Real Estate Exam Math Cheat Sheet

Real estate exam math becomes much easier when you recognize the type of problem, write the correct formula, and keep units consistent. This cheat sheet covers the calculations most commonly tested on the national portion of U.S. real estate licensing exams, including commissions, prorations, property taxes, loan-to-value ratios, interest, area, and seller net proceeds.

Because licensing exams are administered under state-specific rules, always review your state’s current candidate handbook before test day. Several Pearson VUE handbooks identify (43{,}560) square feet per acre and (5{,}280) feet per mile as figures candidates may need to memorize, while proration instructions may specify whether to use a 360- or 365-day year and who owns the day of closing.

The Universal Problem-Solving Method

Use this five-step process for nearly every real estate math question:

1. Identify what the question is asking.
Look for words such as commission, net proceeds, discount points, LTV, assessed value, annual taxes, or prorated rent.

2. Write down the known numbers.
Include the purchase price, loan amount, percentage, number of days, tax rate, or commission rate.

3. Convert percentages to decimals.
- (6\% = 0.06)
- (2.5\% = 0.025)
- (0.5\% = 0.005)

4. Set up the formula before using the calculator.

5. Check the result for reasonableness.
A 6% commission on a \$300,000 sale should be about \$18,000—not \$180,000 or \$1,800.

A useful exam habit is to label every answer with its unit: dollars, dollars per month, square feet, acres, days, or percentage.

Essential Conversions to Memorize

| Measurement | Conversion |
|---|---:|
| 1 acre | (43{,}560) square feet |
| 1 mile | (5{,}280) feet |
| 1 square yard | 9 square feet |
| 1 township | 36 square miles |
| 1 section | 640 acres |
| 1 section | 1 square mile |
| 1 quarter section | 160 acres |
| 1 quarter-quarter section | 40 acres |

Candidate handbooks commonly identify the acre and mile conversions as information that may not be supplied at the test center, although policies vary by state and testing provider.

Land-Measurement Formulas

Square feet to acres

[
\text{Acres}=\frac{\text{Square feet}}{43{,}560}
]

Example:

[
\frac{87{,}120}{43{,}560}=2\text{ acres}
]

Acres to square feet

[
\text{Square feet}=\text{Acres}\times43{,}560
]

Example:

[
3.5\times43{,}560=152{,}460\text{ square feet}
]

Rectangular area

[
\text{Area}=\text{Length}\times\text{Width}
]

Example:

A parcel measuring 150 feet by 200 feet contains:

[
150\times200=30{,}000\text{ square feet}
]

To convert it to acres:

[
\frac{30{,}000}{43{,}560}\approx0.689\text{ acres}
]

Percentages: The Core of Real Estate Math

Most exam calculations use this basic relationship:

[
\text{Part}=\text{Whole}\times\text{Rate}
]

You can rearrange it when necessary:

[
\text{Whole}=\frac{\text{Part}}{\text{Rate}}
]

[
\text{Rate}=\frac{\text{Part}}{\text{Whole}}
]

Example: Find a Percentage

What is 4% of \$275,000?

[
275{,}000\times0.04=\$11{,}000
]

Example: Find the Original Amount

A 5% down payment equals \$20,000. What is the purchase price?

[
\frac{20{,}000}{0.05}=\$400{,}000
]

Example: Find the Rate

A \$12,000 commission was earned on a \$240,000 sale.

[
\frac{12{,}000}{240{,}000}=0.05=5\%
]

Commission Calculations

Basic Commission Formula

[
\text{Commission}=\text{Sales price}\times\text{Commission rate}
]

Example:

A property sells for \$425,000 at a 6% commission rate.

[
425{,}000\times0.06=\$25{,}500
]

Commission Split

If the total commission is split 60/40:

[
\text{Broker or agent share}=\text{Total commission}\times\text{Share percentage}
]

For a \$25,500 commission:

[
25{,}500\times0.60=\$15{,}300
]

[
25{,}500\times0.40=\$10{,}200
]

Commission After Multiple Splits

Suppose:

• Sale price: \$360,000
• Total commission: 6%
• Listing side receives 50%
• Agent receives 70% of the listing side

Step 1: Calculate total commission.

