
- Reverse-check the denominator, label the result nominal when appropriate, show the requested acres or square feet explicitly, and keep civil-township and legal-boundary conclusions outside the arithmetic.
- Unit
- Survey township
- Nominal area
- 36 square miles
- Exam safeguard
- Six miles square
- Unit
- Survey township
- Nominal area
- 23,040 acres
- Exam safeguard
- 36 x 640
- Unit
- Section
- Nominal area
- 1 square mile
- Exam safeguard
- Usually 640 acres
- Unit
- Section
- Nominal area
- 640 acres
- Exam safeguard
- Nominal, not guaranteed
- Unit
- Half section
- Nominal area
- 320 acres
- Exam safeguard
- 640 x 1/2
- Unit
- Quarter section
- Nominal area
- 160 acres
- Exam safeguard
- 640 x 1/4
- Unit
- Half of quarter
- Nominal area
- 80 acres
- Exam safeguard
- 640 x 1/4 x 1/2
- Unit
- Quarter-quarter
- Nominal area
- 40 acres
- Exam safeguard
- 640 x 1/4 x 1/4
- Unit
- Half of quarter-quarter
- Nominal area
- 20 acres
- Exam safeguard
- Three fractions
- Unit
- One acre
- Nominal area
- 43,560 square feet
- Exam safeguard
- Area conversion
Can you follow the calculation from facts to answer?
Calculate a full survey township
Scenario: What is the nominal acreage in a standard PLSS township containing 36 standard sections?
- A standard township contains 36 sections.
- Each standard section is nominally 640 acres.
- 36 x 640 = 23,040 acres.
Answer: The standard survey township contains 23,040 nominal acres.
Calculate a half of a quarter section
Scenario: How many nominal acres are in the S 1/2 of the NE 1/4 of a standard section?
- Begin with 640 acres.
- 640 x 1/4 = 160 acres in the NE quarter.
- 160 x 1/2 = 80 acres in its south half.
Answer: The description contains 80 nominal acres.
Calculate a nested 20-acre aliquot part
Scenario: What is the nominal area of the E 1/2 of the SW 1/4 of the NW 1/4 of a standard section?
- Write 640 x 1/4 x 1/4 x 1/2.
- 640 / 4 / 4 / 2 = 20.
- The rightmost NW quarter is divided first for location.
Answer: The parcel contains 20 nominal acres.
Use actual section acreage
Scenario: A survey states that an irregular section contains 612.8 acres. The described parcel is its N 1/2. What area should be used?
- The problem supplies actual section acreage, so do not substitute 640.
- 612.8 x 1/2 = 306.4 acres.
- The result follows the stated surveyed base.
Answer: The stated north half contains 306.4 acres.
Convert a quarter-quarter to square feet
Scenario: A standard quarter-quarter section contains 40 nominal acres. How many square feet is that?
- One acre contains 43,560 square feet.
- 40 x 43,560 = 1,742,400 square feet.
- The conversion retains the nominal-area assumption.
Answer: The nominal area is 1,742,400 square feet.
Recover a fraction from acreage
Scenario: A standard-section aliquot parcel contains 10 acres. What fraction of the 640-acre section is it?
- 10 / 640 = 1 / 64.
- Three successive quarter divisions produce 1/4 x 1/4 x 1/4 = 1/64.
- One possible form is a quarter of a quarter of a quarter, with location calls required to identify which one.
Answer: Ten acres is a nominal 1/64 of a standard section.
Which math errors cost the most points?
- Trap
- Call one linear mile 640 acres.
- Correction
- One square mile contains 640 acres; a linear mile measures distance only.
- Trap
- Say a township contains 640 acres.
- Correction
- A standard section is 640 acres; a standard township contains 36 sections or 23,040 acres.
- Trap
- Divide by only the last fraction in a description.
- Correction
- Apply every half and quarter to the starting section area.
- Trap
- Read section numbers left to right on every row.
- Correction
- The numbering reverses direction on each successive row.
- Trap
- Assume every actual section is exactly 640 acres.
- Correction
- Use nominal 640 only when no actual irregular acreage controls.
- Trap
- Treat a government lot as an automatic 40-acre parcel.
- Correction
- Use the lot number and surveyed acreage supplied by the controlling record.
- Trap
- Confuse township and range directions.
- Correction
- Township is north or south of a base line; range is east or west of a principal meridian.
