Real Estate Math Formulas Cheat Sheet

Use this real estate math formulas cheat sheet to identify the quantity a question asks for, choose the matching equation, and check your units. For example, commission is sale price × agreed rate, while loan-to-value (LTV) is loan amount ÷ stated value × 100%. Write the setup before using the practice calculator at the end of this page. Your own testing provider’s current outline and candidate bulletin determine the topics and rules for your exam.

The Pearson VUE national/general salesperson outline published for Kansas includes area, valuation, commission, loan costs, settlement, investment, and property-management calculations. The PSI Maryland candidate bulletin also lists transaction calculations, LTV, cap rate, and points in its national-portion outline. These are examples of provider outlines, not a promise that every jurisdiction tests the same mix.

How to use the real estate math formulas cheat sheet

1. Name the unknown. Is the answer a dollar amount, percent, square feet, acres, or days?
2. List the givens with units. Mark a figure as annual or monthly, gross or net, price or loan amount.
3. Write the formula and convert percentages. For example, 2.5% becomes 0.025 when multiplied.
4. Substitute, calculate, and check. A down payment should not exceed the purchase price when the stated loan is smaller than that price. A cap-rate value should be expressed in dollars, not percent.

If the question gives extra numbers, use only the ones the formula needs. For instance, a property-tax amount does not affect a question asking only for LTV.

Area and acreage formulas

For a rectangular parcel, multiply length by width. A 150-foot by 100-foot parcel has 15,000 square feet. Divide by 43,560 square feet per acre to convert that area to about 0.344 acres. The Kansas Pearson VUE outline identifies 43,560 square feet per acre as a conversion to memorize for its exam; check the materials for your own exam.

Irregular shapes need the measurements or decomposition supplied in the problem. Do not apply length × width to a triangle or an irregular lot without first finding the relevant areas.

Commission, loan, and financing formulas

Commission uses the agreed rate

Multiply the sale price by the rate stated in the problem or agreement. If a question then asks for a person’s share, multiply the relevant commission amount by the stated split. Avoid assuming a standard commission rate or that a split applies to the entire transaction commission when the problem says it applies to one brokerage’s share.

LTV and down payment answer different questions

LTV compares a loan with a stated property value. Down payment subtracts the loan from the purchase price. A practice problem may say those two values are the same; in that case a $315,000 loan against a $420,000 purchase price has 75% LTV and a $105,000 down payment. If a problem specifies a different value for LTV, follow that instruction.

For discount points, multiply the loan, not the sale price, by the point percentage. For simple interest, use principal × annual rate × time in years only when the question calls for simple interest; an amortized mortgage payment needs more information and a different calculation.

Income-property valuation formulas

NOI is income after the operating expenses specified by the problem. With $52,000 effective gross income and $16,000 operating expenses, annual NOI is $36,000. At a stated 9% cap rate, indicated value is $36,000 ÷ 0.09 = $400,000. Reversing the relationship, $36,000 ÷ $400,000 × 100% gives a 9% cap rate.

Keep gross rent, effective gross income, and NOI distinct. A gross rent multiplier uses gross rent and must be paired with the same rent period used to derive the multiplier; it is not interchangeable with NOI or a cap rate.

Closing costs, seller net, and prorations

A seller-net question is an accounting setup: start with the sale price and subtract only the stated seller charges and payoff. A buyer-funds question starts with the stated down payment and adds buyer charges, then subtracts deposits or credits the question says have already been paid. Label every amount before adding or subtracting it.

For property-tax proration, first decide who already paid or will pay the annual bill, then allocate the period the other party owes. If the tax is unpaid and the buyer will pay it later, the seller’s share is generally a seller debit and buyer credit in that problem. If the seller prepaid it, the buyer’s remaining share is a buyer debit and seller credit. The agreement and question facts control. A 360- versus 365-day basis and ownership of closing day can change the result. The Kansas Pearson VUE math notes say its proration questions specify the day basis and/or who owns closing day. Do not infer a date-count method from the number 360 alone.

Seven original real estate math practice questions

These are original teaching examples, not actual testing-provider questions. Try each on paper before opening the explanation. The facts supplied in each example govern its answer.

1. Commission from an agreed percentage

A property sells for $420,000. The question states an agreed commission rate of 2.5% of the sale price. What is the total commission under that agreement?

Worked answer: $10,500. The unknown is dollars. Convert 2.5% to 0.025, then multiply: $420,000 × 0.025 = $10,500. Do not multiply by 2.5 or import a rate from another transaction.

2. LTV and down payment

A buyer pays $420,000 and borrows $315,000. Assume the purchase price is also the value used for LTV. Find the LTV and down payment, before other costs.

Worked answer: 75% LTV and $105,000 down payment. LTV = $315,000 ÷ $420,000 × 100% = 75%. Down payment = $420,000 − $315,000 = $105,000. The remaining 25% is the down-payment percentage, not the dollar down payment.

3. Indicated value from NOI and cap rate

An income property has $52,000 effective gross annual income and $16,000 annual operating expenses. The question supplies a 9% cap rate. What value does direct capitalization indicate?

Worked answer: $400,000. First calculate annual NOI: $52,000 − $16,000 = $36,000. Convert 9% to 0.09. Then value = $36,000 ÷ 0.09 = $400,000. Using $52,000 gross income as the numerator would answer a different question.

4. Square feet to acres

A rectangular lot measures 150 feet by 100 feet. Approximately how many acres is it?

Worked answer: 0.344 acres. Area = 150 ft × 100 ft = 15,000 sq ft. Acres = 15,000 sq ft ÷ 43,560 sq ft/acre ≈ 0.344 acres. The square-foot units cancel in the conversion.

5. Seller net proceeds

A home sells for $420,000. The question assigns the seller a $10,500 commission charge, $3,000 in other closing charges, and a $280,000 mortgage payoff. Ignore other adjustments. What is the seller’s net?

Worked answer: $126,500. Start with the sale price and subtract each stated seller item: $420,000 − $10,500 − $3,000 − $280,000 = $126,500. The loan payoff is a reduction in proceeds, even though it is not the buyer’s down payment.

6. Unpaid tax proration

Annual property tax is $3,600. The question uses a 360-day divisor, says the buyer will pay the tax bill after closing, and assigns 150 countable days to the seller after applying its closing-day rule. What is the seller’s proration and the corresponding debit/credit?

Worked answer: $1,500 seller debit and buyer credit. Daily rate = $3,600 ÷ 360 = $10/day. Seller share = $10/day × 150 days = $1,500. The seller has not paid that share; the buyer will later pay the bill, so this example charges the seller and credits the buyer. The 150 days already reflect the question’s closing-day assignment; no date algorithm is needed.

7. Discount points

A buyer takes a $280,000 loan. The problem says the buyer pays 1.5 points at closing. How much do those points cost?

Worked answer: $4,200. One point is 1% of the loan, so 1.5 points is 1.5%. Multiply $280,000 × 0.015 = $4,200. Multiplying the sale price instead would use the wrong base.

For a broader topic plan, use How to Study for the Real Estate Exam. When you are ready to apply these setups to more explained questions, go to Real Estate Salesperson exam practice. Pair national practice with your own jurisdiction’s current outline and candidate bulletin, including its allowed-materials rules.

Real estate math practice calculator

Use the practice calculator below to check a commission, LTV and down payment, cap rate or indicated value, or property-tax proration. It shows the formula and substitution so you can compare each step with your own setup. For proration, enter the seller days from the problem after applying its closing-day rule, then choose the stated 360- or 365-day basis and whether the tax is prepaid or unpaid.