Illinois real estate exam concepts
Land measurement conversions: match the unit before calculating
A 150-foot street frontage can tell you the price of a lot sold by the front foot. It cannot tell you the lot's acreage. Before touching the calculator, write the unit the question asks for. Then decide whether you need a length, an area, a volume or a price.
Last reviewed:
The short answer
One acre equals 43,560 square feet, 4,840 square yards, 10 square chains or 160 square rods. One square mile equals 640 acres. A standard survey section is nominally one square mile; a standard survey township is nominally 36 sections or 23,040 acres. For length, one mile is 5,280 feet, one chain is 66 feet and one rod is 16.5 feet. Multiply acres by 43,560 to get square feet; divide square feet by 43,560 to get acres. Use compatible dimensions and keep actual surveyed acreage separate from nominal grid arithmetic.
Reviewed for October 2026 against the 2026 NIST tables and identified federal and Illinois survey references. PSI national I.B.4 and I.B.5 list measuring structures and land measurement within Property Ownership. The broader Property Ownership category accounts for ten of the 100 scored national broker questions; that is not a separate ten-question allocation to this page. The exercises are original teaching examples, not recalled PSI questions or a validated readiness test. Their stated geometric assumptions do not establish real property boundaries.
Choose the quantity, convert, then check
- Write the answer unit first. Feet or front feet mean length; square feet or acres mean area; cubic feet or cubic yards mean volume. A dollar answer also requires the matching price unit.
- Identify the shape and sufficient dimensions. For a rectangle, use length times width. For a triangle, use one-half times base times perpendicular height. A sloping side is not automatically the height, and frontage alone does not supply depth.
- Put dimensions into compatible units. Convert yards to feet before multiplying by a dimension in feet, or convert both dimensions to yards. Do not multiply a foot measurement by a yard measurement and label the result square feet.
- Convert the finished quantity using the correct power. Three feet equal one yard; nine square feet equal one square yard; twenty-seven cubic feet equal one cubic yard. A length factor cannot stand in for an area or volume factor.
- Use nominal section math only when the question supplies that model. Start with 640 acres and multiply every stated aliquot fraction once. A section's total surveyed acreage does not by itself establish the actual acreage of each described half or quarter.
- Keep precision until the requested final step. Estimate whether the converted number should be larger or smaller, check the unit and then round as directed. A whole-load purchasing instruction may require rounding up; it is not ordinary nearest-unit rounding or a universal exam rule.
| Quantity | Equivalent | Use it for |
|---|---|---|
| 1 foot | 12 inches | Length |
| 1 yard | 3 feet | Length |
| 1 mile | 5,280 feet = 80 chains = 320 rods | Length |
| 1 chain | 66 feet = 4 rods = 100 links | Length |
| 1 rod, pole or perch | 16.5 feet | Length; do not confuse with a square rod |
| 1 link | 0.66 foot | Length |
| 1 square foot | 144 square inches | Area |
| 1 square yard | 9 square feet | Area |
| 1 square rod | 272.25 square feet | Area |
| 1 square chain | 4,356 square feet = 0.1 acre | Area |
| 1 acre | 43,560 square feet = 4,840 square yards = 10 square chains = 160 square rods | Area, regardless of parcel shape |
| 1 square mile | 27,878,400 square feet = 640 acres | Area |
| 1 standard section | 640 nominal acres | An idealized PLSS exercise, not every surveyed section |
| 1 standard survey township | 6 miles by 6 miles = 36 sections = 23,040 nominal acres | Survey township, not necessarily a political township |
| 1 cubic yard | 27 cubic feet | Volume |
| 1 acre-foot | 43,560 cubic feet | Volume: one acre of area times one foot of depth |
The distinctions that matter
| Distinction | How it works | What to notice |
|---|---|---|
| Frontage, perimeter and area | Frontage measures the relevant front edge. Perimeter measures the boundary length. Area measures the enclosed surface. | For a 100-by-200-foot rectangle, frontage on the 100-foot street edge is 100 feet, perimeter is 600 feet and area is 20,000 square feet. The street edge must be identified. |
| A square yard and three square feet | A yard is three feet, so a square yard is three feet by three feet, or nine square feet. | Square the length factor for area and cube it for volume. One cubic yard is 27 cubic feet, not 9. |
| Ten square chains and a square ten chains on each side | Ten square chains equal one acre. A square ten chains by ten chains contains 100 square chains, or ten acres. | A unit name and a side length are different inputs. Read whether the number describes area or each side. |
| Acreage and a fixed shape | An acre is an area unit, not a required rectangle or a required frontage. A square acre has a side about 208.710 feet long. | Do not use 208.710 feet as the side of every acre. Other shapes and dimensions can enclose exactly the same area. |
| Nominal grid math and actual parcel measurement | Standard section and township sizes are useful teaching models. Actual sections, government lots and aliquot parts depend on survey and record evidence. | A supplied actual area for the described parcel can answer its area or price question. A total section area alone does not prove equal areas for every government-measurement half. |
| The international foot and a legacy U.S. survey foot | The international foot is exactly 0.3048 meter. The legacy survey foot has a slightly different metric equivalent. NIST says definitions based on the survey foot should be avoided after 2022 except for historic and legacy applications. | Do not mix the two metric bases in one calculation or silently reinterpret an old record. The ordinary stated foot-to-foot exam relationships remain as shown in the table. |
Work through the facts
A rectangular lot becomes acres
A rectangular parcel measures 330 feet by 264 feet. Find its acreage.