- Trap
- Call a civil township a guaranteed 36-square-mile PLSS township.
- Correction
- Political boundaries can differ from the survey grid.
- Trap
- Use acreage multiplication to identify parcel location.
- Correction
- Area math says how much; the full nested calls say which tract.
- Trap
- Convert acres to square feet by dividing by 43,560.
- Correction
- Multiply acres by 43,560; divide square feet by 43,560 to recover acres.
- Trap
- Treat an online PLSS layer as conclusive boundary evidence.
- Correction
- Mapping is a reference and does not replace controlling survey records and monuments.
- Trap
- Let a broker create or resolve a disputed boundary through exam math.
- Correction
- Boundary creation and retracement require appropriate survey and legal expertise.
Can you solve these original problems?
These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.
1. How many nominal acres are in a standard survey township?
- 23,040 acres
- 640 acres
- 36 acres
- 3,840 acres
Show answer and explanation
Answer: 23,040 acres
A standard township contains 36 sections, and 36 x 640 = 23,040 acres.
2. How many nominal acres are in the W 1/2 of the SE 1/4 of a standard section?
- 80 acres
- 160 acres
- 320 acres
- 40 acres
Show answer and explanation
Answer: 80 acres
640 x 1/4 x 1/2 = 80 acres.
3. How many nominal acres are in a quarter-quarter section?
- 40 acres
- 160 acres
- 80 acres
- 20 acres
Show answer and explanation
Answer: 40 acres
640 x 1/4 x 1/4 = 40 acres.
4. Where is Section 1 located in the standard township numbering pattern?
- Northeast corner
- Northwest corner
- Southeast corner
- Southwest corner
Show answer and explanation
Answer: Northeast corner
The serpentine pattern begins with Section 1 in the northeast and ends with Section 36 in the southeast.
5. A survey says an irregular section contains 620 acres. What starting acreage should an exam calculation use for one-half of that actual section?
- 620 acres
- 640 acres
- 320 acres
- 23,040 acres
Show answer and explanation
Answer: 620 acres
The supplied actual acreage controls the starting base, producing a 310-acre half.
Which numbers and formulas are easy to confuse?
- Terms
- Township line vs. range line
- Difference
- Township lines run east-west and help form north-south tiers. Range lines run north-south and help form east-west columns.
- Question cue
- Tier boundary versus column boundary.
- Terms
- Township number vs. survey township
- Difference
- Township number identifies a tier north or south. A survey township is the roughly six-mile-square unit at a township-range intersection.
- Question cue
- Position label versus area unit.
- Terms
- Survey township vs. civil township
- Difference
- A survey township is a PLSS unit. A civil township is a governmental unit that can have different boundaries.
- Question cue
- Land grid versus local government.
- Terms
- Section vs. square mile
- Difference
- A standard section is intended to be one square mile, but survey irregularities can change actual section area.
- Question cue
- Survey parcel versus ideal area unit.
- Terms
- Linear mile vs. square mile
- Difference
- A mile measures distance. A square mile measures area and contains 640 acres.
- Question cue
- Length versus area.
- Terms
- Aliquot part vs. government lot
- Difference
- An aliquot part is an equal half or quarter subdivision. A government lot is a numbered surveyed parcel often created by irregularity.
- Question cue
- Equal fraction versus surveyed irregular parcel.
- Terms
- Nominal acreage vs. surveyed acreage
- Difference
- Nominal acreage follows ideal conversions. Surveyed acreage reflects the controlling survey facts for the actual parcel.
- Question cue
- Exam standard versus field record.
- Terms
- Quarter section vs. quarter-quarter
- Difference
- A quarter section is nominally 160 acres. A quarter of a quarter is nominally 40 acres.
- Question cue
- One fraction versus two fractions.
- Terms
- Area calculation vs. parcel location
- Difference
- Multiplying fractions gives nominal area. Reading the hierarchy and full PLSS calls identifies which land is described.
- Question cue
- How much versus where.
- Terms
- GIS section line vs. legal survey record
- Difference
- A GIS line is a mapping reference. Original and controlling survey evidence determines legal boundary location.
- Question cue
- Display layer versus boundary authority.
What does the outline expect you to calculate?
- Topic
- Public Land Survey System
- What to know
- PLSS, rectangular survey, government survey, public lands, cadastral survey, principal meridian, base line, township, range, section, and aliquot part
- Best exam move
- Recognize township, range, section, and meridian language as a rectangular-survey description.
