Real estate investors need to employ many different skills in managing their properties. Included in these are land and building measurements. The geometry involved in figuring out land size or internal square feet does not have to be complicated; if you follow the basic steps and view the task of calculation in its specific context, the job is not complicated.
As a starting point, why do you need to be able to measure land and building space? Many possible applications will arise during the course of looking at properties you are thinking about buying, calculating and comparing potential rental income on a size-specific basis, or checking the efficiency of cash flow.
Example: You are considering purchasing a triangular lot in a rural area. The property description identifies the property size as ‘‘5 to 6 acres.’’ You make an offer, and it is accepted; however, you would like to know precisely how much land you are purchasing. The listing also supplies the number of feet for each of the three sides. With the ability to calculate the area of a triangle, you conclude that the land area is slightly more than 4.5 acres. As a result, you write up an amended offer for a reduced purchase price. Your reasoning: The offer was made based on the listing’s claim that the land contained 5 to 6 acres, and it contained only 4.5.
Example: An agricultural area contains numerous storage silos, and you have an opportunity to purchase a piece of land containing four silos of various sizes. The numbers you are given estimating rental value are based on the amount of storage. To calculate this and to verify the claims made by the seller, you need to calculate the volume of each silo.
Example: You are thinking about purchasing several different properties. One listing provides a detailed description of a rectangular lot’s measurements, but it does not provide total square feet. Knowing how to calculate the area of a rectangle enables you to figure out the total square feet, and you can then convert that to acreage.
Example: A rental property is set up as a shared house. Several college students split the cost of common areas and have individual rooms. You need to calculate (1) the overall area, (2) the proportion of the space each tenant occupies, and (3) the prorated responsibility for common areas.
Example: You are thinking about selling an investment property, but before proceeding, you would like to estimate the appraised value. Some local phone calls reveal the typical replacement cost per square foot. To get a fair estimate of the replacement cost for your property, you will need to measure the internal space.
These examples demonstrate that figuring out size, shape, and volume is not merely a theoretical issue or a topic that is of interest only to appraisers and lenders. In fact, every real estate investor will repeatedly run into situations in which these mathematical skills will be valuable. If you depend on the assurances of real estate agents or sellers, you may get estimates only or downright inaccurate information. Land value is estimated based on lot size. The value of improvements is calculated in many ways, and a common appraisal method is calculation of replacement cost, which is expressed in cost per square foot.
Even comparing the cash flow and investment value among several properties that you own or that you are considering buying requires calculations. Figuring out rent on the basis of square feet is a good way to make such comparisons, but that requires the ability to perform those basic calculations. In this chapter, you will find a range of formulas for measuring land area, internal space, and volume, for both standard shapes and odd shapes.
The starting point for most land measurements is figuring out the land’s perimeter. This is the total size of the outer boundary of a shape. For example, a lot can be described as having a perimeter consisting of a series of measurements, one for each side. The perimeter may also be called the size of the edge, boundary, or property line. While perimeter describes the boundary, area is a precise measurement of the size within the shape.
The calculation of area varies with the shape itself. Calculating area for squares and rectangles is very simple, and this serves as the basis for figuring the area of more complex shapes. You need these because not all pieces of land are square or rectangular. Some lots are oddly shaped.
•Formula: Area of a Square or Rectangle
L * W = A
where:
L |
= length |
W |
= width |
A |
= area |
•Excel Program: Area of a Square or Rectangle
A1: |
length |
B1: |
width |
C1: |
=SUM(A1*B1) |
The same formula can be used for either a square or a rectangle. For example, one piece of property is square, measuring 90 by 90 feet. Another is rectangular, measuring 80 by 110 feet. To calculate the area in square feet for each of these shapes:
90 * 90 |
= 8,100 square feet |
80 * 110 |
= 8,800 square feet |
Squares and rectangles may have additional variations, but with the same calculations. A parallelogram has opposite sides that are of equal length (a sort of slanted rectangle), and a rhombus is a type of parallelogram with equal sides that are not at right angles (like a slanted square). The area of all these shapes is calculated on the same basis, but because the shape of the parallelogram and rhombus involve distortion of two sides, the correct formula for these is base multiplied by height, rather than length multiplied by width in calculations of the square and rectangle. These shapes are illustrated in Figure 12.1.
Figure 12.1: Square and Rectangular Shapes
It may also be necessary to convert measurements from other units into feet before making the calculation. Conversions between metric and U.S. measures are summarized in Appendix A. For converting from yards or inches to feet, it may be necessary to combine two conversion formulas.