- 330 feet times 264 feet = 87,120 square feet.
- 87,120 square feet /43,560 square feet per acre = 2 acres.
- Both dimensions were already in feet; the area was converted once.
Answer: 2 acres.
Convert a decimal acre without rounding it first
A parcel contains 2.75 acres. How many square feet is that?
- 2.75 acres times 43,560 square feet per acre.
- The acre units cancel and the product is 119,790 square feet.
- No intermediate rounding is needed.
Answer: 119,790 square feet.
Mixed dimensions need a common unit
A rectangular parcel is 60 yards wide and 120 feet deep. Find square feet and acres.
- 60 yards times 3 feet per yard = 180 feet.
- 180 times 120 = 21,600 square feet.
- 21,600/43,560 = 60/121 acre, about 0.49586777 acre.
Answer: 21,600 square feet, or 0.496 acre to the nearest thousandth. Multiplying 60 by 120 and calling the answer square feet would be incorrect.
A triangle needs perpendicular height
A triangular parcel has a 300-foot base and 220-foot perpendicular height. Find its acreage to the nearest hundredth.
- One-half times 300 times 220 = 33,000 square feet.
- 33,000/43,560 = 25/33 acre, about 0.75757576 acre.
- Round only the final acreage to two decimal places.
Answer: 0.76 acre. The stated perpendicular height, not an unprovided sloping side, makes the calculation possible.
Use chains in both dimensions
A rectangular tract is 20 chains long and 5 chains wide. Find its acres.
- 20 times 5 = 100 square chains.
- One acre contains 10 square chains.
- 100/10 = 10 acres; equivalently 1,320 feet times 330 feet = 435,600 square feet.
Answer: 10 acres. A chain is length; multiplying two chain dimensions produces square chains.
Nested section fractions
Use the idealized 640-acre section model. Find the nominal acreage of the S 1/2 of the NE 1/4 of the section.
- Begin with the full 640-acre section.
- 640 times 1/4 = 160 acres for the northeast quarter.
- 160 times 1/2 = 80 acres for the south half of that quarter.
Answer: 80 nominal acres. The compass directions identify the part; each stated fraction enters the area calculation once.
A frontage price does not use depth
A lot has 150 feet of the identified street frontage and 240 feet of depth. The stated price is $900 per front foot.
- The price unit matches the 150 front feet.
- 150 times $900 = $135,000.
- For a rectangular-area question, 150 times 240 would give 36,000 square feet, but that is not the quantity priced here.
Answer: The indicated frontage-based price is $135,000. This is the stated pricing calculation, not an appraisal of market value.
A cutout must not be counted twice
A 100-by-200-foot rectangular tract has a nonoverlapping 20-by-30-foot rectangular corner cutout excluded. Find the remaining area.
- Outer rectangle: 100 times 200 = 20,000 square feet.
- Excluded cutout: 20 times 30 = 600 square feet.
- Subtract once: 20,000 minus 600 = 19,400 square feet.
Answer: 19,400 square feet. The dimensions and exclusion are expressly supplied; do not invent a missing shape or subtract an overlapping feature twice.
Volume needs a depth conversion
An excavation is 20 feet long, 12 feet wide and 6 inches deep. Ignore waste and find cubic yards. If supplies are sold only in whole cubic-yard units, how many units cover the stated volume?
- 6 inches = 0.5 foot.
- 20 times 12 times 0.5 = 120 cubic feet.