[
360{,}000\times0.06=\$21{,}600
]

Step 2: Calculate the listing side.

[
21{,}600\times0.50=\$10{,}800
]

Step 3: Calculate the agent’s share.

[
10{,}800\times0.70=\$7{,}560
]

The agent earns \$7,560 before any additional deductions.

Finding the Sales Price From Commission

If the commission is \$18,000 at a 6% rate:

[
\text{Sales price}=\frac{18{,}000}{0.06}=\$300{,}000
]

Common Commission Mistake

Do not divide the commission rate among brokers before calculating the total commission unless the question specifically asks for a split. First calculate the total commission, then apply the stated split percentages.

Loan-to-Value Ratios and Down Payments

Loan-to-Value Formula

[
\text{LTV}=\frac{\text{Loan amount}}{\text{Property value}}
]

To express the result as a percentage, multiply by 100.

Example:

A buyer borrows \$240,000 to purchase a \$300,000 property.

[
\frac{240{,}000}{300{,}000}=0.80=80\%\text{ LTV}
]

Find the Loan Amount

[
\text{Loan amount}=\text{Property value}\times\text{LTV}
]

Example:

A property is worth \$500,000, and the lender allows 75% LTV.

[
500{,}000\times0.75=\$375{,}000
]

Find the Down Payment

[
\text{Down payment}=\text{Purchase price}-\text{Loan amount}
]

Using the previous example:

[
500{,}000-375{,}000=\$125{,}000
]

You can also calculate it directly:

[
\text{Down payment}=\text{Purchase price}\times(1-\text{LTV})
]

[
500{,}000\times0.25=\$125{,}000
]

Loan-to-Value Warning

Read carefully to determine whether the question uses:

• Purchase price
• Appraised value
• Market value
• Loan amount
• Cash price

If a lender bases the loan on the lower of the purchase price or appraised value, use the lower figure when the question instructs you to do so.

Discount Points and Loan Fees

One discount point equals 1% of the loan amount.

[
\text{Points cost}=\text{Loan amount}\times\text{Point percentage}
]

Example

A \$280,000 loan carries 2.5 discount points.

[
280{,}000\times0.025=\$7{,}000
]

The borrower pays \$7,000 for the points.

Common Point Mistake

Points are calculated on the loan amount, not the purchase price.

For a \$400,000 purchase with a \$320,000 loan:

- 1 point based on the loan:
[
320{,}000\times0.01=\$3{,}200
]

- Incorrectly using the purchase price:
[
400{,}000\times0.01=\$4{,}000
]

Simple Interest

Annual Interest

[
\text{Interest}=\text{Principal}\times\text{Rate}\times\text{Time}
]

Use time in years.

Example:

Calculate one year of interest on a \$180,000 loan at 5.5%.

[
180{,}000\times0.055\times1=\$9{,}900
]

Monthly Interest

For simple monthly interest:

[
\text{Monthly interest}=\frac{\text{Principal}\times\text{Annual rate}}{12}
]

Example:

[
\frac{180{,}000\times0.055}{12}=\$825
]

Daily Interest

[
\text{Daily interest}=\frac{\text{Annual interest}}{360}
]

or, when instructed:

[
\text{Daily interest}=\frac{\text{Annual interest}}{365}
]

Example using a 360-day year:

[
\frac{9{,}900}{360}=\$27.50\text{ per day}
]

Do not assume 360 or 365 days for a proration question. The exam question or state-specific instructions may identify the required method.

Property Tax Calculations

Assessed Value

[
\text{Assessed value}=\text{Market value}\times\text{Assessment ratio}
]

Example:

A property has a market value of \$400,000 and is assessed at 35%.

[
400{,}000\times0.35=\$140{,}000
]

Property Tax

[
\text{Property tax}=\text{Assessed value}\times\text{Tax rate}
]

Example:

The assessed value is \$140,000, and the tax rate is 2%.

[
140{,}000\times0.02=\$2{,}800
]

Mill Rate

A mill is one-tenth of one percent:

[
1\text{ mill}=0.001
]

The property tax formula is:

[
\text{Tax}=\text{Assessed value}\times\text{Mill rate}
]

Example:

A property has an assessed value of \$250,000 and a tax rate of 18 mills.

