Land description and measurement guide
Section and township area from 640 acres
Start with 640 acres for a standard section, then apply every half and quarter in the description. A standard survey township adds 36 sections. The main trap is using that clean exam model to claim an actual boundary or acreage that the survey record does not establish.
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The short answer
A standard PLSS section is nominally 640 acres, or one square mile. A standard survey township has 36 sections and 23,040 nominal acres. A quarter section is 160 acres; a quarter-quarter is 40 acres. For a standard-section problem, multiply 640 by every stated half or quarter. Read the nested description from the section inward to locate the tract. For irregular land, use the area of the particular parcel supplied by the record or an explicit equal-area assumption. The whole section's acreage alone does not necessarily establish the acreage of its legally described north half.
Reviewed October 24, 2026. Government survey descriptions and land measurement appear in National I.B.3 and I.B.5 of the June 24, 2026 PSI broker outline. The whole Property Ownership area accounts for 10 of 100 scored national questions, not a quota for this calculation. The examples use stated ideal geometry or arithmetic assumptions. They do not create, retrace or certify a parcel boundary.
Choose the area model, then write the fraction chain
- Identify the question's starting facts. Use 640 acres for the stated standard section. For a standard six-mile-by-six-mile survey township, use 36 sections x 640 = 23,040 acres. Six miles square means 36 square miles, not six square miles.
- Write every subdivision. The E 1/2 of the SW 1/4 of the NW 1/4 of a standard section is 640 x 1/4 x 1/4 x 1/2 = 20 nominal acres. Do not omit one of the quarters just because it appears in the middle of the description.
- Separate area from location. Start with the rightmost section-level subdivision, then move left through its smaller parts. Multiplication order does not change the area product, but changing the order of directional calls can identify different land. Township, range and the named principal meridian are location references, not more fractions.
- For multiple separate tracts, calculate each and add only the nonoverlapping areas. Of the describes nesting; and the can identify another tract. A description of the NE quarter and SW quarter is not the same arithmetic as NE quarter of SW quarter.
- Convert the completed area. One acre = 43,560 square feet. Multiply acres by 43,560 to obtain square feet; divide square feet by 43,560 to obtain acres. A mile is length; a square mile is area. Ideal dimensions, such as a quarter-quarter's 1,320-foot sides, require the stated standard-square assumptions.
- For actual irregular land, stop before assuming equal acres. BLM's 2017 specifications distinguish halves by government measurement from halves by equal area. A whole-section total, a lot number or an online map is not enough to guarantee a particular subdivision's acreage. Use the parcel-specific survey information or the explicit assumptions of the math problem. The idealized equal-area BLM visualization is a learning model; it does not replace the more specific rules for locating real subdivisions.
| Row from north to south | Numbers from west to east | What to notice |
|---|---|---|
| 1, north edge | 6, 5, 4, 3, 2, 1 | Section 1 is northeast; the numbering travels west. |
| 2 | 7, 8, 9, 10, 11, 12 | The numbering returns east. |
| 3 | 18, 17, 16, 15, 14, 13 | The numbering travels west again. |
| 4 | 19, 20, 21, 22, 23, 24 | It returns east. |
| 5 | 30, 29, 28, 27, 26, 25 | It travels west. |
| 6, south edge | 31, 32, 33, 34, 35, 36 | Section 31 is southwest; Section 36 is southeast. |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Township line vs. range line | Township lines run east-west and help form north-south tiers. Range lines run north-south and help form east-west columns. | Tier boundary versus column boundary. |
| Township number vs. survey township | Township number identifies a tier north or south. A survey township is the roughly six-mile-square unit at a township-range intersection. | Position label versus area unit. |
| Survey township vs. civil township | A survey township is a PLSS unit. A civil township is a governmental unit that can have different boundaries. | Land grid versus local government. |
| Section vs. square mile | A standard section is intended to be one square mile, but survey irregularities can change actual section area. | Survey parcel versus ideal area unit. |
| Linear mile vs. square mile | A mile measures distance. A square mile measures area and contains 640 acres. | Length versus area. |
