Real estate math worries more exam candidates than almost any other topic, but the math itself is not advanced. Nearly every question uses addition, subtraction, multiplication, division and percentages. What trips people up is knowing which formula to use and setting up the problem correctly under time pressure.
This guide covers how much real estate math is on the exam, the formulas you need, worked examples for each type of problem, common traps, and practice questions with answers. When you finish, keep practicing with our free real estate practice exam.
Table of Contents
How Much Real Estate Math Is on the Exam?
The answer depends on your state and testing company, so check your state’s candidate handbook. As one example, Pearson VUE’s current national content outline, effective April 1, 2025, includes seven real estate math questions out of 80 scored questions on the national salesperson portion, and eight out of 80 on the broker portion. Math also appears inside other topics, such as valuation and financing.
The outline lists these math areas, one question each for salespersons:
- Property area calculations, such as square footage and acreage.
- Property valuation, such as net operating income, capitalization rate, equity and assessed value.
- Commission and compensation.
- Loan financing costs, such as interest, loan-to-value and discount points.
- Settlement and closing costs, such as down payment, net to seller and prorations.
- Investment, such as return on investment, appreciation and depreciation.
- Property management and rental calculations.
Seven questions may not sound like many, but missing most of them can turn a passing score into a failing one. The good news is that real estate math is the most predictable part of the exam. Once you learn the formulas, the questions follow familiar patterns.
Facts You Must Memorize
Pearson VUE’s outline says two conversions are not provided at the test center and should be memorized: 43,560 square feet in an acre and 5,280 feet in a mile. It also says that proration questions will tell you whether to use a 360-day or 365-day year and whether the day of closing belongs to the buyer or the seller. Calculator rules vary, so check your state’s candidate handbook for what is allowed.
The One Formula Behind Most Real Estate Math
Most percentage problems in real estate math are versions of one relationship:
- Part = Whole x Rate
- Whole = Part / Rate
- Rate = Part / Whole
Commission, loan-to-value, taxes, capitalization rates and appreciation all use this pattern. Write down what the question gives you, decide which of the three values is missing, and use the matching version. Convert percentages to decimals first: 6 percent is 0.06 and 7.5 percent is 0.075.
Commission Math
Commission is negotiable between the client and the broker, so real estate math questions always give you the rate. A typical question has several steps.
Example: A home sells for $350,000. The listing agreement sets a 5 percent commission. The listing and buyer brokerages split it equally, and the listing agent receives 60 percent of the listing brokerage’s share. How much does the listing agent earn?
- Total commission: $350,000 x 0.05 = $17,500.
- Listing brokerage’s share: $17,500 / 2 = $8,750.
- Listing agent’s share: $8,750 x 0.60 = $5,250.
The most common mistake is stopping after the first step. Read to the end of the question to see whose share it asks for.
Seller’s Net
Some questions work backward from what the seller wants to keep. Example: A seller wants to net $300,000 after paying a 6 percent commission and $4,000 in other closing costs. What is the lowest sale price that achieves this?
- Add the fixed costs to the desired net: $300,000 + $4,000 = $304,000.
- Divide by what is left after commission: 1 – 0.06 = 0.94.
- $304,000 / 0.94 = $323,404.26.
Do not add 6 percent of $304,000. The commission is figured on the sale price, not on the net.
Financing Math: LTV, Points and Interest
Loan-to-Value Ratio
The loan-to-value ratio (LTV) compares the loan amount with the property’s value. Lenders generally use the lower of the sale price or the appraised value.
Example: A buyer agrees to pay $310,000, and the home appraises at $300,000. The lender will lend 90 percent LTV. What is the maximum loan?
- Use the lower value: $300,000.
- $300,000 x 0.90 = $270,000.
Discount Points
The Consumer Financial Protection Bureau explains that one point equals one percent of the loan amount. Points are based on the loan, not the price. Example: 2 points on a $250,000 loan cost $250,000 x 0.02 = $5,000.
Interest and Amortization
Monthly interest on an amortized loan is the loan balance times the annual rate, divided by 12.
Example: A $200,000 loan at 6.5 percent has a monthly principal and interest payment of $1,264.14. How much of the first payment goes to principal?
- First month’s interest: $200,000 x 0.065 = $13,000 a year, and $13,000 / 12 = $1,083.33.
- Principal: $1,264.14 – $1,083.33 = $180.81.
Exam questions give you the payment amount. You do not need to calculate it from scratch.