[
250{,}000\times0.018=\$4{,}500
]

Some candidate handbooks specifically list property tax calculations as a tested math area and describe the calculation as mill rate multiplied by assessed value.

Convert a Mill Rate

To convert mills to a decimal, divide by 1,000.

• 12 mills (=0.012)
• 25 mills (=0.025)
• 40 mills (=0.040)

Common Property Tax Mistake

Do not multiply the tax rate by market value when the question gives an assessment ratio. First calculate assessed value, then calculate the tax.

Prorations

Proration questions allocate an expense or income between the buyer and seller as of the closing date.

Common prorated items include:

• Property taxes
• Rent
• Interest
• Homeowners’ association dues
• Fuel
• Water or utility charges

Basic Proration Formula

[
\text{Daily amount}=\frac{\text{Annual amount}}{\text{Number of days in the year}}
]

[
\text{Prorated amount}=\text{Daily amount}\times\text{Number of days}
]

Example: Annual Property Taxes

Annual taxes are \$3,650. Closing occurs on June 30, using a 365-day year.

[
\frac{3{,}650}{365}=\$10\text{ per day}
]

If the seller is responsible for 180 days:

[
10\times180=\$1{,}800
]

The seller’s share is \$1,800.

360-Day Example

Annual rent is \$18,000, and the question requires a 360-day year.

[
\frac{18{,}000}{360}=\$50\text{ per day}
]

For 45 days:

[
50\times45=\$2{,}250
]

Paid in Arrears Versus Paid in Advance

This distinction determines who receives the closing adjustment.

• Paid in arrears: The expense is paid after the period has passed. The seller may owe the buyer for the seller’s portion.
• Paid in advance: The expense has already been paid for a future period. The buyer may owe the seller for the buyer’s portion.
• Unpaid expense: The responsible party may receive a debit at closing.
• Credit: A credit benefits the party receiving it.
• Debit: A debit reduces the party’s proceeds or increases the amount due.

Proration Procedure

1. Identify the annual, monthly, or total amount.
2. Determine whether the question uses 360 or 365 days.
3. Calculate the daily amount.
4. Count the responsible days.
5. Determine whether the amount is a buyer debit, seller debit, buyer credit, or seller credit.
6. Review whether the day of closing belongs to the buyer or seller.

Candidate handbooks commonly state that the question will specify the year basis and ownership of the closing day when those details matter.

Common Proration Mistakes

• Counting the same day for both parties
• Using 365 days when the question says 360
• Treating a monthly amount as annual without multiplying by 12
• Reversing a debit and a credit
• Forgetting whether the item was paid in advance or arrears

Seller Net Proceeds

Basic Net-Proceeds Formula

[
\text{Seller net}=\text{Sales price}-\text{Existing liens}-\text{Selling expenses}+\text{Credits}
]

Depending on the question, selling expenses may include:

• Brokerage commission
• Transfer taxes
• Attorney fees
• Recording fees
• Repair credits
• Prorated taxes owed by the seller
• Mortgage payoff

A property sells for \$475,000. The seller pays a 6% commission, has a \$285,000 loan payoff, and pays \$4,500 in other closing costs.

Step 1: Commission.

[
475{,}000\times0.06=\$28{,}500
]

Step 2: Net proceeds.

[
475{,}000-28{,}500-285{,}000-4{,}500=\$157{,}000
]

The seller’s estimated net proceeds are \$157,000.

Finding the Required Sales Price

If the seller needs \$200,000 after paying a 6% commission and \$250,000 mortgage payoff:

[
\text{Required price}\times(1-0.06)-250{,}000=200{,}000
]

[
\text{Required price}\times0.94=450{,}000
]

[
\text{Required price}=\frac{450{,}000}{0.94}\approx\$478{,}723.40
]

The seller would need a sales price of approximately \$478,724 before considering other costs.

Buyer Cash Required at Closing

A buyer’s required cash can include:

• Down payment
• Loan costs
• Discount points
• Prepaid interest
• Prepaid taxes and insurance
• Closing costs
• Earnest-money deposit credit

Formula

[
\text{Cash required}=\text{Down payment}+\text{Buyer costs}-\text{Credits}
]

A buyer purchases a \$320,000 property with 80% financing. Buyer closing costs are \$6,000, and the buyer already paid \$5,000 in earnest money.