- 120/27 = 40/9 cubic yards, about 4.44444444.
Answer: The geometric volume is 40/9 cubic yards. The separate whole-unit buying instruction requires 5 units. Waste, compaction and actual purchasing specifications are not supplied.
Use the supplied actual area for that parcel
The exercise supplies an accepted surveyed area of 40.7 acres for the particular parcel being priced, with a stated rate of $1,200 per acre.
- The stated actual parcel area is the pricing quantity.
- 40.7 times $1,200 = $48,840.
- Do not replace the supplied 40.7 acres with a remembered nominal 40-acre quarter-quarter model.
Answer: The indicated price is $48,840. This does not settle a boundary dispute or establish the area of any different parcel.
Mistakes to avoid
- Multiply square feet by 43,560 to get acres. Divide by 43,560. Acres to square feet goes in the other direction and multiplies.
- A square yard is 3 square feet and a cubic yard is 9 cubic feet. The correct factors are 9 for area and 27 for volume.
- A 100-foot front edge tells me the acreage. Frontage alone lacks the depth and shape information needed for area.
- Acre means a square with a fixed side length. Acre describes area, not shape. The square-acre side length is a conditional illustration.
- Every surveyed section is exactly 640 acres. 640 is nominal. Use the appropriate supplied survey facts and do not determine real boundaries by a classroom shortcut.
- An actual 660-acre section guarantees 330 acres in its north half. Government subdivision can use linear midpoints or proportions rather than equal areas. The section total alone is insufficient.
- Round every intermediate result. Keep exact values until the requested final step. Follow a stated whole-unit purchasing condition separately.
Check your understanding
These are original teaching questions, not recalled or predicted PSI questions. Answer first, then explain why the other choices fail.
1. How many square feet are in 1.5 acres?
- 43,560
- 65,340
- 87,120
- 21,780
Show answer and explanation
Answer: B. 65,340
1.5 times 43,560 = 65,340 square feet. The starting quantity is acres, so multiply to obtain square feet.
2. A rectangular lot measures 110 feet by 198 feet. What is its area?
- 10,890 square feet
- 616 square feet
- 21,780 square feet
- 43,560 square feet
Show answer and explanation
Answer: C. 21,780 square feet
110 times 198 = 21,780 square feet, equal to one-half acre. Adding the sides does not calculate the area.
3. Using the nominal 640-acre model, what is the NW 1/4 of the SE 1/4 of a standard section?
- 80 acres
- 320 acres
- 40 acres
- 160 acres
Show answer and explanation
Answer: C. 40 acres
640 times 1/4 times 1/4 = 40 nominal acres. Apply each stated fraction once; the directions do not supply another multiplication factor.
4. How many feet are in 12 chains?
- 198 feet
- 792 feet
- 1,980 feet
- 660 feet
Show answer and explanation
Answer: B. 792 feet
12 times 66 = 792 feet. The question asks for length, not square chains or area.
5. A triangle has a 160-foot base and 100-foot perpendicular height. What is its area?
- 16,000 square feet
- 26,000 square feet
- 43,560 square feet
- 8,000 square feet
Show answer and explanation
Answer: D. 8,000 square feet
One-half times 160 times 100 = 8,000 square feet. The perpendicular height is expressly supplied.
6. How many square feet are in 480 square yards?
- 1,440
- 4,320
- 160
- 480
Show answer and explanation
Answer: B. 4,320
480 times 9 = 4,320 square feet. Nine is the area conversion; three is the linear yard-to-foot factor.
7. A square has sides of 10 chains each. What is its area?
- 10 acres
- 0.1 acre
- 1 acre
- 100 acres
Show answer and explanation
Answer: A. 10 acres
10 times 10 = 100 square chains. Divide by 10 square chains per acre to obtain 10 acres. Ten square chains, as an area quantity, would instead be 1 acre.
8. A standard nominal survey township contains how many acres?
- 3,600
- 36
- 640
- 23,040
Show answer and explanation
Answer: D. 23,040
36 nominal sections times 640 acres per section = 23,040 nominal acres. A political township need not coincide with the survey township.
9. Which statement alone supplies enough information to calculate rectangular area?
- Both perpendicular side lengths, in compatible units
- One side is twice another, with no length given
- A description as near the road
- 100 feet of frontage only
Show answer and explanation
Answer: A. Both perpendicular side lengths, in compatible units
A rectangle needs its two perpendicular dimensions. Frontage or a ratio without a size does not establish area.
