- Official section
- National I.B.2: Legal Descriptions and Measurement
- Broker weight
- Part of 10% of the national portion
- Expected scored items
- The current PSI broker outline assigns about 10 of 100 scored national items to Property Ownership
Property Ownership exam concept
Land measurement conversions
Most land math is a unit problem wearing a real estate costume. Write the requested unit first, calculate the shape in one consistent unit, then convert once at the end. That order prevents the two errors the exam expects: confusing length with area and multiplying when you should divide.
Last updated: August 1, 2026
What is the difference at a glance?
Short answer: Memorize 43,560 square feet per acre, 640 acres per square mile or nominal section, 36 sections per nominal survey township, 5,280 feet per mile, 66 feet per chain, 16.5 feet per rod, and 9 square feet per square yard. Calculate rectangle area as length times width and triangle area as one-half base times perpendicular height. Convert acres to square feet by multiplying by 43,560 and square feet to acres by dividing by 43,560. Keep linear, square, and cubic units separate, and treat section and township acreage as nominal unless the question supplies surveyed acreage.
This guide follows the calculations and measurement content in the PSI broker outline effective June 24, 2026. NIST Handbook 44 Appendix C for 2026 is the primary conversion reference. Federal policy discontinued general use of the U.S. survey foot after December 31, 2022 except for historic and legacy applications, but ordinary exam problems use the conventional foot-based relationships stated here. Surveyed parcel area can differ from simple nominal PLSS or geometric math. Sources were checked through August 1, 2026.
What changes from one term to the next?
- Terms
- Linear feet vs. square feet
- Difference
- Linear feet measure one dimension. Square feet measure two-dimensional area.
- Question cue
- Boundary length versus parcel area.
- Terms
- Square feet vs. cubic feet
- Difference
- Square feet measure area using length times width. Cubic feet measure volume using length times width times height or depth.
- Question cue
- Two dimensions versus three.
- Terms
- Acre vs. square mile
- Difference
- An acre is 43,560 square feet. A square mile contains 640 acres.
- Question cue
- Parcel unit versus large-area unit.
- Terms
- Mile vs. square mile
- Difference
- A mile is 5,280 linear feet. A square mile is a mile by a mile and contains 27,878,400 square feet.
- Question cue
- Length versus area.
- Terms
- Yard vs. square yard
- Difference
- A yard is 3 linear feet. A square yard is 3 feet by 3 feet, or 9 square feet.
- Question cue
- Factor of 3 versus factor of 9.
- Terms
- Perimeter vs. area
- Difference
- Perimeter adds boundary lengths. Area measures the surface enclosed by the boundary.
- Question cue
- Fencing versus land size.
- Terms
- Front foot vs. square foot
- Difference
- A front foot prices each linear foot of frontage. A square foot prices each unit of area.
- Question cue
- Street edge versus full parcel.
- Terms
- Section vs. township
- Difference
- A nominal section is one square mile and 640 acres. A nominal survey township contains 36 sections and 23,040 acres.
- Question cue
- One grid square versus 36 squares.
- Terms
- Nominal acreage vs. surveyed acreage
- Difference
- Nominal acreage follows theoretical grid or geometry. Surveyed acreage reflects the controlling boundaries and actual professional work.
- Question cue
- Exam model versus field and record result.
- Terms
- Multiply vs. divide by 43,560
- Difference
- Multiply acres to obtain square feet. Divide square feet to obtain acres.
- Question cue
- Large units to small multiply; small units to large divide.
How does the distinction change the answer?
Rectangular lot to acres
Scenario: A rectangular parcel measures 330 feet by 264 feet. How many acres does it contain?
- Area equals 330 times 264, or 87,120 square feet.
- The question requests acres, so divide by 43,560.
- 87,120 divided by 43,560 equals 2.
Answer: The parcel contains 2 acres.
Acres to square feet
Scenario: A buyer wants the square footage of a 2.75-acre parcel.