Step 1: Loan amount.

[
320{,}000\times0.80=\$256{,}000
]

Step 2: Down payment.

[
320{,}000-256{,}000=\$64{,}000
]

Step 3: Cash needed at closing.

[
64{,}000+6{,}000-5{,}000=\$65{,}000
]

Rent, Income, and Capitalization

Gross Rental Income

[
\text{Gross rental income}=\text{Monthly rent}\times12
]

Example:

[
\$2{,}200\times12=\$26{,}400
]

Gross Rent Multiplier

[
\text{GRM}=\frac{\text{Property price}}{\text{Gross monthly rent}}
]

Example:

A property sells for \$360,000 and rents for \$3,000 per month.

[
\frac{360{,}000}{3{,}000}=120
]

To estimate value:

[
\text{Value}=\text{Monthly rent}\times\text{GRM}
]

Net Operating Income

[
\text{NOI}=\text{Effective gross income}-\text{Operating expenses}
]

Do not subtract mortgage principal, mortgage interest, depreciation, or income taxes when calculating NOI unless the question gives a specific alternative instruction.

Capitalization Rate

[
\text{Cap rate}=\frac{\text{NOI}}{\text{Value}}
]

Value From NOI and Cap Rate

[
\text{Value}=\frac{\text{NOI}}{\text{Cap rate}}
]

Example:

A property produces \$48,000 in NOI and has a 6% capitalization rate.

[
\frac{48{,}000}{0.06}=\$800{,}000
]

NOI From Value and Cap Rate

[
\text{NOI}=\text{Value}\times\text{Cap rate}
]

A \$600,000 property with a 7% cap rate produces:

[
600{,}000\times0.07=\$42{,}000\text{ NOI}
]

Profit, Loss, and Appreciation

Profit

[
\text{Profit}=\text{Selling price}-\text{Adjusted basis}
]

Loss

[
\text{Loss}=\text{Adjusted basis}-\text{Selling price}
]

Percentage Gain

[
\text{Percentage gain}=\frac{\text{Gain}}{\text{Original investment}}\times100
]

Example:

An investor buys for \$250,000 and sells for \$285,000.

[
285{,}000-250{,}000=\$35{,}000
]

[
\frac{35{,}000}{250{,}000}=0.14=14\%
]

Appreciation

[
\text{Appreciated value}=\text{Original value}\times(1+\text{Appreciation rate})
]

Example:

A \$300,000 property appreciates 8%.

[
300{,}000\times1.08=\$324{,}000
]

Equity

Basic Equity Formula

[
\text{Equity}=\text{Property value}-\text{Debt}
]

Example:

A property is worth \$450,000, and the owner owes \$310,000.

[
450{,}000-310{,}000=\$140{,}000
]

Equity Percentage

[
\text{Equity percentage}=\frac{\text{Equity}}{\text{Property value}}\times100
]

[
\frac{140{,}000}{450{,}000}\times100\approx31.11\%
]

Depreciation

For straight-line depreciation:

[
\text{Annual depreciation}=\frac{\text{Depreciable basis}}{\text{Useful life}}
]

Land is generally not depreciable for this calculation, so the question may require you to subtract land value from total property value first.

Example:

• Total value: \$500,000
• Land value: \$100,000
• Building value: \$400,000
• Useful life: 40 years

[
\frac{400{,}000}{40}=\$10{,}000\text{ annual depreciation}
]

Area, Volume, and Building Measurements

Square Footage

[
\text{Square footage}=\text{Length}\times\text{Width}
]

For several rooms, calculate each room separately and add the results.

Example:

• Living room: (20\times15=300) square feet
• Bedroom: (12\times14=168) square feet
• Office: (10\times10=100) square feet

[
300+168+100=568\text{ square feet}
]

Cubic Volume

[
\text{Volume}=\text{Length}\times\text{Width}\times\text{Height}
]

Example:

[
20\times15\times8=2{,}400\text{ cubic feet}
]

Common Exam Traps

Using the Wrong Base Number

A percentage may apply to:

• Sales price
• Loan amount
• Assessed value
• Market value
• Equity
• Gross income
• Net operating income

Circle the number to which the percentage applies before calculating.

