Real Estate Exam Math Formulas: Every Calculation You Need to Know

Math anxiety is one of the most common concerns among real estate exam candidates — and it's also one of the most unnecessary. The math on the real estate licensing exam is predictable, formula-driven, and entirely manageable with the right preparation. In fact, the same 10–12 calculation types appear on virtually every exam, and once you've practiced them, they become reliable points in your score column. This guide covers every formula you need, complete with step-by-step examples.

Commission Calculations

Commission questions are among the most common math problems on the exam. They test your ability to calculate total commission, split it between agents and brokers, and account for various fee arrangements.

Basic Commission

Example: A property sells for $350,000 at a 6% commission. What is the total commission?
Solution: $350,000 × 0.06 = $21,000

Commission Splits

The total commission is typically split four ways: listing broker, listing agent, selling broker, and selling agent. Questions often involve cascading splits.

Example: A $400,000 home sells with a 6% commission. The listing and selling brokers split the commission 50/50. The listing broker pays their agent 60% of the listing side. How much does the listing agent earn?
Solution: Total commission = $400,000 × 0.06 = $24,000. Listing side = $24,000 × 0.50 = $12,000. Listing agent = $12,000 × 0.60 = $7,200

Net to Seller

Example: A seller wants to net $200,000 after paying a 6% commission and $4,000 in closing costs. What must the sale price be?
Solution: Let S = sale price. S − 0.06S − $4,000 = $200,000. 0.94S = $204,000. S = $204,000 ÷ 0.94 = $217,021.28

Property Tax Calculations

Property tax questions require understanding mill rates, assessed value, and tax rates. A "mill" is one-tenth of one cent, or $1 of tax per $1,000 of assessed value.

Annual Property Tax

Example: A property has an assessed value of $250,000. The mill rate is 45 mills. What is the annual tax?
Solution: ($250,000 ÷ 1,000) × 45 = 250 × 45 = $11,250

Tax Rate When Assessed at a Percentage of Market Value

Many states assess property at a percentage of market value. You must apply the assessment ratio first.

Example: A property's market value is $500,000. The assessment ratio is 40%. The mill rate is 50. What is the annual tax?
Solution: Assessed value = $500,000 × 0.40 = $200,000. Tax = ($200,000 ÷ 1,000) × 50 = $10,000

Proration Calculations

Proration allocates expenses between buyer and seller at closing. The most common proration items are property taxes and prepaid rent. Know whether you're using a 360-day (banker's year) or 365-day (calendar year) method — the exam will specify.

General Proration Formula

Example (360-day year): Annual property taxes are $3,600. Closing is on March 15 (the seller owns the property through March 14). The seller is responsible for taxes from January 1 through the day before closing. The buyer pays for taxes starting on the day of closing. How much does the seller owe at closing?
Solution: Seller's days = January (31) + February (28) + March 1–14 (14) = 73 days. Daily rate = $3,600 ÷ 360 = $10 per day. Seller owes = 73 × $10 = $730. The buyer receives a credit of $730.

Loan and Mortgage Calculations

Financing math covers loan-to-value ratios, discount points, and qualification ratios. These are heavily tested and very practical.

Loan-to-Value Ratio (LTV)

Example: A buyer purchases a home for $300,000 with a $240,000 loan. What is the LTV?
Solution: $240,000 ÷ $300,000 = 0.80 = 80%

Discount Points

Example: A borrower takes a $200,000 loan and pays 2 discount points. What is the cost?
Solution: $200,000 × 2 ÷ 100 = $4,000

Housing Expense Ratio (Front-End Ratio)

Example: A borrower earns $6,000 per month. Their monthly housing expense (PITI) is $1,680. Lenders typically cap this ratio at 28%. Does this borrower qualify?
Solution: $1,680 ÷ $6,000 = 0.28 = 28% — exactly at the typical limit

Total Debt-to-Income Ratio (Back-End Ratio)

Typically capped at 36%. Includes housing expense plus all other recurring debts (car loans, student loans, credit card minimums).

Area and Measurement Calculations

These appear frequently, often embedded in valuation or listing questions. Know your conversions.

Key Conversions

• 1 acre = 43,560 square feet
• 1 square mile = 640 acres
• 1 mile = 5,280 feet
• 1 square yard = 9 square feet

Example: A rectangular lot measures 150 feet by 200 feet. What is its area in acres?
Solution: Area = 150 × 200 = 30,000 sq ft. Acres = 30,000 ÷ 43,560 ≈ 0.689 acres

Example: Calculate the square footage of a rectangular room measuring 15 feet 6 inches by 12 feet. Answer in square feet.
Solution: 15.5 × 12 = 186 square feet

Appraisal and Valuation Formulas

Gross Rent Multiplier (GRM)

Example: A comparable property sold for $240,000 and generates $2,000 in monthly rent. What is the GRM?
Solution: $240,000 ÷ $2,000 = 120

Using GRM to estimate value: If the GRM is 120 and a property generates $1,800 per month in rent, the estimated value is $1,800 × 120 = $216,000.

Capitalization Rate (Cap Rate)

Example: A property generates $50,000 in NOI and has a market cap rate of 8%. What is the estimated value?
Solution: $50,000 ÷ 0.08 = $625,000

Depreciation (Straight-Line)

For residential investment property, the IRS allows depreciation over 27.5 years. Only the improvement value (not land) is depreciated.

Profit and Loss on Sale

Example: An investor bought a property for $200,000, made $30,000 in capital improvements, and took $40,000 in depreciation. They sell for $280,000 with $20,000 in selling costs. What is the gain?
Solution: Adjusted basis = $200,000 + $30,000 − $40,000 = $190,000. Net sale proceeds = $280,000 − $20,000 = $260,000. Gain = $260,000 − $190,000 = $70,000

Percentage and Rate Problems

Many exam questions test your ability to calculate the "percent of" or "percent change."

Percent of One Number to Another

Percent Change

Example: A home originally listed at $310,000 sells for $294,500. By what percentage did the seller reduce the price?
Solution: Change = $310,000 − $294,500 = $15,500. Percentage = ($15,500 ÷ $310,000) × 100 = 5%