Area and Acreage Math
- Rectangle or square: length x width.
- Triangle: 1/2 x base x height.
- Acres: square feet / 43,560.
Example: A lot is 330 feet by 660 feet. How many acres is it? 330 x 660 = 217,800 square feet, and 217,800 / 43,560 = 5 acres.
Example: A triangular parcel has a 100-foot base and an 80-foot height. Its area is 1/2 x 100 x 80 = 4,000 square feet.
For irregular shapes, split the area into rectangles and triangles, find each area and add them. Watch units: if one side is in yards, convert to feet first (1 yard = 3 feet, and 1 square yard = 9 square feet). For legal descriptions and section acreage, see our guide to the rectangular survey system.
Property Tax Math
Property taxes are usually figured from the assessed value, which may be a percentage of market value, times the tax rate. Tax rates are sometimes expressed in mills. One mill is one-tenth of a cent, or $0.001 per dollar of assessed value, so 25 mills equals 0.025.
Example: A home has a market value of $300,000 and is assessed at 80 percent of market value. The tax rate is 25 mills. What is the annual tax?
- Assessed value: $300,000 x 0.80 = $240,000.
- Tax: $240,000 x 0.025 = $6,000.
Proration Math
In real estate math, prorating divides an expense or income between buyer and seller based on who owned the property for each part of the period. The steps are always the same: find the daily amount, count the days, and decide who owes whom.
Example: Annual property taxes of $3,650 are paid in arrears, meaning at the end of the year, and have not been paid yet. Closing is June 30 in a non-leap year. Use a 365-day year, and the seller owns the day of closing. How much is the proration, and who is credited?
- Daily amount: $3,650 / 365 = $10.
- Seller’s days, January 1 through June 30: 31 + 28 + 31 + 30 + 31 + 30 = 181 days.
- Seller’s share: 181 x $10 = $1,810.
- Because the buyer will pay the full bill later, the seller is debited $1,810 and the buyer is credited $1,810.
If taxes had been paid in advance, the result would flip: the buyer would reimburse the seller for the days after closing. Our article on the closing agent explains who prepares these figures at settlement.
Valuation and Investment Math
Net Operating Income and Capitalization Rate
Net operating income (NOI) is effective gross income minus operating expenses. Mortgage payments are not operating expenses and are not subtracted. The capitalization rate links income and value: Value = NOI / Cap rate, and Cap rate = NOI / Value.
Example: A building has potential gross income of $120,000, a 5 percent vacancy and collection loss, and operating expenses of $42,000. At a 9 percent cap rate, what is its value?
- Vacancy loss: $120,000 x 0.05 = $6,000.
- Effective gross income: $120,000 – $6,000 = $114,000.
- NOI: $114,000 – $42,000 = $72,000.
- Value: $72,000 / 0.09 = $800,000.
Remember the inverse relationship: for the same NOI, a higher cap rate means a lower value. Read more in our guide to the income capitalization approach.
Gross Rent and Gross Income Multipliers
A gross rent multiplier (GRM) compares price with gross rent, ignoring expenses. Many textbooks use monthly rent for a GRM on one- to four-unit homes and annual income for a gross income multiplier (GIM) on larger properties. Always use the rent period the question gives you.
Example: A house sells for $300,000 and rents for $2,000 a month. GRM = $300,000 / $2,000 = 150. Example: A building sells for $600,000 with $40,000 in annual gross income. GIM = $600,000 / $40,000 = 15. See our article on the gross rent multiplier for more.
Depreciation in the Cost Approach
Straight-line depreciation spreads the loss in value evenly over a building’s economic life. Example: A building would cost $500,000 to replace today and has a 50-year economic life. After 10 years, accrued depreciation is ($500,000 / 50) x 10 = $100,000, so the depreciated building value is $400,000. Add the land value separately, because land does not depreciate. Our guide to the cost approach covers this method.
Appreciation, Equity and Return
- Appreciation rate: (new value – original value) / original value. A home bought for $200,000 and now worth $230,000 has appreciated $30,000 / $200,000 = 15 percent.
- Equity: market value – loan balance. A $400,000 home with a $250,000 loan balance has $150,000 in equity.
- Return on investment: profit / amount invested.
Real Estate Math Terms to Know
Many real estate math questions are really vocabulary questions in disguise. If you know what the terms mean, the setup is usually obvious.
- Amortization: paying off a loan with regular payments that cover interest and part of the principal. Early payments are mostly interest.