- The starting unit is acres and the requested unit is square feet.
- Multiply 2.75 by 43,560.
- The product is 119,790 square feet.
Answer: The parcel contains 119,790 square feet.
Square yards to square feet
Scenario: A paved courtyard contains 480 square yards. What is its area in square feet?
- One square yard equals 9 square feet, not 3.
- Multiply 480 by 9.
- The product is 4,320 square feet.
Answer: The courtyard contains 4,320 square feet.
Triangular parcel
Scenario: A triangular parcel has a base of 300 feet and a perpendicular height of 220 feet. Find its acreage.
- Area equals one-half times 300 times 220.
- The area is 33,000 square feet.
- 33,000 divided by 43,560 is approximately 0.758 acre.
Answer: The parcel contains about 0.76 acre when rounded to the nearest hundredth.
Nested section fraction
Scenario: What is the nominal acreage of the S 1/2 of the NE 1/4 of a standard section?
- Begin with 640 acres.
- The northeast quarter contains 160 nominal acres.
- The south half of that quarter contains 80 nominal acres.
Answer: The described aliquot part contains 80 nominal acres.
Price per front foot
Scenario: A commercial lot has 150 feet of street frontage and is priced at $900 per front foot. The depth is 240 feet.
- The price unit is front feet, so the 150-foot frontage is the relevant quantity.
- Multiply 150 by $900 to obtain $135,000.
- The depth would matter for area analysis but not for the stated front-foot price calculation.
Answer: The indicated price is $135,000.
The U-N-I-T method for land math
- Unit wanted: write the requested answer unit, such as feet, square feet, acres, or price.
- Numbers and shape: list only useful dimensions and identify rectangle, triangle, circle, section fraction, or direct conversion.
- In one system: convert all input dimensions to compatible units before using an area formula.
- Technique: apply length times width, one-half base times height, nested section fractions, or the correct conversion factor.
- Test the result: label the unit, delay rounding, estimate size, and confirm that the conversion direction makes sense.
- Transfer to value: if price is involved, make the land-area unit match the price unit before multiplying or dividing.
- Starting unit
- 1 foot
- Equivalent
- 12 inches
- Exam use
- Linear dimensions
- Starting unit
- 1 yard
- Equivalent
- 3 feet
- Exam use
- Linear conversion
- Starting unit
- 1 square yard
- Equivalent
- 9 square feet
- Exam use
- Area conversion
- Starting unit
- 1 mile
- Equivalent
- 5,280 feet
- Exam use
- Distance and boundary
- Starting unit
- 1 rod
- Equivalent
- 16.5 feet
- Exam use
- Legacy survey calls
- Starting unit
- 1 chain
- Equivalent
- 66 feet or 4 rods
- Exam use
- Legacy survey calls
- Starting unit
- 1 acre
- Equivalent
- 43,560 square feet
- Exam use
- Parcel area
- Starting unit
- 1 square mile
- Equivalent
- 640 acres
- Exam use
- Section and large tract
- Starting unit
- 1 section
- Equivalent
- 640 nominal acres
- Exam use
- PLSS fraction math
- Starting unit
- 1 survey township
- Equivalent
- 36 sections or 23,040 nominal acres
- Exam use
- PLSS grid math
Where do similar terms create traps?
- Trap
- Using 3 square feet per square yard
- Correction
- A square yard is 3 feet by 3 feet, so it contains 9 square feet.
- Trap
- Multiplying square feet by 43,560 to get acres
- Correction
- Divide square feet by 43,560. Multiply only when converting acres to square feet.
- Trap
- Using frontage as area
- Correction
- Frontage is a linear dimension. Area requires another dimension and a known shape.
- Trap
- Confusing a mile with a square mile
- Correction
- A mile is length. A square mile is area and contains 640 acres.
- Trap
- Forgetting one-half in a triangle
- Correction
- Triangle area is one-half base times perpendicular height.
