Level 14: Real Estate Math - Chapter 1: Measurements

Square Mile

As I explained in the last screen, one section is equal to one square mile. To break things down a little more, 1 square mile is equal to 5,280 square feet. If 5,280 feet make a mile, then 5,280 feet by 5,280 feet make a square mile. A square mile is equal to 640 acres.

The Importance of Measurements

As an agent, your buyer might have all sorts of questions for you that could be answered with a little measurement arithmetic. For example: "Will my 25-seat, 40-foot denim couch fit in this living room?" "This room is 15' by 12', but how in the world am I supposed to know how many square feet that is?" "My friend Jeremy says he owns two acres of land upstate. I think he's lying. How can I prove it?" Knowing the way property measurement works can help an agent answer their client's questions. Properties are often described in terms of their measurements. If a home is described as a 1,200-square-foot bungalow or a 2,400-square-foot brownstone, you already know a decent amount about that property. Additionally, buyers might have stipulations based on measurements. They may want a property larger than 1000 square feet, for example, or a place on a lot larger than two acres. When it comes down to it, knowing your way around dimensions, square footage, acreages, and the like will help you help your client. No, the agent's job isn't to give an accurate survey of the property's boundaries. That job is left up to a different group of professionals. But it is an agent's job to help frame the decisions that a buyer makes, and one important buying factor for most people is the size of a property.

Price Per Square Foot

As you spend time in the real estate world, you'll begin to hear a lot about a property's price per square foot. Homebuyers will often want to know, "What's the price per square foot for this house?" This metric gives prospective homebuyers an "apples to apples" way to compare the cost of two similar properties. While the price per square foot is not the only factor to consider when purchasing a house, it is an important factor that homebuyers consider. I'm going to teach you how to calculate it. (It's easy.)

Irregular Disclaimer

If the idea of having to find the exact area of an irregular lot scares you, don't worry. You're not the only one! It would scare me too if robots could feel fear. As I have stated before, finding the exact, legal square footage of a property isn't the job of a real estate agent. The advertised square footage of the property must be measured by a professional. Additionally, an agent should check with their local regulations to see what their requirements are. So, while finding the area of a weird-looking lot would certainly impress your buyer, and is a helpful skill to have, it's not something you should keep yourself up at night about.

Acreage: The Size of Land

In this chapter, we discussed square footage: a unit of area measurement most commonly used to measure the size of a building. Let's now discuss acreage: a unit of area measurement used to measure the size of land.

Calculating Cost Per Square Foot

It's quite simple, Mustafa. Take a look at the formula above and follow these steps: Step 1: Find the house's total square footage.Step 2: Find the house's asking price.Step 3: Divide the house's total square footage by the houses's asking price.Step 4: Celebrate! Mustafa, got that down? Let's practice.

Solving for Acreage: Property A

Jane, a prospective homebuyer, is interested in purchasing 1314 Wagon Wheel Circle. The survey says that the property's lot size dimensions are 484 ft x 315 ft. Question: Using this information, how many acres is the lot? Step 1: Identify the land's square footage. We can identify the land's square footage by multiplying the length and width of the land (just like we did for a property's square footage). For this problem, we'll multiply 484 ft. by 315 ft. Result: 484 ft x 315 ft = 152,460 sq ft Step 2: Divide by 43,560 feet. You remember that one acre equals 43,560 feet, right? Good. For our last step (Yes, only 2 steps!), we divide the square footage of our land by 43,560 feet. This answer will give us our property's size in acres. Result: 152,460 sq ft ÷ 43,560 feet = 3.5 acres Solving for Property A's Acreage: Recap To identify how many acres a plot of land is, we need to: Identify the square footage of the land Divide the land's square footage by 43,560 feet Easy-peasy, Mustafa! Now, time for you to practice it on your own.

Square Footage Example: Janelle's Room

Janelle's bedroom is 15' by 11'. With these numbers, we can then calculate her bedroom's square footage. 15 x 11 = 165 sq ft Janelle's bedroom is 165 square feet.