- Debit and credit: on a settlement statement, a debit is an amount a party owes, and a credit is an amount a party receives or is given credit for.
- Effective gross income: potential gross income minus vacancy and collection losses.
- Equity: the owner’s interest in the property, equal to market value minus the loans against it.
- Assessed value: the value a taxing authority places on property to calculate taxes.
- Economic life: the period over which improvements contribute to a property’s value, used in straight-line depreciation.
- Arrears: paid at the end of the period, as many property taxes and mortgage interest are.
For a longer list, see our guide to common real estate terms.
A Simple Real Estate Math Study Plan
You do not need to study real estate math for weeks on end. A focused plan works better:
- Week 1: Learn part = whole x rate and practice commission, LTV, points and tax problems until they feel automatic.
- Week 2: Work area, acreage, interest and proration problems. Write out every step, including the day count.
- Week 3: Study NOI, cap rates, GRM, depreciation and appreciation, then mix all problem types in timed sets.
Keep a page of formulas and rewrite it from memory every few days. Review every missed question and name the exact mistake, such as wrong base or wrong period. If real estate math is your weakest area, our article on how long you should study for your real estate exam can help you fit it into your overall schedule.
Common Real Estate Math Traps
- Using the wrong base. Points are based on the loan, LTV on the lower of price or appraisal, and commission on the sale price.
- Forgetting to convert percentages. 7.5 percent is 0.075, not 0.75.
- Subtracting debt service from NOI. Mortgage payments are not operating expenses.
- Mixing monthly and annual figures. Convert everything to the same period before you divide.
- Stopping one step early. Multi-step commission and proration questions often ask for the last number, not the first.
- Ignoring the proration instructions. Use the day count and closing-day rule the question gives you.
A good real estate math habit is to estimate before you calculate. If your answer for a 5 percent commission on a $350,000 sale is $175,000, you have misplaced a decimal.
Real Estate Math Practice Questions
Try each question before you read the answer.
1. How many square feet are in a 3-acre parcel?
Answer: 130,680 square feet. 3 x 43,560 = 130,680.
2. A $420,000 sale carries a 6 percent commission, split 50/50 between brokerages. The buyer’s agent receives 70 percent of her brokerage’s share. How much does the buyer’s agent earn?
Answer: $8,820. $420,000 x 0.06 = $25,200; half is $12,600; and $12,600 x 0.70 = $8,820.
3. A property sells for $600,000 and produces $45,000 in net operating income. What is the cap rate?
Answer: 7.5 percent. $45,000 / $600,000 = 0.075.
4. A buyer offers $250,000, and the home appraises at $245,000. The lender allows 95 percent LTV. What is the maximum loan?
Answer: $232,750. The lender uses the lower value: $245,000 x 0.95 = $232,750.
5. Property assessed at $180,000 is taxed at 30 mills. What is the annual tax?
Answer: $5,400. $180,000 x 0.030 = $5,400.
6. Annual taxes of $4,380 are paid in arrears. Closing is March 31 in a non-leap year, using a 365-day year, and the seller owns the day of closing. What is the proration?
Answer: $1,080, debited to the seller and credited to the buyer. $4,380 / 365 = $12 a day; January through March 31 is 90 days; 90 x $12 = $1,080.
Frequently Asked Questions
Is real estate math hard?
Most of it is basic arithmetic and percentages. The challenge is reading carefully, choosing the right formula and working accurately under time pressure. Regular practice makes the question patterns familiar.
Can I use a calculator on the real estate exam?
Many testing programs allow a basic, non-programmable calculator or provide one on screen, but rules differ. Check your state’s candidate handbook before exam day.
What real estate math formulas should I memorize?
Part = whole x rate, LTV, points, monthly interest, area and acreage, mills, proration steps, NOI and value = NOI / cap rate, GRM, and straight-line depreciation. Also memorize 43,560 square feet per acre and 5,280 feet per mile.
How should I study for real estate math?
Learn one formula at a time, work several examples, then mix problem types in timed practice so you learn to recognize which formula a question needs.
Key Takeaways
- Pearson VUE’s national salesperson outline includes seven real estate math questions out of 80 scored items.
- Most percentage problems use part = whole x rate.
- Memorize 43,560 square feet per acre and 5,280 feet per mile.
- NOI excludes mortgage payments, and value = NOI / cap rate.
- Prorations follow three steps: daily amount, number of days, and who is debited or credited.
Ready to practice? Take a free, timed practice exam and see how you do on real estate math alongside every other exam topic.