- Topic
- Principal meridian
- What to know
- North-south reference, initial point, range, east, west, meridian number, Illinois, legal description, and survey framework
- Best exam move
- Use the named principal meridian to anchor east-west range position.
- Topic
- Base line
- What to know
- East-west reference, initial point, township tiers, north, south, correction, standard parallel, and survey origin
- Best exam move
- Use the base line to understand north-south township position.
- Topic
- Township designation
- What to know
- Tier, six-mile strip, north, south, T notation, base line, row of townships, survey township, and civil distinction
- Best exam move
- Read township number as position north or south, not as a 36-section area calculation by itself.
- Topic
- Range designation
- What to know
- Column, six-mile strip, east, west, R notation, principal meridian, range line, township intersection, and location
- Best exam move
- Read range number as position east or west of the named meridian.
- Topic
- Survey township
- What to know
- Six miles by six miles, 36 square miles, 36 sections, 23,040 acres, township and range intersection, nominal area, and correction
- Best exam move
- Multiply 36 sections by 640 acres when the question asks for a standard township's nominal area.
- Topic
- Section
- What to know
- One square mile, 640 acres, one mile per side, subdivision unit, numbered 1 through 36, nominal, actual survey, and legal description
- Best exam move
- Begin aliquot math with 640 only when no actual section acreage is supplied.
- Topic
- Serpentine numbering
- What to know
- Section 1, northeast, westward first row, Section 6, reverse direction, alternating rows, Section 36, southeast, and township diagram
- Best exam move
- Trace the alternating rows instead of numbering every row in the same direction.
- Topic
- Half section
- What to know
- North half, south half, east half, west half, one-half, 320 acres, rectangular dimension, and nominal area
- Best exam move
- Multiply 640 by one-half for 320 nominal acres.
- Topic
- Quarter section
- What to know
- NE, NW, SE, SW, one-fourth, 160 acres, half-mile sides, aliquot part, and equal subdivision
- Best exam move
- Multiply 640 by one-fourth for 160 nominal acres.
- Topic
- Quarter-quarter section
- What to know
- Nested quarter, 40 acres, one-sixteenth section, 1,320 feet per side nominally, smallest common subdivision, and aliquot description
- Best exam move
- Multiply 640 by one-fourth twice for 40 nominal acres.
- Topic
- Nested aliquot parts
- What to know
- Right-to-left reading, half, quarter, multiplication, denominator, several fractions, location, area, and parentheses
- Best exam move
- Write 640 times every fraction before performing arithmetic.
- Topic
- Right-to-left location
- What to know
- Section first, first subdivision, further subdivision, NW of SE, S half of NE quarter, location hierarchy, and description reading
- Best exam move
- Locate from the rightmost large tract toward the leftmost final subdivision.
- Topic
- Square-mile conversion
- What to know
- One mile, 5,280 feet, square mile, 27,878,400 square feet, 640 acres, section, and area unit
- Best exam move
- Keep a linear mile separate from a square mile of area.
- Topic
- Government lots
- What to know
- Irregular parcel, lot number, fractional section, correction, water boundary, prior claim, surveyed acreage, plat, and field notes
- Best exam move
- Use the lot's stated survey area rather than treating it as an equal quarter by assumption.
- Topic
- Correction and convergence
- What to know
- Earth curvature, meridian convergence, standard parallel, correction line, guide meridian, excess, deficiency, north and west tiers, and irregular section
- Best exam move
- Remember why actual acreage can differ from the 640-acre ideal.
- Topic
- Survey versus civil township
- What to know
- Congressional township, PLSS unit, political township, local government, proper name, numerical designation, boundary, area, and overlap
- Best exam move
- Do not use the 23,040-acre PLSS formula for a civil township unless the facts establish matching boundaries.
- Topic
- Controlling acreage and record
- What to know
- Nominal area, actual area, original monument, plat, field notes, deed, patent, survey, GIS line, assessor map, and professional determination
- Best exam move
- Use the actual figure supplied and treat online mapping as reference rather than conclusive boundary proof.
How should you drill this calculation?
- Session
- Session 1
- Focus
- Memorize PLSS anchors
- Proof you are ready
- Recall 36 sections, 640 acres, 23,040 acres, 43,560 square feet, and the section-number corners without notes.