| Aliquot part vs. government lot | An aliquot description uses the PLSS half/quarter subdivision framework. A government lot is identified by its lot designation and survey record. Neither label guarantees an ideal acreage for irregular land. | Equal fraction versus surveyed irregular parcel. |
| Nominal acreage vs. surveyed acreage | Nominal acres follow the ideal exam model. Actual parcel acres require the appropriate survey facts. Even a supplied whole-section total does not automatically divide equally among its legal subdivisions. | Use parcel-specific area or an explicit equal-area assumption. |
| Quarter section vs. quarter-quarter | A quarter section is nominally 160 acres. A quarter of a quarter is nominally 40 acres. | One fraction versus two fractions. |
| Area calculation vs. parcel location | Multiplying fractions gives nominal area. Reading the hierarchy and full PLSS calls identifies which land is described. | How much versus where. |
| GIS section line vs. legal survey record | USGS says the PLSS representation on US Topo maps is not legally authoritative. A useful GIS display does not replace the controlling survey evidence. | Display layer versus boundary authority. |
Work through the facts
Calculate a full survey township
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
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
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.
An explicit equal-area arithmetic assumption
A math problem supplies a 612.8-acre tract and expressly says to calculate a parcel containing exactly one-half of its area. It is not asking you to locate a legal N 1/2 boundary.
- The problem expressly supplies an equal-area division.
- 612.8 x 1/2 = 306.4 acres.
- That arithmetic does not establish that the legally described north half of an irregular section has this area.
Answer: The requested equal-area amount is 306.4 acres under the stated assumption.
Convert a quarter-quarter to square feet
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
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.
A section total does not supply every subdivision area
An irregular section totals 620 acres. You are asked for the actual acreage of its N 1/2, but no subdivision plat, dimensions or equal-area assumption is supplied.
- 640 acres would ignore the stated irregularity.
- 620 / 2 = 310 is half the total arithmetically, but the facts do not establish that the legal N 1/2 is an equal-area half.
- The governing survey subdivision and parcel-specific evidence are needed.
- An acreage recital does not automatically override the controlling boundary evidence. This question does not supply enough evidence to resolve that issue.
Answer: The actual acreage of the legally described N 1/2 cannot be determined from the total alone.
Add separate nonoverlapping tracts
A standard-section problem asks for the combined area of the NE 1/4 and the SW 1/4 of the same section. The two tracts do not overlap.
- Each quarter is 640 x 1/4 = 160 nominal acres.
- The word and identifies two separate tracts.
- 160 + 160 = 320 acres. Multiplying the quarters instead would answer a different description.
Answer: The combined area is 320 nominal acres.
Mistakes to avoid
- Call one linear mile 640 acres. One square mile contains 640 acres; a linear mile measures distance only.
- Say a township contains 640 acres. A standard section is 640 acres; a standard township contains 36 sections or 23,040 acres.
- Divide by only the last fraction in a description. Apply every half and quarter to the starting section area.
- Read section numbers left to right on every row. The numbering reverses direction on each successive row.
- Assume every actual section is exactly 640 acres. Use the ideal 640-acre model when the question calls for it. For actual irregular subdivisions, neither 640 nor a simple fraction of the whole-section total is automatically the parcel area.
- Treat a government lot as an automatic 40-acre parcel. Use the lot number and surveyed acreage supplied by the controlling record.
- Confuse township and range directions. Township is north or south of a base line; range is east or west of a principal meridian.
- Call a civil township a guaranteed 36-square-mile PLSS township. Political boundaries can differ from the survey grid.
- Use acreage multiplication to identify parcel location. Area multiplication says how much under the stated model. The ordered calls and full description identify which tract; equal area does not mean identical location.
- Convert acres to square feet by dividing by 43,560. Multiply acres by 43,560; divide square feet by 43,560 to recover acres.
