Real Estate Math Formulas Cheat Sheet for the Exam
Every real estate math formula you need for the licensing exam — commission, proration, cap rate, GRM, LTV, and DTI. Free study guide with examples.
Real estate math formulas make up 10–15% of the licensing exam, and this cheat sheet covers every formula you need to pass — commission, proration, cap rate, GRM, LTV, DTI, and area calculations. This is a formula reference, not a textbook chapter. Each formula includes the equation, when to use it, and a worked example.
Real estate math uses basic arithmetic and simple algebra. No calculus. No advanced statistics. If you can multiply, divide, and solve for one unknown, you can earn every math point on your real estate license exam.
Sections below cover commission and splits, prorations, property valuation, lending formulas, area and transfer tax, memorization strategies, and a free practice exam link.
Commission and Split Formulas
Commission formulas are the most frequently tested math topic on the real estate exam because they can be asked from three different angles — finding the commission, finding the rate, or finding the sale price.
Commission is the percentage of the sale price paid to the brokerage, then split between the listing and selling agents. Understanding agency relationships helps clarify who earns what in a transaction.
The T-bar method (Total on top, Part and Rate on bottom) helps candidates rearrange the formula quickly. Place Sale Price on top, Commission on the bottom left, Rate on the bottom right. Cover the value you need to find. For additional real estate exam math practice, see our dedicated tips page.
Three variations of the commission formula follow.
Commission rate formula
The commission rate formula calculates the dollar amount an agent earns from a sale: Commission = Sale Price × Commission Rate.
Example 1 — Find the commission: Sale Price = $350,000. Commission Rate = 6%. Commission = $350,000 × 0.06 = $21,000.
Rearrangement — Find the sale price: Sale Price = Commission ÷ Rate. Commission = $15,000. Rate = 5%. Sale Price = $15,000 ÷ 0.05 = $300,000.
Rearrangement — Find the rate: Rate = Commission ÷ Sale Price. Commission = $18,000. Sale Price = $400,000. Rate = $18,000 ÷ $400,000 = 0.045 = 4.5%.
On the exam, you will see all three variations. Practice rearranging until the T-bar becomes automatic.
Commission split between agents
Commission splits divide the total commission between the listing brokerage and the selling brokerage, then between the broker and the agent within each brokerage.
Example: Sale price = $400,000. Total commission = 6%. Total commission = $400,000 × 0.06 = $24,000. Split 50/50 between brokerages = $12,000 each. Listing agent has a 70/30 split with broker: agent receives $12,000 × 0.70 = $8,400.
Exam trap: The question may give you the agent’s commission calculations and ask for the total commission. Work backward: Agent earned $8,400 at a 70% split → brokerage share = $8,400 ÷ 0.70 = $12,000 → total commission = $12,000 × 2 = $24,000.
Net to seller = Sale Price − Commission. A seller who pays 6% commission on a $400,000 sale nets $376,000.
Finding sale price from commission
Finding the sale price from commission reverses the standard formula: Sale Price = Commission ÷ Commission Rate.
Example: An agent earned $9,000 at a 3% commission rate. Sale Price = $9,000 ÷ 0.03 = $300,000.
Common exam variation: “A seller received $285,000 after paying a 5% commission. What was the sale price?” $285,000 = 95% of Sale Price. Sale Price = $285,000 ÷ 0.95 = $300,000.
Key distinction: “net to seller” problems require dividing by (1 − rate), not by rate. The seller received what remains after commission, so $285,000 represents 95%, not 100%.
After commission, prorations are the second most common math topic on the exam.
Proration Formulas
Proration formulas divide shared expenses between the buyer and seller based on how many days each party owns the property during a billing period.
Two methods exist. The 365-day year method uses actual calendar days and appears on most exams. The 360-day year method (banker’s year — 12 months × 30 days) appears on some state-specific portions.
The critical first step in any proration problem: determine whether the expense is prepaid or in arrears. Prepaid means the seller already paid — the buyer credits the seller. Arrears means unpaid — the seller credits the buyer. This single distinction determines the direction of the credit during the closing process.
Day of closing: in most states, the buyer is responsible for the day of closing.
Property tax proration
Property tax proration calculates how much of the annual tax bill the seller owes and how much the buyer owes based on the closing date.