Forgetting to Convert Percentages

Never multiply by 6 instead of (0.06). Entering the whole-number percentage can make an answer 100 times too large.

Rounding Too Early

Keep several decimal places during intermediate calculations. Round only at the end unless the question specifically instructs otherwise.

Confusing Annual and Monthly Figures

If rent is \$2,500 per month:

[
2{,}500\times12=\$30{,}000\text{ annually}
]

If taxes are \$6,000 annually:

[
\frac{6{,}000}{12}=\$500\text{ monthly}
]

Reversing Buyer and Seller

For prorations, identify who owes the expense and who receives the adjustment. A debit reduces a party’s position; a credit improves it.

Ignoring the Wording

Words such as “excluding,” “including,” “before costs,” “after commission,” “based on assessed value,” and “net of” change the calculation.

A Fast Formula List

Percentages

[
\text{Part}=\text{Whole}\times\text{Rate}
]

Commission

[
\text{Commission}=\text{Sales price}\times\text{Commission rate}
]

LTV

[
\text{LTV}=\frac{\text{Loan}}{\text{Value}}
]

Down payment

[
\text{Down payment}=\text{Price}-\text{Loan}
]

Points

[
\text{Points cost}=\text{Loan}\times\text{Points rate}
]

[
I=P\times R\times T
]

[
\text{Tax}=\text{Assessed value}\times\text{Tax rate}
]

[
\text{Assessed value}=\text{Market value}\times\text{Assessment ratio}
]

Proration

[
\text{Daily amount}=\frac{\text{Annual amount}}{360\text{ or }365}
]

[
\text{Proration}=\text{Daily amount}\times\text{Responsible days}
]

Seller net

[
\text{Net}=\text{Price}-\text{Liens}-\text{Expenses}+\text{Credits}
]

NOI

[
\text{NOI}=\text{Income}-\text{Operating expenses}
]

Cap rate

[
\text{Cap rate}=\frac{\text{NOI}}{\text{Value}}
]

Value from cap rate

[
\text{Value}=\frac{\text{NOI}}{\text{Cap rate}}
]

Land area

[
1\text{ acre}=43{,}560\text{ square feet}
]

How to Study Real Estate Exam Math

1. Memorize the core conversions.
Start with (43{,}560) square feet per acre, (5{,}280) feet per mile, percentage-to-decimal conversions, and the basic formulas.

2. Practice by problem type.
Complete a set of commission questions, then a set of prorations, then taxes and LTV problems. This helps you recognize patterns.

3. Show every step.
Writing the setup reduces careless errors and makes it easier to identify where a mistake occurred.

4. Practice without relying on memorized answer choices.
Real exam questions may change the numbers or ask for a different part of the formula.

5. Review your state handbook.
The national portion may use common formulas, but state-specific requirements, calculator rules, rounding instructions, and tax conventions can differ. Official candidate handbooks emphasize reviewing the examination content outline and applicable math instructions before testing.

6. Use timed practice.
Once the formulas are familiar, complete mixed problem sets under time pressure.

7. Consider structured preparation.
LeapRealEstate.com can be a helpful next step for organized real estate exam training, practice questions, and review support when you want to turn this formula sheet into a complete study plan.

Final Test-Day Checklist

Before submitting a math answer, ask:

• Did the percentage become a decimal?
• Did I use the correct base number?
• Did I distinguish monthly from annual amounts?
• Did I use 360 or 365 days as instructed?
• Did I count the correct number of days?
• Did I identify the correct buyer or seller debit?
• Did I calculate points from the loan amount?
• Did I use assessed value for property taxes?
• Did I delay rounding until the final step?
• Does the answer make practical sense?

The strongest real estate exam math strategy is not memorizing dozens of isolated formulas. It is recognizing the relationship among the numbers, writing the correct setup, and checking whether the result fits the facts.

Authoritative Sources

• [ARELLO, Real Estate Mathematics Items: Principles & Examples]
• [Pearson VUE, Texas Real Estate Candidate Handbook]
• [Pearson VUE, Montana Board of Realty Regulation Candidate Handbook]
• [Pearson VUE, Indiana Real Estate Candidate Handbook]
• [National Association of REALTORS®, Real Estate Math: Can You Crunch the Numbers?]