- Trap
- Using the sloped side as triangle height
- Correction
- Height must be perpendicular to the chosen base unless the question states a right angle that makes the side perpendicular.
- Trap
- Adding dimensions for area
- Correction
- Adding sides finds part of a perimeter. Multiply compatible dimensions to find rectangle area.
- Trap
- Multiplying nested section denominators without the 640 base
- Correction
- Start with 640 acres and apply each stated fraction to that base.
- Trap
- Assuming every surveyed section is exactly 640 acres
- Correction
- The grid value is nominal. Use actual acreage when the question or survey supplies it.
- Trap
- Mixing yards and feet in one area formula
- Correction
- Convert both dimensions to the same linear unit before multiplying.
- Trap
- Rounding after every calculator step
- Correction
- Keep full precision through intermediate work and round only as requested at the end.
- Trap
- Leaving an answer unlabeled
- Correction
- Write the unit. A bare 640 could mean feet, acres, square feet, dollars, or something else.
Can you separate the terms in a new fact pattern?
These questions are original study items aligned to the published outline. They are not copied, recalled, or predicted PSI questions.
1. How many square feet are in 1.5 acres?
- 21,780
- 43,560
- 65,340
- 87,120
Show answer and explanation
Answer: 65,340
Multiply 1.5 acres by 43,560 square feet per acre. The result is 65,340 square feet.
2. A rectangular lot measures 110 feet by 198 feet. How many square feet does it contain?
- 616
- 10,890
- 21,780
- 43,560
Show answer and explanation
Answer: 21,780
Multiply length by width: 110 times 198 equals 21,780 square feet, which is one-half acre.
3. What is the nominal acreage of the NW 1/4 of the SE 1/4 of a standard section?
- 20 acres
- 40 acres
- 80 acres
- 160 acres
Show answer and explanation
Answer: 40 acres
A section is 640 nominal acres. One quarter is 160 acres, and one quarter of that is 40 acres.
4. How many feet are in 12 chains?
- 198 feet
- 660 feet
- 792 feet
- 1,980 feet
Show answer and explanation
Answer: 792 feet
One chain equals 66 feet. Twelve times 66 equals 792 feet.
5. A triangular lot has a 160-foot base and a 100-foot perpendicular height. What is its area?
- 8,000 square feet
- 16,000 square feet
- 26,000 square feet
- 43,560 square feet
Show answer and explanation
Answer: 8,000 square feet
Use one-half times base times height: 0.5 times 160 times 100 equals 8,000 square feet.
Where do these ideas appear on the outline?
- Topic
- Linear measurement
- What to know
- Inch, foot, yard, mile, link, rod, pole, perch, chain, frontage, depth, boundary, perimeter, length, width, radius, diameter, and compatible units
- Best exam move
- Use linear units for a single dimension and do not report a length answer in square feet.
- Topic
- Area measurement
- What to know
- Square inch, square foot, square yard, acre, square mile, square rod, square chain, section, township, rectangle, square, triangle, irregular tract, and two dimensions
- Best exam move
- Area units are squared because two perpendicular dimensions are multiplied.
- Topic
- Volume measurement
- What to know
- Cubic foot, cubic yard, acre-foot, length, width, height, depth, excavation, concrete, water, and three dimensions
- Best exam move
- Do not use an area conversion for a question that multiplies three dimensions and requests volume.
- Topic
- Feet, yards, and miles
- What to know
- 12 inches per foot, 3 feet per yard, 5,280 feet per mile, 1,760 yards per mile, linear conversion, multiply, divide, and unit cancellation
- Best exam move
- Moving from a larger length unit to a smaller one multiplies; moving back to the larger unit divides.
- Topic
- Square feet and square yards
- What to know
- 1 square yard, 9 square feet, 1 square foot, 144 square inches, area factor, flooring, parcel area, multiply by 9, and divide by 9
- Best exam move
- Square the linear relationship: 3 feet by 3 feet equals 9 square feet per square yard.
