Real Estate Exam Math Formulas: Complete Guide with Examples

Math questions on the real estate exam are actually some of the easiest points to earn — if you know the formulas. Unlike conceptual questions that can be tricky, math problems have one correct answer. Learn these formulas and you'll pick up guaranteed points.

The T-Bar Method (Your Secret Weapon)

Before diving into formulas, learn the T-bar method. It works for any problem involving Part, Whole, and Rate. Draw a T shape: Part goes on top, Whole and Rate go on the bottom. Cover what you're solving for — the remaining elements show the operation.

• To find Part: Whole × Rate
• To find Whole: Part ÷ Rate
• To find Rate: Part ÷ Whole

Commission Calculations

Formula: Sale Price × Commission Rate = Commission

Example 1: Finding Commission Amount

A home sells for $450,000 with a 6% commission. What is the commission?

Solution: $450,000 × 0.06 = $27,000

Example 2: Finding Sale Price

An agent earned $15,000 commission at 5%. What was the sale price?

Solution: $15,000 ÷ 0.05 = $300,000

Example 3: Commission Splits

A home sells for $500,000 at 6% commission. The listing broker gets 60% of the listing side. How much does the listing broker receive?

Solution: $500,000 × 0.06 = $30,000 total → $30,000 ÷ 2 = $15,000 listing side → $15,000 × 0.60 = $9,000

Loan-to-Value (LTV) Ratio

Formula: Loan Amount ÷ Property Value = LTV Ratio

Example

A buyer purchases a $400,000 home with a $320,000 loan. What is the LTV?

Solution: $320,000 ÷ $400,000 = 0.80 = 80% LTV

Why it matters: LTV above 80% typically requires PMI on conventional loans.

Income Property Calculations

Cap Rate Formula

Formula: Net Operating Income (NOI) ÷ Property Value = Cap Rate

A property generates $50,000 NOI and is valued at $625,000. What's the cap rate?

Solution: $50,000 ÷ $625,000 = 0.08 = 8% cap rate

Finding Property Value Using Cap Rate

Formula: NOI ÷ Cap Rate = Property Value

An investor wants an 8% return. A property has $60,000 NOI. What should they pay?

Solution: $60,000 ÷ 0.08 = $750,000

Gross Rent Multiplier (GRM)

Formula: Sale Price ÷ Gross Annual Rent = GRM

A property sells for $240,000 and generates $24,000 annual rent. What's the GRM?

Solution: $240,000 ÷ $24,000 = GRM of 10

Property Tax Calculations

Formula: Assessed Value × Tax Rate = Annual Property Tax

Example

A property is assessed at $280,000. The tax rate is $2.50 per $100 of assessed value. What's the annual tax?

Solution: ($280,000 ÷ 100) × $2.50 = 2,800 × $2.50 = $7,000

Alternative method: $280,000 × 0.025 = $7,000 (converting $2.50 per $100 to 2.5%)

Proration Calculations

Formula: Annual Amount ÷ Days in Year × Days Owed = Prorated Amount

Note: Some states use 365 days (actual), others use 360 days (banker's year). Know which your state uses.

Example: Property Tax Proration

Annual property tax is $3,650. Closing is March 15. Seller has prepaid taxes for the full year. How much credit does seller receive? (Using 365-day year, seller owned Jan 1 - March 14 = 73 days)

Solution: $3,650 ÷ 365 = $10/day → Seller owned 73 days → Buyer owes seller credit for remaining 292 days → 292 × $10 = $2,920 credit to seller

Area Calculations

Formulas:

• Rectangle: Length × Width = Area
• Triangle: (Base × Height) ÷ 2 = Area
• 1 Acre = 43,560 square feet
• 1 Square Mile = 640 acres

Example: Price Per Square Foot

A 2,400 sq ft home sells for $360,000. What's the price per square foot?

Solution: $360,000 ÷ 2,400 = $150 per sq ft

Example: Acreage

A lot is 200 feet × 435.6 feet. How many acres?

Solution: 200 × 435.6 = 87,120 sq ft → 87,120 ÷ 43,560 = 2 acres

Net to Seller Calculations

Formula: Sale Price - Commission - Closing Costs - Mortgage Payoff = Net to Seller

Example

Seller wants to net $200,000. Commission is 6%, closing costs are $5,000, mortgage payoff is $150,000. What sale price is needed?

Solution: Let X = sale price. X - 0.06X - $5,000 - $150,000 = $200,000 → 0.94X = $355,000 → X = $377,660

Practice Tips

• Always convert percentages to decimals (6% = 0.06)
• Use the same calculator you'll use on test day
• Estimate answers first to catch obvious errors
• Double-check that your answer makes sense
• Practice 10+ math problems every day