•Formula: Conversion, Yards to Feet
Y * 3 = F
where:
Y |
= yards |
F |
= feet |
•Excel Program: Conversion, Yards to Feet
A1: |
yards |
B1: |
=SUM(A1*3) |
•Formula: Conversion, Inches to Feet
I ÷ 12 = F
where:
I |
= inches |
F |
= feet |
•Excel Program: Conversion, Inches to Feet
A1: |
inches |
B1: |
=SUM(A1/12) |
Example: You are given the measurements of a lot in yards and inches. The length is described as 12 yards, 22 inches, and the width is 11 yards, 4 inches. To convert these to feet:
Length:
12 yards * 3 |
= 36 feet |
22 inches ÷ 12 |
= 1.83 feet |
Total feet: 36 + 1.83 |
= 37.83 feet |
Width:
11 yards * 3 |
= 33 feet |
4 inches ÷ 12 |
= 0.33 feet |
Total feet: 33 + 0.33 |
= 33.33 feet |
Area:
37.83 * 33.33 = 1,260.87 square feet
The provision of land measurements in yards and inches may be unusual, as most measurements are expressed in feet or square feet. However, it is useful to be prepared for any required conversion task.
Land comes in all shapes and sizes, and measurements may be presented to you in various calculating systems. So it may also be necessary to convert square feet to acres, or vice versa. There are 43,560 square feet in one acre. Converting square feet to acreage requires division of the total number of square feet by the square feet in one acre.
•Formula: Conversion, Square Feet to Acres
F ÷ 43,560 = A
where:
F |
= square feet |
A |
= number of acres |
•Excel Program: Conversion, Square Feet to Acres
A1: |
square feet |
B1: |
=SUM(A1/43,560) |
For example, you previously calculated the size of a lot at 1,260.87 square feet. To calculate the same size in acres:
1,260.87 ÷ 43,560 = 0.029 acres, or 2.9% of one acre
If you need to convert in the opposite direction, you need to multiply the number of acres by 43,560.
•Formula: Conversion, Acres to Square Feet
A * 43,560 = F
where:
A |
= acres |
F |
= square feet |
•Excel Program: Conversion, Acres to Square Feet
A1: |
acres |
B1: |
=SUM(A1*43560) |
For example, a seller is advertising a piece of land for sale. The size listed in the ad is 1.35 acres. Another ad lists the size of a lot as three-quarters of an acre (or 75 percent of one acre). To figure the square feet for each piece of land:
1.35 * 43,560 |
= 58,806 square feet |
0.75 * 43,560 |
= 32,670 square feet |
There are many practical applications of these basic land calculations. In order to compare the size of different properties, you need to know how to express varying measurements in the same way, so computation and conversion formulas are both necessary. You may also need to convert different calculating methods for one piece of property. This comes up when you need to compare several different properties in terms of both acreage and the floor-area ratio. This is a percentage-based comparison between a building’s area and the total land area.
Example: You are thinking of making an offer on one of three properties. Because you want to keep open the possibility of expanding the property later or selling off a portion of the land, you are looking at properties for sale with residential improvements and land. You find the following properties:
Property A: |
2.7 acres and a 2,200-square-foot house |
Property B: |
3.0 acres and a 2,000-square-foot house |
Property C: |
3.3 acres and a 2,200-square-foot house |
In order to compare floor-area ratios for each of these properties, two steps are required. First, you need to convert acres to square feet, using the formula previously introduced, A = 43,560 F:
Property A: 2.7 * 43,560 |
= 117,612 square feet |
Property B: 3.0 * 43,560 |
= 130,680 square feet |
Property C: 3.3 * 43,560 |
= 143,748 square feet |
Next, you need to divide the building area by the land area.
•Formula: Floor-Area Ratio
B ÷ L = F
where:
B |
= building area |
L |
= land area |
F |
= floor-area ratio |
• Excel Program: Floor-Area Ratio
A1: |
building area |
B1: |
land area |
C1: |
=SUM(A1/B1) |
There are four additional variations on measurement of area. The first is the gross building area. This is a measurement of the exterior area of a building, without consideration for what is contained within it. For example, for a property measuring 43 feet by 50 feet (a straightforward rectangle), the gross building area is:
43 * 50 = 2,150 square feet
This is the basic rectangle formula for figuring area. It becomes more complex when you deal with a building that has variations in shape or multiple stories.
