Download a 20-page formula guide and practice workbook organized around the seven official math areas, or use the complete 43-formula reference with examples online. The PDF includes 35 selected relationships, 15 original questions and worked answers. No account needed.
Reviewing more than math? Read the whole-exam cram sheet or download the free National and State PDF. It covers all 14 exam areas in two pages.
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Pearson VUE assigns seven scored National/General Sales Agent questions to Real Estate Math Calculations, one in each official area. Four test application and three test analysis. Start with the 35 core relationships, memorize 43,560 square feet per acre and 5,280 feet per mile, then use the complete reference for additional setups. These are Pass Texas study relationships, not a required formula list issued by Pearson. Check the official math outline.
Name the amount you are solving for before reaching for a calculator. These common setups help you choose; the full reference below supplies the other relationships.
| If you need to… | Start here | Check before calculating |
|---|---|---|
| Find total commission | Sale price × stated commission rate | Use the rate supplied in the question. Commission is negotiable. |
| Find an agent's share | Brokerage's commission share × agent split | Start with the amount that reaches that brokerage, not the full sale price. |
| Find annual property tax | Taxable value ÷ 100 × rate per $100 | Use that taxing unit's exemptions. If taxable value is already given, do not subtract exemptions again. |
| Prorate an annual charge | Annual charge ÷ stated year basis × allocated days | Read the 360/365-day instruction and who owns closing day. Then assign the debit or credit. |
| Find value from income | Annual NOI ÷ capitalization rate as a decimal | Use net operating income, not gross rent or income after mortgage payments. |
| Find discount points | Loan amount × points ÷ 100 | One point is 1% of the loan. It is not 1% of the purchase price. |
| Convert square feet to acres | Square feet ÷ 43,560 | Multiply by 43,560 when converting acres back to square feet. |
In the PDF, formulas are on pages 3–9, the 15 practice questions on pages 10–13, and worked answers on pages 14–17. Print the questions separately, then use the miss log on page 18 to record the setup you need to practice. Open the worked answers.
Want to apply math alongside the other exam areas? Use the 120-question PDF with explained answers, or take the free timed practice exam.
Download the formula guide and practice workbook, study worked examples online, or print the 35 core relationships.
Pass Texas
Texas sales agent exam prepPrintable math reference
Sale Price × Commission Rate = Commission
$250,000 × 6% = $15,000
Brokerage Share × Agent Split % = Agent Share
$7,500 brokerage share × 60% = $4,500
Commission ÷ Commission Rate = Sale Price
$15,000 ÷ 6% = $250,000
All rates and splits here are hypothetical, negotiated terms. Calculate the brokerage share before the agent share. Source
Annual Amount ÷ (360 or 365) = Daily Rate
$3,650 ÷ 365 = $10/day
Daily Rate × Days Owned = Proration
$10/day × 180 days = $1,800
Follow the specified year length and closing-day allocation. Unpaid seller taxes usually mean seller debit/buyer credit; a buyer reimbursing the seller for a prepaid buyer expense reverses the entries. Source
Annual NOI ÷ Property Value = Cap Rate
$50,000 ÷ $500,000 = 10%
Annual NOI ÷ Cap Rate = Property Value
$50,000 ÷ 10% = $500,000
Sale Price ÷ Gross Rent = GRM
$500,000 ÷ $60,000 = 8.33
NOI is annual for cap-rate calculations. Match monthly or annual gross rent to the GRM you are using.
The $140,000 exemption applies to school-district tax. Use assessed value after any applicable limitation, then subtract that unit's exemptions. The $1.00 tax rate is hypothetical. Check the Comptroller guidance.