10. An actual section is stated to contain 660 acres. No subdivision dimensions or area of its north half are supplied. What is the actual acreage of the north half?
- The total alone does not establish that part's actual area
- Always 330 acres
- Always 165 acres
- Always 320 acres
Show answer and explanation
Answer: A. The total alone does not establish that part's actual area
Government subdivision need not create equal areas. Do not apply the nominal 640-acre model to decide actual boundaries or blindly halve a surveyed total.
11. A rectangle is 30 yards by 60 feet. How many square feet does it contain?
- 5,400
- 16,200
- 1,800
- 600
Show answer and explanation
Answer: A. 5,400
30 yards = 90 feet. Then 90 times 60 = 5,400 square feet. Both dimensions must be in compatible units before the product is labeled square feet.
12. A lot has 120 feet of identified frontage. At $750 per front foot, what is the stated indicated price?
- $16,000
- $750
- $120,000
- $90,000
Show answer and explanation
Answer: D. $90,000
120 front feet times $750 per front foot = $90,000. Depth is unnecessary for this particular pricing unit; it would matter for an area calculation.
13. An excavation is 20 feet long, 12 feet wide and 6 inches deep. Ignoring waste, what is its volume in cubic feet?
- 120
- 10
- 1,440
- 240
Show answer and explanation
Answer: A. 120
Convert 6 inches to 0.5 foot, then 20 times 12 times 0.5 = 120 cubic feet. Do not multiply the inch depth as though it were feet.
14. Which statement about an acre is correct?
- It must be a square
- It must have 208.710 feet of street frontage
- It is a volume unit
- It is 43,560 square feet regardless of the enclosing shape
Show answer and explanation
Answer: D. It is 43,560 square feet regardless of the enclosing shape
An acre measures area. A square acre has an approximately 208.710-foot side, but an acre need not be square or have that frontage.
15. A circle has radius 20 feet. Use pi = 3.1416 as supplied here. What is its area?
- 125.664 square feet
- 62.832 square feet
- 400 square feet
- 1,256.64 square feet
Show answer and explanation
Answer: D. 1,256.64 square feet
Area is pi times radius squared: 3.1416 times 20 times 20 = 1,256.64 square feet. The supplied pi convention belongs to this exercise, not a claimed universal PSI rule.
16. A rectangular parcel is 100 feet wide and contains one acre. What is its perpendicular depth?
- 43.56 feet
- 4,356 feet
- 435.6 feet
- 208.710 feet
Show answer and explanation
Answer: C. 435.6 feet
43,560 square feet /100 feet = 435.6 feet. Area divided by width gives the other length for the expressly rectangular parcel. The square-acre side does not apply to this rectangle.
Common questions
How many square feet are in an acre?
One acre contains 43,560 square feet. Multiply acres by 43,560 to get square feet; divide square feet by 43,560 to get acres. For example, 87,120 square feet equals 2 acres. Keep the requested unit beside the calculation so you can see which units cancel.
How many square yards are in an acre?
An acre contains 4,840 square yards because 43,560 square feet divided by 9 square feet per square yard equals 4,840. The factor is 9, not 3. A yard-to-foot conversion is linear; square yards and square feet measure area.
How many acres are in a square mile, section or township?
One square mile equals 640 acres. A standard PLSS section is nominally one square mile, and a standard survey township is nominally 36 sections, six miles by six miles, or 23,040 acres. Actual surveyed sections and townships can differ. A political township is not necessarily the same area or boundary as a survey township.
How many feet are in a chain or rod?
A chain is 66 feet, four rods or 100 links. A rod, also called a pole or perch in this measurement context, is 16.5 feet. A link is 0.66 foot. One mile is 5,280 feet, 80 chains or 320 rods. Do not replace a length unit with a square version when the question asks for a boundary distance.
What are square chains and square rods?
A square chain is 66 feet by 66 feet, or 4,356 square feet; ten square chains equal one acre. A square rod is 16.5 feet by 16.5 feet, or 272.25 square feet; 160 square rods equal one acre. A square with ten-chain sides contains 100 square chains, not ten, and therefore contains ten acres.
Can I find acreage from frontage alone?
No. Frontage supplies a length. You need enough dimensions and the correct shape to find area. For a rectangle, multiply frontage by perpendicular depth in compatible units. A price per front foot uses the stated frontage directly; a price per square foot or per acre needs the corresponding area instead.
How do I handle mixed feet and yards?