- Treat an online PLSS layer as conclusive boundary evidence. Mapping is a reference and does not replace controlling survey records and monuments.
- Let a broker create or resolve a disputed boundary through exam math. Boundary creation and retracement require appropriate survey and legal expertise.
- Always replace 640 with the irregular section total and multiply. Do that only if the problem expressly assumes equal-area subdivision or provides the relevant parcel-specific base. Government-measurement halves do not necessarily contain equal areas.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. What is the nominal acreage of a standard six-mile-by-six-mile survey township?
- 3,840 acres
- 23,040 acres
- 640 acres
- 36 acres
Show answer and explanation
Answer: B. 23,040 acres
6 x 6 = 36 square miles, and 36 x 640 = 23,040 acres. 3,840 incorrectly treats six miles square as six square miles; 640 is the standard section base.
2. In a standard section, how many nominal acres are in the W 1/2 of the SE 1/4?
- 40 acres
- 80 acres
- 160 acres
- 320 acres
Show answer and explanation
Answer: B. 80 acres
640 x 1/4 x 1/2 = 80 acres. Both fractions matter. For location, find the SE quarter first, then its west half.
3. How many nominal acres are in a quarter-quarter section under the standard model?
- 160 acres
- 20 acres
- 80 acres
- 40 acres
Show answer and explanation
Answer: D. 40 acres
640 x 1/4 x 1/4 = 40 acres, or 1/16 of the standard section. A single quarter is 160; half of a quarter-quarter is 20.
4. Which corner contains Section 1 in the standard township numbering pattern?
- Southeast
- Northeast
- Southwest
- Northwest
Show answer and explanation
Answer: B. Northeast
The north row reads 6,5,4,3,2,1 from west to east. Numbering begins at the northeast and alternates direction on subsequent rows; Section 36 ends at the southeast.
5. An irregular section totals 620 acres. No subdivision dimensions, parcel-specific area or equal-area assumption is supplied. What is the actual acreage of its legally described N 1/2?
- Always 160 acres
- Always 310 acres
- It cannot be established from the whole-section total alone
- Always 320 acres
Show answer and explanation
Answer: C. It cannot be established from the whole-section total alone
Government-measurement subdivision is not necessarily division into equal areas. 310 is the arithmetic half of 620, but the facts do not establish that it is the area of the legal N 1/2. Obtain the relevant survey evidence rather than substituting a nominal or unsupported actual figure.
6. A standard-section parcel is the E 1/2 of the SW 1/4 of the NW 1/4. What is its nominal area?
- 40 acres
- 80 acres
- 20 acres
- 10 acres
Show answer and explanation
Answer: C. 20 acres
640 x 1/4 x 1/4 x 1/2 = 20 acres. Locate the NW quarter, then its SW quarter, then the east half of that tract. The order of location calls matters even though the area factors can be multiplied in any order.
7. A government lot is expressly shown as 37.6 acres on the supplied parcel record. What square-foot figure follows from that stated area?
- 1,637,856 square feet
- 43,560 square feet
- 1,638 square feet
- 1,742,400 square feet
Show answer and explanation
Answer: A. 1,637,856 square feet
37.6 x 43,560 = 1,637,856 square feet. Do not replace the stated lot area with the nominal 40 acres of a quarter-quarter. This conversion uses the supplied parcel area; it does not decide a boundary dispute.
Common questions
How many acres are in a section?
A standard PLSS section is nominally 640 acres, or one square mile. Actual sections and their subdivisions can vary. Use the standard value for the ideal exam problem and the appropriate parcel-specific facts for an actual survey question.
How many acres and sections are in a township?
A standard survey township is six miles by six miles:36 square miles,36 sections and 23,040 nominal acres. Six miles square describes the side length of a square; it does not mean six square miles. A civil township is a separate governmental concept.
How many acres are in a quarter, quarter-quarter and half of a quarter-quarter?