Assessed Value − Applicable Exemptions = Taxable Value
$310,000 assessed − $140,000 school exemption = $170,000
Taxable Value ÷ 100 × Tax Rate per $100 = Tax
$170,000 ÷ 100 × $1.00 = $1,700 school tax
Potential Gross Income − Vacancy & Collection Loss + Other Income = EGI
$120,000 − $6,000 + $2,000 = $116,000
Effective Gross Income − Operating Expenses = NOI
$116,000 − $46,000 = $70,000 NOI
Vacant Units ÷ Total Units = Vacancy Rate
5 ÷ 100 = 5%
Occupied Units ÷ Total Units = Occupancy Rate
95 ÷ 100 = 95%
Annual Rent ÷ Square Feet = Annual Rent per Sq Ft
$24,000 ÷ 2,000 = $12 per sq ft per year
NOI excludes debt service, income taxes and depreciation. A vacancy rate by unit count equals the lost-rent percentage only when rents are equal or the problem says to use it. Source
Length × Width = Area (sq ft)
50 ft × 100 ft = 5,000 sq ft
Square Feet ÷ 43,560 = Acres
87,120 sq ft ÷ 43,560 = 2 acres
Price ÷ Square Footage = Price per Sq Ft
$500,000 ÷ 2,500 sq ft = $200/sq ft
Principal × Annual Rate × Time in Years = Interest
$200,000 × 6% × 1 year = $12,000
Loan Balance × Annual Rate ÷ 12 = Monthly Interest
$200,000 × 6% ÷ 12 = $1,000
Loan Amount × Fee Rate = Origination Fee
$200,000 × 1% = $2,000
Loan Amount × Points (as %) = Point Cost
$200,000 × 2 points (2%) = $4,000
Monthly P&I Payment − Monthly Interest = Principal Paid
$1,500 payment − $1,000 interest = $500 principal
Loan Balance × Stated Penalty Rate = Prepayment Penalty
$180,000 × 2% = $3,600
Time must be in years when the simple-interest rate is annual. Monthly interest alone is not the full mortgage payment. One point costs 1% of the loan; it does not guarantee a fixed rate reduction. Source
Loan Amount ÷ Property Value = LTV
$180,000 ÷ $200,000 = 90% LTV
Purchase Price − Loan Amount = Buyer Down Payment
$200,000 − $180,000 = $20,000
Follow the question's value basis. Fannie Mae purchase loans generally use the lower of price and appraisal; refinance loans use appraised value. Source
Sale Price − Payoff − Selling Costs = Seller Net
$425,000 − $298,000 − $31,375 = $95,625
(Target Net + Payoff + Fixed Costs) ÷ (1 − Selling-Cost Rate) = Required Price
($85,000 + $298,000 + $3,000) ÷ 94% = $410,638.30
Down Payment + Unpaid Costs + Prepaids − Credits − Deposit = Cash to Close
$60,000 + $7,500 + $2,100 − $1,000 − $5,000 = $63,600
Sale Price ÷ Tax Unit × Rate = Transfer Tax
$300,000 ÷ $1,000 × $2 = $600
Recorded Units × Fee per Unit = Recording Fee
12 pages × $5 per page = $60
Cash to close is the additional amount due after deposits and credits. Seller net is cash after payoff and costs, not gain for tax purposes. For a National transfer-tax problem, use the given rate even though Texas has no statewide fee-simple transfer tax. Source
Monthly P&I Payment + Monthly Taxes + Monthly Insurance = PITI
$2,400 + $310 + $145 = $2,855/month
Housing Payment ÷ Gross Monthly Income = Front-End Ratio
$2,576 ÷ $9,200 = 28%
(Housing Payment + Monthly Debt) ÷ Gross Monthly Income = Back-End Ratio
($2,576 + $625) ÷ $9,200 = 34.79%
Use gross monthly income. Include other housing costs when the question supplies them. The example percentages are calculation results, not universal approval limits.
Current Value − Total Secured Debt = Equity
$420,000 − $286,000 = $134,000
Current Value − Purchase Price = Appreciation
$420,000 − $350,000 = $70,000
Original Value − Current Value = Depreciation
$350,000 − $315,000 = $35,000
Annual Return ÷ Cash Invested = ROI
$12,000 ÷ $150,000 = 8% ROI
Sale Price − Selling Costs − Acquisition & Improvement Costs = Profit or Loss
$430,000 − $20,000 − $365,000 = $45,000 profit
Initial Basis + Capital Improvements − Depreciation = Adjusted Basis
$350,000 + $40,000 − $25,000 = $365,000
Amount Realized − Adjusted Basis = Gain
$410,000 − $365,000 = $45,000 gain
For gain, amount realized is sale price minus selling expenses, before mortgage payoff. Adjusted basis accounts for depreciation allowed or allowable. Exclusions can change how much gain is taxable. Source
Comparable Sale Price + Adjustment = Adjusted Price
$415,000 + $12,000 = $427,000
Comparable Sale Price − Adjustment = Adjusted Price
$415,000 − $8,000 = $407,000
Adjust the comparable toward the subject: add for an inferior feature and subtract for a superior one. Do not adjust the subject instead.
Study method
1. Name the setup. Decide whether the question is commission, proration, tax, area, income math, LTV, or seller net before touching the calculator.
2. Write one line. Put the formula on your scratch board, then plug in numbers. Keep the rates and units consistent.
3. Check the final ask. Read the last sentence and answer the quantity it asks for.
4. Drill mixed math. A formula sheet is only useful when you can recognize which formula belongs to the question.
Texas property tax is a rate per $100 of taxable value.
Percent rates must become decimals before multiplying.
Prorations need the right owner days and 360/365 basis before the math.
LTV uses the lending value stated in the question. Down payment is purchase price minus the loan.
The outline assigns one scored question to each area below. A question may draw on more than one skill within that area. Our 12 formula groups organize your study; they do not change the exam weights.
Square footage and acreage
Cap rate, taxes, value, and CMA
Total commission and agent splits
Interest, fees, points, and LTV
Proration, cash, seller net, and PITI
Equity, return, basis, and gain
EGI, NOI, and vacancy
Write your setup and answer first. Then open the explanation to check where each number belongs. These are original practice problems, not live exam questions.
A property sells for $320,000. The agreed total commission is 5%. The listing brokerage receives half, and its sales agent receives 70% of that share. What does the agent earn?