- Topic
- Acre conversion
- What to know
- 43,560 square feet, 4,840 square yards, 160 square rods, 10 square chains, 1/640 square mile, multiply to square feet, divide to acres, decimal acre, and rounding
- Best exam move
- Write 43,560 beside every acreage question before choosing multiplication or division.
- Topic
- Square mile conversion
- What to know
- 640 acres, 27,878,400 square feet, mile by mile, section, large tract, multiply, divide, and nominal area
- Best exam move
- Treat one square mile as 640 acres and distinguish it from one linear mile.
- Topic
- Rod and chain
- What to know
- Rod, pole, perch, 16.5 feet, chain, 66 feet, 4 rods per chain, 100 links per chain, 80 chains per mile, 320 rods per mile, survey description, and legacy unit
- Best exam move
- Convert older survey units to feet before combining them with modern dimensions.
- Topic
- Rectangle and square area
- What to know
- Length times width, side squared, frontage, depth, feet, yards, acres, consistent units, calculator, label, and decimal
- Best exam move
- Multiply dimensions only after both are expressed in the same linear unit.
- Topic
- Triangle area
- What to know
- One-half, base, perpendicular height, right angle, irregular parcel, diagonal, sloped side, square feet, acres, and combined shapes
- Best exam move
- Use one-half times base times perpendicular height, not base times a sloping side.
- Topic
- Circle basics
- What to know
- Radius, diameter, pi, circumference, area, radius squared, 3.1416, circular parcel, round pool, linear edge, and square area
- Best exam move
- Use pi times radius squared for area and pi times diameter for circumference only when the question supplies a circle.
- Topic
- Irregular parcel strategy
- What to know
- Divide, rectangle, triangle, add areas, subtract cutout, sketch, dimensions, common unit, missing height, approximation, survey, and no invented dimension
- Best exam move
- Break the figure into familiar shapes, calculate each, then add or subtract as the diagram requires.
- Topic
- Government section math
- What to know
- 640 acres, half section 320, quarter section 160, half-quarter 80, quarter-quarter 40, half-quarter-quarter 20, nested fractions, nominal, and aliquot part
- Best exam move
- Start at 640 and multiply by every stated fraction once.
- Topic
- Survey township math
- What to know
- Six miles by six miles, 36 square miles, 36 sections, 23,040 acres, section numbering, correction, convergence, and nominal grid
- Best exam move
- Multiply 36 sections by 640 acres for a nominal full-township result.
- Topic
- Frontage and depth
- What to know
- Linear frontage, street line, waterfront, depth, rectangular assumption, price per front foot, price per square foot, area, irregular boundary, and no area from frontage alone
- Best exam move
- Use frontage as length unless the question also gives depth and a shape for area.
- Topic
- Pricing by area
- What to know
- Price per square foot, price per acre, total price, parcel area, unit rate, multiply, divide, land value, comparable, and unit consistency
- Best exam move
- Convert the parcel into the same unit used by the price before multiplying.
- Topic
- Rounding and reasonableness
- What to know
- Exact intermediate result, decimal, fraction, requested precision, nearest hundredth, premature rounding, estimate, reasonableness, label, and calculator entry
- Best exam move
- Keep full precision until the end and ask whether the answer should be larger or smaller than the starting number.
- Topic
- Surveyed versus calculated area
- What to know
- Nominal acreage, deed acreage, survey acreage, government lot, correction, boundary calls, monument, curve, terrain, projection, professional surveyor, and title
- Best exam move
- Use supplied surveyed facts when given and do not let simple exam formulas overrule a legal survey record.
How do you make the distinction stick?
- Session
- Session 1
- Focus
- Memorize the conversion spine
- Proof you are ready
- Write 43,560, 640, 36, 5,280, 66, 16.5, and 9 with each matching unit from memory three times.
