Exam math
Area, acreage and section conversion
Three constants carry almost all the land arithmetic on this examination: 43,560 square feet in an acre, 640 acres in a section, 36 sections in a township. This works both directions from any of them.
Your figures
Used to value the parcel. Land is often quoted per acre and sometimes per square foot, so check which the question gives you.
Parcel size
1 ac
43,560 square feet. One acre is 43,560 square feet, which is the single most useful constant in this part of the exam.
A section is 640 acres
The three constants
One acre is 43,560 square feet. One section is one square mile, which is 640 acres. A township is 36 sections, six miles by six miles. Those three carry almost all the land description arithmetic on the exam.
Complete results, no email, no account. Every calculation here is backed by a tested fixture, so the figure you see is the figure the test asserts. How we verify
Fractional section descriptions
Read a description such as the NW 1/4 of the SE 1/4 from the end backwards, dividing as you go. Or multiply the denominators and divide 640 by the result, which is faster.
40 acres
640 ÷ (4 × 4) = 640 ÷ 16 = 40
Value at $300,000 an acre: $12,000,000
How this is calculated
Rectangular parcels are width times depth for square feet, divided by 43,560 for acres, or divided by nine for square yards. An irregular lot is normally split into rectangles and triangles and summed, with a triangle being half the base times the height.
The rectangular survey system runs on townships and sections. A township is six miles by six miles, containing 36 sections, and each section is one square mile, which is 640 acres. Section 1 sits in the north-east corner and numbering runs right to left, then left to right on the next row, ending at section 36 in the south-east corner.
To read a fractional description, work from the end backwards and divide, or multiply the denominators together and divide 640 by the product. The NW 1/4 of the SE 1/4 is 640 divided by 16, which is 40 acres. Chaining more divisions works the same way: quarter of a quarter of a quarter is 640 divided by 64, which is 10 acres.
The other two description methods, metes and bounds and lot-block-tract, are covered in Property Ownership and Land Use Controls.