$320,000 × 0.05 × 0.50 × 0.70
$5,600The total commission is $16,000. The listing brokerage receives $8,000, then pays the agent 70% of that amount. Each percentage applies to a different base.
Watch for this: Do not take 70% of the entire commission. These are hypothetical agreed rates, not standard commission rates.
Annual property taxes are $3,650, paid in arrears. Use a 365-day year. The question assigns 120 days to the seller and makes the closing day the buyer’s responsibility. What is the seller’s tax adjustment?
$3,650 ÷ 365 × 120
$1,200 seller debit and buyer creditThe daily tax is $10. The seller owes $1,200 for the assigned ownership period. Because the buyer will pay the bill later, the seller gives the buyer a credit at closing.
Watch for this: Use the day count and closing-day instruction in the question. Do not silently switch to a 360-day year.
A property has $72,000 in annual effective gross income and $24,000 in annual operating expenses. Its value is $600,000. What is the capitalization rate?
($72,000 − $24,000) ÷ $600,000
8%Net operating income is $48,000. Divide it by the property value to get 0.08, then express the result as a percentage.
Watch for this: Using $72,000 would give 12%, but cap rate uses NOI. Do not deduct mortgage payments from NOI.
A qualifying homestead has an assessed value of $310,000 after any value limitation. Use a $140,000 school-district exemption and a hypothetical school tax rate of $1.00 per $100. No other exemptions apply. What is the annual school tax?
($310,000 − $140,000) ÷ 100 × $1.00
$1,700The school district taxes $170,000 of value. Dividing by 100 gives 1,700 taxable units, each charged $1.00. This calculates only the school tax, not the combined bill.
Watch for this: Do not apply the school exemption to city or county taxes. Calculate those separately using their own exemptions and rates.
A home costs $300,000 and appraises at $280,000. The question limits the loan to 80% of the lower amount. With no other financing, how much of the price must the buyer pay from their own funds, before closing costs?
$300,000 − ($280,000 × 0.80)
$76,000The loan is $224,000. Subtract it from the $300,000 price to find the buyer's contribution. That includes the $20,000 appraisal gap plus $56,000, or 20% of the lending value.
Watch for this: A 20% down payment on the purchase price would be only $60,000. It misses the fact that the loan uses a different value base.
Ready for a mixed set? Try 15 free math questions with explanations. No account needed.
Try this routine, then spend the next session on the setups you missed. It is a study suggestion, not an official exam requirement.
Start with the core view. Cover the equations, write each relationship from memory, and circle anything that needs a peek.
Before calculating, say the category first: commission, proration, property tax, income math, area, LTV, seller net, or appraisal.
Use mixed practice after the sheet. The exam will not label the formula for you, so recognition matters as much as arithmetic.
Use a calculator to check your work or the full guide to study a method in more detail.
Formula sheet: no. Pearson prohibits personal notes and reference materials in the examination room. The administrator supplies note-taking materials. Wait until the exam begins before writing on them.
Calculator: yes, if it meets Pearson's policy. Pearson VUE recommends bringing a calculator, since the test center does not provide one. Acceptable calculators are hand-held, battery or solar-powered financial calculators used in real estate, finance, accounting, and business; they may have storage capabilities but must not contain alpha (letter) keys. Calculator rules can change, so confirm the current Pearson VUE Texas Real Estate Candidate Handbook before test day. Mathematical labels such as sin and cos are allowed.
Units and rounding: memorize 43,560 square feet per acre and 5,280 feet per mile. Follow the proration basis and closing-day allocation in the question. Keep intermediate values unrounded when possible, then use the requested precision or standard rounding.
Sources: candidate handbook, pages 9-10 and outline calculation notes, page 4.
Pearson VUE's current Texas sales outline assigns 7 scored National items to Real Estate Math Calculations: 4 application questions and 3 analysis questions. The seven official subareas are property area, valuation, commission, loan financing, settlement and closing, investment, and property management.
Pearson VUE does not publish a required formula list. Start with the 35 selected relationships in the 20-page guide, especially commission, proration, property tax, area, LTV, seller net, NOI, cap rate, and financing costs. Use the complete 43-formula web view to review additional setups and reverse calculations.
No. Use this cheat sheet before the exam to build memory. You should be able to write the formulas from memory and recognize which formula a word problem is asking for.
Watch for a correct calculation using the wrong input: a tax rate applied before exemptions, a proration using the wrong year length, or gross rent substituted for NOI. Label the value, time period and units before calculating.
Use it as a reference while you learn, then practice without it. If you can recall a formula but keep choosing the wrong one, spend the next session explaining what each word problem asks you to find before calculating.
Last reviewed October 13, 2026. This review covers the formulas, examples and PDF against sources effective through October 12, 2026. PDF edition 3.1 uses the same corrected formulas. Prices, rates and lending terms in examples are hypothetical. This is independent study material, not an official Pearson VUE or TREC formula sheet.