Formula: Daily Rate = Annual Tax ÷ 365. Seller’s Share = Daily Rate × Days Seller Owned. Buyer’s Share = Daily Rate × Days Buyer Owned.
Example — Taxes in arrears: Annual tax = $4,380. Closing date = April 10 (day 100 of the year). Daily rate = $4,380 ÷ 365 = $12.00/day. Seller owned January 1 through April 9 = 99 days. Seller’s share = 99 × $12.00 = $1,188 credit to buyer.
If taxes were prepaid by the seller, the calculation reverses. The buyer credits the seller for the buyer’s portion: $4,380 − $1,188 = $3,192.
On the exam, read carefully whether taxes are “paid” or “due.” That single word determines who credits whom.
Rent proration
Rent proration applies when an income-producing property sells mid-month and the tenant has already paid rent to the seller.
Formula: Daily Rent = Monthly Rent ÷ Days in Month. Buyer’s Credit = Daily Rent × Remaining Days.
Example: Monthly rent = $1,500. Closing date = March 12. Daily rate = $1,500 ÷ 31 = $48.39/day. Buyer owns March 12–31 = 20 days. Buyer credit = $48.39 × 20 = $967.74.
Rent is always prepaid (tenants pay in advance). The seller always credits the buyer for the remaining days of the month. This rule simplifies proration calculations for rent — you never need to determine prepaid vs. arrears.
Proration mastered. Next: property valuation formulas used in the income approach.
Property Valuation Formulas
Property valuation formulas on the real estate exam focus on two approaches to estimating investment property value — the capitalization rate and the gross rent multiplier.
Both formulas belong to the income capitalization approach to appraisal. Cap rate uses net operating income (after expenses). GRM uses gross rent (before expenses). This distinction is a common exam trap — mixing up NOI and gross rent produces wrong answers.
These formulas appear on both the national and state portions of the real estate license exam.
Capitalization rate (Cap Rate = NOI ÷ Value)
The capitalization rate converts a property’s net operating income into an estimated market value — and the exam tests all three rearrangements of this formula.
Three forms of the cap rate formula:
- Cap Rate = NOI ÷ Value
- Value = NOI ÷ Cap Rate
- NOI = Value × Cap Rate
Example: NOI = $36,000/year. Cap Rate = 8%. Value = $36,000 ÷ 0.08 = $450,000.
NOI = Gross Income − Operating Expenses. NOI does not include mortgage payments (debt service). If the question gives you gross income and expenses, subtract expenses first before applying the cap rate formula.
Exam trap: A question states gross income of $60,000 and operating expenses of $24,000 with a cap rate of 8%. NOI = $60,000 − $24,000 = $36,000. Value = $36,000 ÷ 0.08 = $450,000. Using gross income instead of NOI gives $750,000 — wrong.
For a deeper breakdown of all three appraisal methods, see our dedicated guide.
Gross rent multiplier (GRM = Price ÷ Gross Rent)
The gross rent multiplier estimates property value using gross rental income — it is a quicker but less precise alternative to the cap rate method.
Two forms:
- GRM = Sale Price ÷ Annual Gross Rent
- Value = GRM × Annual Gross Rent
Example: Comparable properties sell at 8× gross rent. Subject property gross rent = $48,000/year. Estimated Value = 8 × $48,000 = $384,000.
Key difference from cap rate: GRM uses gross rent (before expenses). Cap rate uses NOI (after expenses). GRM ignores operating costs entirely.
GRM is a ratio, not a percentage. Do not convert to a percent. A GRM of 8 means the property sells for 8 times its annual gross rent.
Valuation formulas covered. Lending formulas follow.
Lending and Qualification Formulas
Lending formulas on the real estate exam test whether you understand how lenders evaluate borrowers and properties — loan-to-value ratio and debt-to-income ratio are the two most tested.
LTV measures property risk — how much of the property’s value is financed. DTI measures borrower risk — how much of the borrower’s income goes to debt payments. Both ratios have threshold values that trigger requirements: PMI for LTV above 80%, loan denial for DTI above 43% under QM rules.
For a complete overview of ltv dti pmi thresholds and their exam implications, see our dedicated guide.
Loan-to-value ratio
The loan-to-value ratio measures what percentage of the property’s appraised value is financed by the loan: LTV = Loan Amount ÷ Appraised Value.