Under the standard 640-acre model, a quarter is 160 acres; a quarter-quarter is 40 acres; and half of a quarter-quarter is 20 acres. Keep every half and quarter in the multiplication chain.
How do I read a nested aliquot description?
For E 1/2 of SW 1/4 of NW 1/4 of a section, locate the section, then its NW quarter, then that tract's SW quarter, then its east half. The standard area is 640 x 1/4 x 1/4 x 1/2 =20 acres. Reordering the directional subdivisions can change location even when it produces the same acreage. Direction letters identify location; they do not change the fractional area in the ideal model.
Do I multiply or add the fractions in a legal description?
Multiply nested of-the fractions for one tract. For separately described nonoverlapping tracts joined by and, calculate each area and add them. Check for overlap before adding. Punctuation and the full wording can change the meaning; do not draft a new legal description from the arithmetic.
How are township sections numbered?
Begin with 1 at the northeast corner and travel west to 6. The next row runs 7 through 12 eastward. Continue alternating directions until the south row runs 31 through 36 from west to east. The table above shows all six rows in their north-to-south order.
How long is a quarter-quarter section on each side?
In an ideal square section with one-mile sides, a quarter-quarter is one-quarter mile by one-quarter mile, or 1,320 feet by 1,320 feet. That produces 40 acres. These dimensions are an ideal-model result, not guaranteed dimensions of every actual aliquot parcel.
Does township mean north-south and range mean east-west?
In the PLSS designation, township numbering locates the tier north or south of the base line. Range numbering locates it east or west of the named principal meridian. The township and range labels do not multiply the area of the described section fraction.
Is a survey township the same as an Illinois civil township?
No. A survey or congressional township is part of the land grid. A civil or political township is a governmental unit whose boundaries need not match it. Do not assign 23,040 acres to a named civil township merely because it is called a township.
Can I take half an irregular section's total acreage to find its north half?
Not automatically. BLM's 2017 specifications explain that halves by government measurement follow the subdivision of boundary lines, without making equal area the controlling test unless contrary intent is explicitly shown. The total alone does not establish the actual acreage of the legal north half. An exam problem that expressly asks for one-half of an area supplies a different arithmetic assumption.
Are government lots always 40 acres?
No. Use the area shown for the particular lot or the information supplied by the problem. A government lot is not simply another name for a quarter-quarter, and its number does not encode its acreage.
Are PLSS lines on an online map legal boundary proof?
USGS states that the PLSS representation on US Topo maps is not legally authoritative. Mapping can help you find records and understand the framework, but a display is not a substitute for the controlling survey evidence and appropriate professional boundary work.
Are these official Illinois broker exam questions?
No. They are seven original teaching questions reviewed October 24, 2026 against the cited PSI, BLM, USGS and Illinois assessment-mapping sources. They are not recalled or predicted PSI items, a legal survey or a validated measure of readiness.
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Official sources and scope
Reviewed October 24, 2026. BLM's 2017 specifications are the source for the distinction between government-measurement halves and equal-area arithmetic. The BLM regional page's Willamette Meridian example is not an Illinois reference meridian. The January 2026 Illinois manual is assessor education, not a definitive legal interpretation, and its exercise directions are not PSI-wide rounding rules. The calculations use their stated assumptions. Neither an acreage recital nor an online layer automatically resolves conflicting boundary evidence. The original irregular-section half example has been replaced with an expressly equal-area arithmetic example and a separate insufficient-information example.
- PSI Illinois booklet, June 24, 2026: National I.B.3 and I.B.5
- BLM land legal descriptions: standard township, section and numbering framework; regional examples only
- BLM 2017 Specifications for Descriptions of Land, printed 8-11: nominal units, description order, lots and government-measurement halves
- USGS: PLSS representation on US Topo maps is not legally authoritative
- Illinois DOR PTAX-1-M, January 2026: measurements, rectangular survey, political townships and aliquot exercises
This is exam preparation, not advice for a specific transaction. State law and the applicable facts control. Our editorial and corrections process explains how to report an issue.