For example, look at Figure 12.2. This is a building whose area cannot be calculated using the rectangular formula alone. The outer area is 40 x 60 feet, or 2,400 total square feet; however, an indented area measures 10 x 10 feet, or 100 square feet. In this case, the area can be easily adjusted by deducting 100 from the gross area and concluding that the gross building area is actually 2,300 square feet.
The calculation may be more complex when a series of outer-wall changes are involved. You may need to calculate several additions to or subtractions from the initial calculation or make a series of smaller area calculations. Returning to Figure 12.2, you could also divide this property into three sections: the upper left section, measuring 30 x 10 feet; the lower left section, measuring 20 x 10 feet; and the right-hand section, measuring 30 x 60 feet:
30 x 10 |
= 300 |
20 x 10 |
= 200 |
30 x 60 |
= 1,800 |
Total |
2,300 |
The result is the same. This approach will be appropriate when the number of variations in outer size makes using the first method by itself too complex.
You may also need to calculate usable square footage, which is a valuable comparative tool. This is a ratio used in commercial property analysis or in multifamily buildings, where some parts of the interior of the building are not available. For example, a building may contain six units, with wall and utility space in between.
Figure 12.2: Odd-Shaped Building Area
When a property includes numerous units and nonrental space, the calculation of usable space can become complex. It may seem a minor point, but when added together, the combined nonusable areas can become a significant portion of the building’s total area.
The tendency to calculate these areas’ sizes may complicate the rental issues. In other words, the calculation of how much rent to charge can be vastly simplified by simply calculating the square feet of each unit and determining fair market rent based on unit area. A comparison to other properties, or even to classified ads, provides a fair and reasonable estimate of what you can charge for a space. If the typical 400-foot unit goes for $550 per month, and the typical 600-foot unit commands $700, you can calculate the relative value of units without also needing to look at nonusable space. It makes sense to simplify your calculations. As long as you know how much rent you need to generate for a building, you can easily prorate the total based on rental area. For example, if you need to generate $2,000 per month, and your building has three units (with square feet of 400, 550, and 575 feet), you can prorate the $2,000 total by unit. Total square feet add up to 1,525, so the units’ percentages are 26 percent, 36 percent, and 38 percent (rounded). And your rents should be $520 (26 percent x $2,000); $720 (36 percent x $2,000); and $760 (38 percent x $2,000).
The calculation of nonusable square feet is more important for comparisons between properties and an analysis of efficiency in a building’s space. You pay for the whole building, even when a portion cannot be rented out. So if one building has about 8 percent nonusable space and another has 16 percent, the second building provides far less efficiency, 84 percent rental space versus 92 percent for the first one. For example, if you estimate that market rents are approximately $1.30 per square foot of rental space, the nonusable space becomes an important factor. In a building with a total of 1,800 feet, a nonusable total of 16 percent (288 feet) represents reduced rents of $374 per month. If a comparable building of the same overall size has only 8 percent nonusable space (144 feet), the lost rent is half, or $187.
Considering that cash flow is usually a critical issue for rental properties (not to mention maximizing value by also maximizing rental income), the nonusable space may be significant when determining which building to purchase. The feasibility of the rental property is going to be determined by design efficiency. You cannot simply raise rents to make up for the inefficiency in design; you will need to conform to a range of market rates.
The immediate cash flow is only one of two concerns. The second is market value of the property. By definition, nonusable space is valueless. When you want to sell your property, its value will be determined by market rates, and, in practice, market rates are determined by rental square feet and not by total square feet. So if nonusable space is equal to 16 percent of the total area, whereas another building’s is only 8 percent, then your building will have twice as much valueless space.
This does not mean that in all cases it is fair or realistic to ignore nonusable space in calculating rents. This space should be classified in two ways. First is the space that has no aesthetic value to renters, such as utility space, internal systems, and walls. Second is the common area space, which is not actually nonusable. Consider the difference in rental attractiveness between units in a fourplex. The ground floor has street-level doorway access, but the second floor includes a foyer, staircase, and hallways. Those areas may serve as gathering places, out-of-unit but usable areas, and areas that add value to the units. In these situations, it is fair and reasonable to add some extra rental costs to the upstairs units.