Convert the dimensions to one compatible length unit before applying the area formula. Sixty yards by 120 feet becomes 180 feet by 120 feet, or 21,600 square feet. You could instead use 60 yards by 40 yards to obtain 2,400 square yards, then multiply by 9. Both routes give the same area.
How do I calculate a triangular or irregular parcel?
Use one-half times base times perpendicular height for a triangle. For a stated composite shape, split it into nonoverlapping rectangles, triangles or other known figures, then add or subtract their areas as appropriate. If a needed dimension or the shape is missing, say what is missing. Do not invent a perpendicular height from a sloping side or treat every four-sided parcel as a rectangle.
How do I calculate a section fraction?
For an explicitly nominal 640-acre section, multiply 640 by each stated fraction. A quarter of a quarter is 640 times 1/4 times 1/4 = 40 nominal acres. Read the description outward from the section to locate the part. This exercise is not a method for determining actual irregular government-lot boundaries or guaranteeing equal areas in every surveyed half.
Is a half section always 320 acres?
320 acres is the idealized 640-acre model result. Actual section subdivision can differ, and a government-measurement half need not contain exactly half of the section's measured area. A supplied total alone is not enough to determine the actual area of an unspecified part. Use appropriate survey and record evidence for real property, or the particular parcel area expressly supplied by the exercise.
Does every acre have a 208.710-foot side?
No. A square enclosing an acre has a side approximately equal to the square root of 43,560, about 208.710 feet. An acre can have a different shape, frontage and perimeter. The figure is a square-only illustration, not a universal lot dimension.
How are area and volume conversions different?
Area uses two dimensions: one square yard equals 9 square feet. Volume uses three: one cubic yard equals 27 cubic feet. Convert inches of depth to feet before multiplying a foot-based length and width. One acre-foot is 43,560 cubic feet, because it combines one acre of area with one foot of depth.
Should I round land calculations at every step?
Keep exact factors and full intermediate precision, then round the final result as the question directs. For 33,000 square feet, acreage is 25/33, about 0.75757576; the nearest hundredth is 0.76 acre. A separate instruction to buy only whole units can require rounding upward. Do not turn a workbook exercise's convention into a universal PSI rounding rule.
Did the U.S. survey-foot change alter old parcel boundaries?
NIST says definitions based on the U.S. survey foot should be avoided after December 31, 2022 except for historic and legacy applications. The international foot is exactly 0.3048 meter; the legacy survey foot has a slightly different metric equivalent. This unit policy is not permission to redraw an old boundary or silently change the basis of a historic survey. Follow the identified units and appropriate professional survey analysis.
Can an exam conversion replace an Illinois boundary survey?
No. Illinois boundary-survey standards call for record evidence, fieldwork and appropriate boundary-law analysis. Nominal acreage, a simplified drawing, a tax-map outline or a multiplication exercise does not settle title or the position of a boundary. A supplied accepted survey area can be used in its stated math question without claiming that the calculation establishes the legal line.
How do I find a missing rectangular dimension from acreage?
Convert the acreage to square feet, then divide by the known positive width or depth in feet. One acre divided by a 100-foot width gives 43,560/100 = 435.6 feet of depth. The shape must be a rectangle and the denominator must be nonzero; area and a single edge do not determine the dimensions of every irregular parcel.
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Official sources and scope
NIST supplies the unit relationships; the geometry examples are original applications. Federal PLSS guidance distinguishes nominal teaching figures from actual subdivision and government lots. Illinois standards require survey evidence and professional boundary analysis. The 2026 edition label does not mean these long-established arithmetic relationships newly took effect in 2026. Neither the survey-foot policy nor an acreage calculation changes a recorded boundary.
- PSI Illinois booklet, June 24, 2026: measuring structures and land
- OpenStax Prealgebra 2 e 9.4: rectangles, triangles and trapezoids
- OpenStax Prealgebra 2 e 9.5: circles and composite figures
- BLM 2017 Specifications for Descriptions of Land, printed 8-11: nominal units, description order, lots and government-measurement halves
- Illinois DOR PTAX-1-M, January 2026: measurements, rectangular survey, political townships and aliquot exercises
- USGS: PLSS representation on US Topo maps is not legally authoritative
- NIST Handbook 44, 2026 AppendixC: exact length, area and volume units
- NIST revised unit conversion factors: 2026 current and legacy survey units
- NIST Handbook 44 current edition: 2026 and AppendixC
- 68 Ill.Adm.Code 1270.56: boundary-survey purpose, evidence and analysis
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.