Example: Loan = $240,000. Appraised Value = $300,000. LTV = $240,000 ÷ $300,000 = 0.80 = 80%.
PMI rule: Conventional loans with LTV above 80% require private mortgage insurance. PMI protects the lender, not the borrower.
Down payment connection: Down Payment = Appraised Value − Loan Amount. A 20% down payment = 80% LTV. A 10% down payment = 90% LTV.
Exam trap: LTV uses appraised value, not purchase price. If the appraisal comes in lower than the offer, LTV increases. A $300,000 purchase with a $280,000 appraisal and $240,000 loan: LTV = $240,000 ÷ $280,000 = 85.7% — PMI required.
Debt-to-income ratio
The debt-to-income ratio measures what percentage of a borrower’s gross monthly income goes toward debt payments: DTI = Total Monthly Debt ÷ Gross Monthly Income.
Two types of DTI:
- Front-end DTI (housing ratio) = Mortgage Payment ÷ Gross Income. Conventional max: ~28%.
- Back-end DTI (total debt ratio) = All Debt Payments ÷ Gross Income. Conventional max: ~36%. QM max: 43%.
Example: Gross monthly income = $8,000. Mortgage payment = $1,600. Front-end DTI = $1,600 ÷ $8,000 = 20%. Total monthly debt = $2,400. Back-end DTI = $2,400 ÷ $8,000 = 30%. Both within limits — loan approved.
Exam tip: DTI always uses gross (pre-tax) income, not net (take-home) income. Using net income inflates the ratio and produces the wrong answer.
Lending formulas done. Area and transfer tax calculations follow.
Area and Transfer Tax Calculations
Area and transfer tax calculations appear on every real estate exam — area problems test basic geometry, and transfer tax problems test rate application.
Area formulas:
- Rectangle = Length × Width
- Triangle = ½ × Base × Height
- Circle = π × r²
Key conversion: 1 acre = 43,560 sq ft.
Example: A lot measures 200 ft × 300 ft. Area = 200 × 300 = 60,000 sq ft. Acres = 60,000 ÷ 43,560 = 1.38 acres.
Transfer tax formula: Tax = (Sale Price ÷ Tax Unit) × Rate per Unit.
Example: Transfer tax rate = $1.10 per $1,000. Sale Price = $250,000. Tax = ($250,000 ÷ $1,000) × $1.10 = $275.
Mill rate: 1 mill = $1 per $1,000 of assessed value. Property Tax = Assessed Value × Mill Rate ÷ 1,000.
Example: Assessed value = $200,000. Mill rate = 25. Property tax = $200,000 × 25 ÷ 1,000 = $5,000.
For the difference between market value and assessed value and how it affects tax calculations, see our guide on market assessed value.
Formulas covered. Memorization strategies follow.
How to Memorize Real Estate Math for the Exam
Memorizing real estate math formulas requires active practice — reading them once will not build the recall speed you need during a timed exam.
- Create formula flashcards. Formula on the front, worked example on the back. Review daily for a minimum of two weeks before exam day.
- Practice the T-bar method for commission, proration, and LTV problems. Total on top, Part and Rate on the bottom. It works for any “part/whole/rate” problem — one method covers three formula types.
- Do 5 math problems per day starting 3 weeks before your exam. Consistency beats cramming. Five daily problems across 21 days = 105 practiced calculations.
- Take timed practice quizzes focused exclusively on math. Our free practice exam includes a math-only section. Time pressure reveals which formulas you know and which you are still looking up.
- Learn to identify the formula type from the question. “What is the capitalization rate?” = Cap Rate = NOI ÷ Value. “What did the seller net?” = Net = Sale Price − Commission. Recognizing the pattern is half the work.
Most candidates who fail the math section did not practice enough. The formulas are simple. Speed and accuracy require repetition. Build both into your exam study plan starting three weeks out.
Requirements may change — verify with your state’s Real Estate Commission.
Test Your Knowledge — Free Practice Exam
Test your real estate math skills with our free real estate practice exam — includes commission, proration, cap rate, GRM, LTV, and area calculation questions for all 50 states.
Math questions are mixed into the full exam just like the real test — no separate math section. This mirrors the actual exam experience where math appears alongside property law, contracts, and agency questions.
Review your results by topic area to see which formulas need more practice.