The method is one of individual choice, however. It may not be fair to charge the same per-foot value for common areas, but clearly, the units with access to those additional areas should pay more per square foot than the units lacking the same features. A similar problem arises when you consider access to porch or yard areas. In the same building, for example, a ground-level porch and fenced-yard features may offset the foyer and hallway amenities of upper units. In all instances such as these, you will need to make value judgments and adjust rents based on what the market will bear. The cost per square foot is not ironclad but has to be adjusted up for conveniences and down for what units may lack. That price per square foot could be based on availability (or lack) of washer and dryer, transportation, or other features (noise levels, traffic, density).
The point is, there is no universally used standard for calculating rentable square feet. In cases where market rates are expressed in terms of unit size, it may be critical to include common areas such as hallways and to ignore the space taken up by interior and exterior walls, laundry rooms, and other nonrentable space. In the previous example, the unusable area was the size of a 500-square-foot apartment, so the difference can be substantial. Looking at the drawing of the fourplex, you might not realize how much area is involved in this, and while the illustration simplified the measurements to make the point, a landlord might advertise these units as containing 520 square feet (units 1 and 2) and 400 square feet (units 3 and 4) or, more realistically, as containing the net of 428 and 320 square feet.
For example, let’s assume that the advertised rentable area is based on the exterior of the building rather than on the actual interior square feet. In this situation, the hallway common area is split about equally, and you could simply use an approximation. So this complex may be said to contain four units, two measuring 520 square feet and two measuring 400 square feet. The explanation that common areas and unusable areas are counted as part of the total is acceptable as long as the standard is used consistently. You also assume that tenants recognize the inclusion of area that is not available to them. Smart tenants may actually measure the interior usable space to make their own comparisons between available units.
Finally, the loss ratio reveals the number of square feet in a building that cannot be rented out. This is also a valuable comparative calculation because building designs differ. Two buildings with identical gross building area may contain different rentable areas because of hallway and corridor configurations, laundry rooms, lobbies, stairways and elevators, heating and cooling equipment areas, common storage rooms, and, of course, interior walls.
In multiunit residential buildings (as well as in commercial rentals), owners may compute the relationship between net rentable area and gross building area and subsequently charge tenants a proportionate additional rent for the portion represented in the loss ratio.
•Formula: Loss Ratio
N ÷ G = L
where:
N |
= nonrentable area |
G |
= gross building area |
L |
= loss ratio |
•Excel Program: Loss Ratio
A1: |
nonrentable area |
B1: |
gross building area |
C1: |
=SUM(A1/B1) |
Figuring area for square and rectangular shapes is not complex. Unfortunately, land does not always come in these simple shapes. Some land is triangular or oddly shaped. In some types of land calculations, you may even need to calculate the area of a circle. For example, if you are calculating a crop yield for land that is farmed in a circular pattern because of the available watering system, it would not be accurate to count the square acreage, since actual yield will be less. You may also need to calculate the volume of buildings of different shapes. If you want to know the storage capacity of a silo, which is a cylinder, you need to know how to figure that capacity.
Triangles present a particular challenge because they contain three sides rather than four, and they come in different forms. An equilateral triangle has three sides that are equal in length. Another type of triangle has two equal sides and a third side of a different length. And a third type of triangle has three sides, all of which are different in length.
A starting point for calculating the area of a triangle is calculating the number of feet for each of the sides. You should not be as concerned with angles for this discussion, because for land investors, the emphasis is invariably on the amount of land involved. To calculate area, you need to know two measurements: base and altitude. The base is any of the sides of the triangle, and the altitude is the shortest distance from the base to the point where the other two sides meet. This is illustrated in Figure 12.3 for all three variations of a triangle’s shape. In any of the variations, area is figured by multiplying the base by the altitude and dividing the result by 2.
Figure 12.3: Base and Altitude of Triangles
•Formula: Area of a Triangle
(b * a) ÷ 2 = A
where:
b |
= base |
a |
= altitude |
A |
= area |
•Excel Program: Area of a Triangle
A1: |
base |
B1: |
altitude |
C1: |
=SUM(A1/B1)/2 |
(Note: In calculations involving triangles, lowercase designations are used for base and altitude. Uppercase letters are reserved for identifying the angles of triangles, and lowercase letters are consistently used for the length of the sides. Lowercase letters are used in calculations for some other shapes as well.)
You can also use altitude in figuring the area of a trapezoid. This shape contains four sides, of which at least two are of different lengths, as illustrated in Figure 12.4.
Figure 12.4: Trapezoid
To calculate the area of a trapezoid, add the two bases (top and bottom lengths) and divide the sum by 2, then multiply that answer by the altitude.