- Session
- Session 2
- Focus
- Separate length, area, and volume
- Proof you are ready
- Classify 30 requested units as linear, square, or cubic and choose the number of dimensions needed.
- Session
- Session 3
- Focus
- Calculate regular shapes
- Proof you are ready
- Solve 10 rectangles, 10 triangles, and five combined-shape parcels with compatible units.
- Session
- Session 4
- Focus
- Convert acres and square feet
- Proof you are ready
- Complete 20 two-way conversions and state aloud why each problem multiplies or divides by 43,560.
- Session
- Session 5
- Focus
- Master section fractions
- Proof you are ready
- Solve 20 aliquot-part acreage questions by starting at 640 and applying every fraction once.
- Session
- Session 6
- Focus
- Run the U-N-I-T method
- Proof you are ready
- Score at least 90% under time and show unit wanted, numbers and shape, compatible units, technique, test, and any value step for each miss.
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.
Turn the comparison into a test-day decision
From concept to decision
Drill this topic, then review the explanation
Pass Illinois gives you original national and Illinois questions, topic-by-topic study, clear explanations, timed practice, flashcards, progress tracking, and Math Coach. Start free, find the weak distinction, and focus the next session there.
Questions students ask about Land Measurement Conversions
How many square feet are in an acre?
One acre contains 43,560 square feet. To convert acres to square feet, multiply by 43,560. To convert square feet to acres, divide by 43,560. Keep the direction straight by asking which answer unit the question requests.
How many acres are in a square mile?
One square mile contains 640 acres and 27,878,400 square feet. A standard section in the government rectangular survey system is nominally one square mile, so the exam commonly treats a section as 640 acres.
How many acres are in a township?
A standard survey township is nominally six miles by six miles, or 36 square miles. With 640 acres per square mile, its nominal area is 23,040 acres. Actual surveyed townships and sections can include corrections and irregularities.
How many feet are in a mile?
One mile contains 5,280 feet. One chain contains 66 feet, one rod contains 16.5 feet, and one mile contains 80 chains or 320 rods. These survey units can appear in older descriptions and conversion questions.
How many square feet are in a square yard?
One square yard contains 9 square feet because a yard is 3 feet and area uses both dimensions: 3 feet times 3 feet equals 9 square feet. Do not use 3 as the square-area conversion factor.
How do you convert square feet to acres?
Divide the square-foot area by 43,560. For example, 87,120 square feet divided by 43,560 equals 2 acres. If dimensions are given first, calculate the area in square feet before converting.
How do you calculate the area of a rectangular lot?
Multiply length by width, using compatible units. A lot 120 feet by 180 feet contains 21,600 square feet. Divide 21,600 by 43,560 to obtain about 0.496 acre if the question requests acres.
How do you calculate the area of a triangular lot?
Multiply base by perpendicular height and divide by 2. A triangle with a 200-foot base and 120-foot perpendicular height contains 12,000 square feet. A sloping side is not the height unless it is perpendicular to the base.
What is the difference between linear feet and square feet?
Linear feet measure length, such as frontage, fencing, or a boundary. Square feet measure area, such as a parcel or floor. A 100-foot frontage does not reveal area unless another dimension or a complete shape is supplied.
Are these official PSI exam questions?
No. They are original questions aligned to the national Property Ownership calculations in the PSI outline effective June 24, 2026. The 2026 NIST measurement tables, federal PLSS guidance, and current Illinois survey standards were reviewed through August 1, 2026.
Primary sources
- PSI Illinois Candidate Information Booklet dated June 24, 2026
- NIST Handbook 44, current 2026 edition
- NIST Handbook 44 Appendix C, 2026 General Tables of Units of Measurement
- NIST revised survey-unit conversion factors, updated February 3, 2026
- U.S. Bureau of Land Management, Public Land Survey System description guide
- 68 Ill. Adm. Code 1270.56, current Illinois minimum survey standards
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.