- Session
- Session 2
- Focus
- Calculate aliquot parts
- Proof you are ready
- Solve 30 half, quarter, quarter-quarter, and three-level nested descriptions from 640 acres.
- Session
- Session 3
- Focus
- Read location calls
- Proof you are ready
- Sketch 20 right-to-left aliquot descriptions and distinguish their area from their location.
- Session
- Session 4
- Focus
- Handle irregular areas
- Proof you are ready
- Solve 20 supplied-acreage and government-lot scenarios without forcing the nominal section size.
- Session
- Session 5
- Focus
- Convert and reverse
- Proof you are ready
- Convert 20 section fractions to acres and square feet and recover 20 fractions from acreage.
- Session
- Session 6
- Focus
- Complete a mixed PLSS set
- Proof you are ready
- Score at least 90% and justify every base, fraction, direction, nominal label, irregularity, and survey boundary.
Do not count recognition as mastery. Close the notes and explain the rule, apply it to a new fact pattern, and identify why each distractor fails.
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Questions students ask about Section, Township, and Aliquot-Part Area Calculations
How many acres are in a section?
A standard section in the Public Land Survey System is nominally one square mile or 640 acres. The word nominal matters. Actual surveyed sections can differ because of convergence, correction lines, water, prior claims, boundaries, and government lots.
How many sections are in a survey township?
A standard survey township is nominally six miles by six miles and contains 36 sections. At 640 nominal acres per section, a full standard township contains 23,040 nominal acres, subject to actual survey irregularities.
How many acres are in a quarter section?
A quarter of a standard 640-acre section contains 160 nominal acres. A quarter of that quarter, called a quarter-quarter section, contains 40 nominal acres. Continue multiplying the fractions in the order written.
How do you calculate nested section fractions?
Start with the stated section acreage, usually 640 in a simplified problem, and multiply every fraction. The south half of the northeast quarter is 640 times one-fourth times one-half, or 80 nominal acres. Reading right to left locates the land, but multiplication gives the same area either way. For example, the east half of the southwest quarter of the northwest quarter is located by starting with the northwest quarter, selecting its southwest quarter, and then taking the east half of that smaller tract. Its nominal area is 20 acres.
How many acres are in half of a quarter-quarter section?
A quarter-quarter section is 640 times one-fourth times one-fourth, or 40 acres. Half of that is 20 nominal acres. Write all three fractions before multiplying so no division is skipped.
How are sections numbered in a township?
Sections begin with Section 1 in the northeast corner, run west to Section 6, then reverse east on the next row. This back-and-forth pattern continues to Section 36 in the southeast corner. It is often called boustrophedonic or serpentine numbering.
Is a survey township the same as a civil township?
No. A PLSS or congressional survey township is a land-survey unit identified by township and range. A civil or political township is a local-government unit whose name, boundaries, and area do not necessarily match the survey township.
What is an aliquot part?
An aliquot part is an equal fractional subdivision made through halves or quarters of a section or its subdivisions. Examples include the NE quarter and the S half of the NW quarter. A government lot is a separately numbered irregular surveyed parcel, not merely another assumed equal aliquot fraction.
Should every real section be treated as exactly 640 acres?
No. Use 640 for a standard exam calculation only when the question gives no surveyed acreage or irregular-lot facts. When a plat, survey, patent, deed, or problem supplies actual acreage, use that evidence instead of forcing the nominal number.
Are these official Illinois broker exam questions?
No. They are original calculations aligned to the PSI Illinois broker outline effective June 24, 2026. Current BLM survey materials, USGS guidance, and the 2026 Illinois Department of Revenue assessor-mapping manual were checked through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- U.S. Bureau of Land Management, PLSS land legal descriptions
- U.S. Bureau of Land Management, Manual of Surveying Instructions
- U.S. Bureau of Land Management, aliquot-part guidance
- U.S. Geological Survey, current guidance on PLSS map lines and legal records
- Illinois Department of Revenue PTAX-1-M, 2026 assessor mapping manual
The current official outline controls the tested scope. Statutes, regulations, and official agency materials control when a general study rule and a jurisdiction-specific rule differ.
Editorial status
Checked against primary sources
The Pass Illinois editorial team last checked this guide on August 1, 2026. Every practice question is an original study item, and the source links above let you verify the rules that support the lesson.