•Formula: Area of a Trapezoid
[(b1 + b2) / 2] * a = A
where:
b1 |
= base number 1 |
b2 |
= base number 2 |
a |
= altitude |
A |
= area |
•Excel Program: Area of a Trapezoid
A1: |
base number A |
B1: |
base number 2 |
C1: |
altitude |
D1: |
=SUM[(A1+B1)/2]*C1 |
It may be necessary to combine the calculations for squares with those for triangles to calculate the area of odd-shaped lots. For example, you may need to break down an odd-shaped lot into a rectangle and one or more triangles, calculate the area of each part, then add them.
A different approach is required in calculating the area of a circle. The outer line is called the circumference, and the diameter is a straight line from any point on the circle through the middle to the opposite side. The radius is a straight line from any point on the circumference to the exact middle point of the circle. When circles are perfect, calculations of area are not complex, but when a segment of a circle is excluded, the computation is far more complex (and beyond the scope of this book). We limit our calculations to situations like the one previously described, needing to know the area of a circular piece of agricultural land that is shaped that way because of a watering system.
To figure the area of a circle, you need to employ the value of pi. This is the 16th letter of the Greek alphabet, and it is used in mathematical formulas to denote the value of circumference divided by diameter. No matter what the size of a circle may be, pi is always the same. Pi is denoted using the Greek letter π and is equal to 3.1416.
•Formula: Pi
C ÷ D = π
where:
C |
= circumference of a circle |
D |
= diameter of a circle |
π |
= value of pi (3.1416) |
•Excel Program: Pi
A1: |
circumference of a circle |
B1: |
diameter of a circle |
C1: |
=SUM(A1/B1) |
While many uses of pi or approximations of it have been used throughout history—including estimates in the Bible (“And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about.” I Kings 7:23, Authorized [King James] Version)—the first approximation in mathematical form is credited to Archimedes (287–212 BC). His formula is called an approximation because pi is not an exact value. Archimedes summarized pi as:
223 ÷ 71 < π < 22 ÷ 7
Recognizing that pi does not have an exact value, most calculations can be dependably made using 3.1416. This is a midpoint between the two sides of Archimedes’ equation. The decimal equivalent of 223 ÷ 71 is 3.1408, and the decimal equivalent of 22 ÷ 7 is 3.1429. So the formula developed by Archimedes states that 3.1408 is less than pi, which is less than 3.1429.
All of this is important because an approximation of pi is needed to find the area of a circle. The formula involves squaring the radius and multiplying the result by pi.
•Formula: Area of a Circle
π x r2 = A
where:
π |
= pi |
r |
= radius |
A |
= area |
•Excel Program: Area of a Circle
A1: |
3.1429 |
B1: |
radius |
C1: |
=SUM(3.1429*(B1*B1)) |
For example, if the radius of a circular piece of land (the distance from the circumference to the exact middle of the circle, or one-half the diameter) is 82 feet, the area is:
3.1419 * 822 = 21,132.86 square feet
One final type of measurement that real estate investors may need in some circumstances is volume. This has several possible applications. Appraisals of some property may be performed on the basis of volume, or the size within a three-dimensional shape (a cube or a cylinder, for example). You need two basic formulas, one for the volume of a rectangular solid (including squares and rectangles) and one for the volume of a cylinder (such as a grain silo, for example).
The volume of a rectangular solid is an expansion of the linear land area. Volume adds a third dimension because land measurement involves only length and width. Volume also includes height.
•Formula: Volume of a Rectangular Solid
L * W * H = V
where:
L |
= length |
W |
= width |
H |
= height |
V |
= volume |
•Excel Program: Volume of a Rectangular Solid
A1: |
length |
B1: |
width |
C1: |
height |
D1: |
=SUM(A1*B1*C1) |
For example, suppose you are comparing prices for industrial warehouse storage facilities. For such properties, internal storage height is an important valuation feature, so you make your comparison based on a measurement of volume rather than floor space. You are reviewing three buildings, and their measurements are length, width, and height:
Building A: 90 * 85 * 24 feet |
= 183,600 cubic feet |
Building B: 105 * 60 * 30 feet |
= 189,000 cubic feet |
Building C: 115 * 75 * 18 feet |
= 155,250 cubic feet |
In this comparison, the third building would appear to have the largest area based on length and width, but when the relatively low height is considered, is becomes clear that the volume for the first two buildings is more desirable—at least in terms of storage capacity related to height itself. So if storage capacity is more significant in deciding between properties, the calculation of comparative volume is crucial to making an informed decision.