Solving for Cost Per Square Foot: Kevin's House

Kevin is looking at houses on the west side of Yonkers. He wants to find a house for less than $200 per square foot that's close to downtown. Kevin is looking at a house this afternoon. The owner is asking for $252,000. The MLS listing states that the house has 1,105 square feet. Question: At this asking price, does this house meet Kevin's request of less than $200 per square foot? Kevin's Cost Per Square Foot: Identify the Known Variables Step 1: Identify the known variables Here's what we know: The asking price ($252,000) The total square footage of the house (1,105 ft.) Result: Price Per Square Ft = $252,000 ÷ 1,105 ft. Step 2: Divide We've got our variables — it's now time for us to solve the problem. $252,000 ÷ 1,105 = $228.05 Result: $228.05 per sq ft With a price of $228 per square foot, this house doesn't meet Kevin's requirements for a house that costs less than $200 per sq.ft. on the west side of Yonkers. It's important to note that the price per square foot will vary depending on many factors. A new house will probably have a higher cost per square foot, as it is in better condition and is less likely to need repairs.

An Irregular Example

Let's take a look at the dimensions of the irregular lot in this image. Notice that not every dimension is given. I did that just to make it a little tougher for you. But don't worry, I'll walk you through it! As you can tell, the lot is made up of two separate rectangles. So your first job is to find the dimensions of both rectangles. This will take a little bit of easy math to figure out. If we break the lot into two rectangles, we already know that the bottom one is 40 feet by 30 feet. We have been given those dimensions. We also know that the right side of the lot is 50 feet long and the border on the bottom left side is 30 feet long. The difference between those two is going to be the length of the top left side of the plot. 50 - 30 = 20 feet So, the top rectangle is 20 feet by 25 feet. So the top rectangle's dimensions are 20' x 25'. 20 x 25 = 500 square feet The bottom rectangle's dimensions are 40' x 30'. 40 x 30 = 1,200 square feet Now we just have to add those two together to get the size of the whole lot. 500 + 1,200 = 1,700 square feet

1 Acre = 43,560 Square Feet

Mustafa, 1 acre = 43,560 square feet. Memorize this conversion rate — you'll need to know it by heart for your real estate licensing exam. repeat after me1 acre = 43,560 square feet1 acre = 43,560 square feet1 acre = 43,560 square feet

How to Calculate Square Footage

Now that you know what square footage is, let's talk about how you calculate it. To calculate square footage, all you need are two factors: Length Width You can calculate the square footage of an area by multiplying these two factors together.

Triangular Lots

One of the shapes that an agent is sure to encounter is a triangle. You probably know about triangles, right, Mustafa? It'd be kind of weird if you didn't. But besides being the shape of club sandwiches, pizza slices, and wizard hats, a triangle is also the shape of many real estate lots. There is a simple way to find the area of a triangle. Divide the base of the triangle by 2 and then multiply that number by the height of the triangle. I'll show you on the next screen. The lot in this image is a right triangle. It's base is 54' and it's height is 80'. So, how do we find the area? Step 1: Divide the base by 2. So, 54 ÷ 2 = 27. Step 2: Multiply the answer by the height. So, 27 x 80 = 2,160 sq. ft. The area of this triangular-shaped lot is 2,160 square feet.

Perry's Perimeter

Perry, on the other hand, has a slightly irregular lot. It's the shape of two rectangles, one bigger than the other. The dimensions of his lot are 50' x 30' x 30' x 20' x 20' x 50'. So, what is Perry's perimeter? Perry's Perimeter: Answer Finding the perimeter of the dimensions 50' x 30' x 30' x 20' x 20' x 50' is simple. Just add up those numbers! 50' + 30' + 30' + 20' + 20' + 50' = 200 feet So, the perimeter of Perry's irregular lot is 200 feet!

Equations

Reminder: You can always maneuver an equation to solve other problems. Suppose a sales agent is asked to lease 1,500 square feet of warehouse space at $3 per square feet per year. What's the total price a tenant would spend to rent all of that warehouse space? $3 (Price per Square Foot) x 1,500 (Square Foot) = $4,500 (Price). Boom! A tenant could rent all of the warehouse space for $4,500

Finding the Area of Irregular Lots

So, now we know how to find the area of a triangular and rectangular space. But if you think about all the homes, apartments, and lots you've seen, often times they aren't just one shape. They are made up of a combination of different shapes. To find the total square footage of a lot or home that is irregularly shaped, the area must be broken up into smaller, manageable shapes. We won't get into too much detail, and I won't make you go step by step into measuring a bunch of different pieces, but you should have an idea of how an irregular lot or home's size is measured. Think about it like this: the square footage of a home is the sum of all the individual rooms and areas of a home's square footage.