To calculate the volume of a cylinder, combine the calculation of the area of a circle with the height. To do this, multiply pi times the square of the radius and the height.
•Formula: Volume of a Cylinder
π * r2 x H = V
where:
π |
= pi |
r |
= radius |
H |
= height |
V |
= volume |
•Excel Program: Volume of a Cylinder
A1: |
3.1429 |
B1: |
radius |
C1: |
height |
D1: |
=SUM(A1*(B1*B1)*C1) |
Knowing how to calculate the area or volume for any size of lot or building is a necessary skill. In reviewing legal descriptions of land or comparing building and land sizes between different properties, you also need to be aware of the different systems in use for describing land.
The system that has been in use for the longest time is called metes and bounds. This is a good system for accurately describing land with an irregular shape, as is often the case. Metes and bounds begin at a specific starting point (a monument or known landmark) and identify the precise direction and length of each piece of a property’s perimeter, always ending up at the point of beginning. Calculations of metes and bounds are based on the azimuth system and on the bearing system for identifying direction. This is necessary because boundary lines do not always run exactly north, south, east, and west. Actual boundary lines may have any number of degrees in between those exact directions.
The azimuth system is a method for identifying compass direction based on a circle in which north is at the top. In using this system to calculate metes and bounds, the readings always begin at the northernmost boundary and move clockwise. Because a circle contains 360 degrees, due south would be 180 degrees, due east would be 90 degrees, and due west would be 270 degrees. The eight major divisions of the circle are summarized in Figure 12.5.
Figure 12.5: Degrees of a Circle
Of course, there are any number of angles in between these major eight points. Using the azimuth system, the direction of the property line is described in terms of a specific angle.
Under the bearing system, the circle is divided into four parts, and each direction is described as having a precise bearing. The four quadrants of the circle are northeast (NE), southeast (SE), southwest (SW), and northwest (NW). In writing down a bearing, three parts are included: the first letter indicating the direction (N, E, S, or W); the degrees, minutes, and seconds; and the second letter within the quadrant (E or W). For example, a bearing description reading N 80 ° 20’ 32” E precisely describes a line’s direction at an angle moving east and rising at a specific angle; next, the description would describe the exact number of feet the line travels in that direction.
The United States Geological Survey (USGS) system is also known as the grid system and is used to describe land boundaries in surveys. This system consists of a north-south line called a principal meridian and an east-west line called a baseline. Additional lines run parallel to each of these, placed at intervals of 24 miles in either direction. These are referred to as guide meridians and correction lines. The 24-mile squares that result are called checks or quadrangles.
The USGS Public Land Survey System is described in detail at https://nationalmap.gov/small_scale/a_plss.html.
Dividing these squares into smaller tracts at six-mile intervals are range lines; these define smaller groupings of square land areas called townships. A township’s north-south line is called a range, and the east-west line is called a tier. This system leads to the labeling of areas by specific location, so on plat maps, an area can be described by township number and by range, such as “Township 3 North, Range 2 West,” which tells you exactly where the land is on a map that is labeled and numbered.
Figure 12.6 provides an example of the USGS system showing these various lines and their names.
Under this system, every quadrangle contains 16 townships, each 6 miles square in size. Each of these townships is further divided into 36 smaller squares, each 1 mile square in size. These units are called sections. They can be further divided into subsections of 40 acres. These can be even further broken down into individual tracts.
A final breakdown of land is the lot and block system. When property within a city or town is described, a lot number is usually further identified as belonging to a tract, which in turn is found within a section. Tracts are broken down into smaller blocks, and those blocks are divided into lots. Each of these distinct units of land is given a number, so that a plat map identifies a specific property in terms of size, shape, and ownership. Legal descriptions may identify a piece of land as “lot 4, block 1, tract 17 of plat 42.” This tells you exactly which piece of land is involved. Or a legal description may involve metes and bounds and describe the property exactly, giving the starting point and the compass degrees and number of feet for each turn.
While precise calculations of land are going to be more complex for odd-shaped lots than for simple squares or rectangles, the exact calculations are not difficult to master. Applying these calculations to a completely platted map further aids in describing land, so that buyers, sellers, assessors, and real estate salespeople can all agree on where land is located and its exact size.
Figure 12.6: USGS Land Line System
Do real estate investors need to become expert mathematicians? No, but they do need to be able to employ a variety of formulas, used for many reasons. The more capable you are in applying these calculations, the better your decision making will be regarding real estate investments.