Square Footage: Used to Compare Building Sizes

The most common measurement that buyers consider when searching for a home is the square footage of the home. Square footage is a unit of area measurement. Buyers and sellers most commonly use square footage as a way to compare the size of buildings.

Perimeter

The perimeter of a lot is a rather simple measurement. The perimeter is the boundary of the property. To find out what the perimeter is of a property, all you have to do is add the boundary lines together. For example, let's say I, Ace, buy a perfectly square lot measuring 100' x 100'. That would mean that there are 4 sides to my lot, each one being 100 feet long. 100 + 100 + 100 + 100 = 400 The perimeter of my beautiful new square lot is 400 feet.

Other Units of Measurement

There are other measurements that might come up during your real estate career. If you remember back when we talked about legal property descriptions, you learned all about townships and sections. 1 section = 1 square mile = 640 acres 1 township = 36 sections = 36 square miles One that we haven't talked about in this course yet is a hectare. A hectare is a metric unit of measurement equal to 10,000 square meters. A hectare is also equal to 2.471 acres.

Square Footage and Tina

Tina is looking to purchase a home in the Plattsburgh area. To help, her agent set up a MLS search query that provides Tina with Plattsburgh homes within her price range. Here is this week's results: 1301 Castle DriveFeatures: 1300 SQ FT, 3 Bedrooms, 2 BathPrice: $275,000 1200 Davis LaneFeatures: 1100 SQ FT, 3 Bedrooms, 2 BathPrice: $275,000 6602 Krollton DriveFeatures: 1500 SQ FT, 3 Bedrooms, 2 BathPrice: $280,000 As Tina looked at the results, she noticed that 1200 Davis Lane and 1301 Castle Drive were both for sale at $275,000, and both had three bedrooms and two baths. However, 1301 Castle Drive has 200 more square feet than 1200 Davis Lane. 200 more square feet for the same price! Tina also knows that square footage isn't the only factor to consider. For example, 1301 Castle Drive might be in poorer condition than 1200 Davis Lane, or the layout of 1200 Davis Lane might be much more appealing. Recap: Tina (and most home buyers) use square footage as a measurement tool to compare the size of buildings.

Frontage (Front Feet)

What should keep you up at night is front feet. Just kidding, don't lose any sleep over front feet. But seriously, you should know what front feet are. The frontage is the portion of the boundary of a lot that borders the street. Frontage is measured in front feet. A front foot is the unit used to measure a property that borders a street. One front foot is one foot of property bordering the street. When giving the dimensions of a property, the front feet are always stated first. For example, if a property is 150' x 313', the property has a frontage of 150 feet, or, 150 front feet.

A Note About Calculating a House's Total Square Footage: Don't

While calculating a simple, rectangular area (such as a bedroom) is easy, calculating the square footage of a house is much more difficult. Houses have lots of corners, so calculating the square footage of a house is usually a bit more complicated than just multiplying two factors. If a license holder incorrectly calculated the square footage of a house, they may be liable for misrepresentation. For this reason, license holders should always search for and cite a source for square footage instead of calculating square footage on their own.

Math Workshop: Jenny's Farm

Your friend, Jenny, has a small farm just outside of Woodstock. She knows the dimensions of her property are 1,386 ft by 451 ft. *Don't forget, if you need to refer back to the details of the story when working through the problem, you can access them by clicking on the question image. Jenny's Farm: Explanation 1 Answer: The square footage of Jenny's land is 625,086 sq ft. Explanation: By multiplying 1,386 ft by 451 ft, we find that the total square footage of the land is 625,086 ft. Jenny's Farm: Explanation 2 Answer: There are a total of 14.35 acres on Jenny's land. Explanation: By dividing the land's square footage (625,086 sq ft) by 1 acre (43,560 ft), we find that Jenny's land has 14.35 acres.

Chapter 1 Key Terms

✏️ acre: a unit of area measurement used to determine the size of land — 1 acre = 43,560 square feet ✏️ hectare: metric unit used to measure the area of land; one hectare equals 2.471 acres or 10,000 square meters ✏️ front foot: standard unit used to measure a boundary of the property that borders a street; one front foot is one foot of property bordering the street