Real Estate Math
Cheat Sheet (2026)
Every formula you need for the real estate licensing exam — organized by category with examples and exam tips. Math accounts for 10–15% of most exams.
Commission & Income
Gross Commission
Sale Price × Commission Rate
Example
$400,000 × 6% = $24,000
Commission rate is usually split between listing and buyer's agent brokerages.
Agent Net Commission
Gross Commission × Agent Split %
Example
$24,000 × 50% = $12,000 agent share
Typical splits are 50/50, 60/40, or 70/30 between broker and agent.
Commission on Net
(Sale Price − Seller's Costs) × Commission Rate
Example
Seller wants $380,000 net → List price = $380,000 ÷ (1 − 0.06) = $404,255
Used when seller specifies a net amount rather than a gross price.
Required Listing Price
Desired Net ÷ (1 − Commission Rate)
Example
Net $380,000 ÷ 0.94 = $404,255 list price
Critical formula — appears frequently on exam.
Financing & Loans
Loan-to-Value (LTV)
Loan Amount ÷ Appraised Value
Example
$320,000 ÷ $400,000 = 80% LTV
LTV above 80% typically requires PMI (private mortgage insurance).
Loan Amount from LTV
Appraised Value × LTV %
Example
$400,000 × 80% = $320,000 loan
Lenders use the lower of purchase price or appraised value.
Down Payment
Purchase Price − Loan Amount
Example
$400,000 − $320,000 = $80,000 down
Or: Purchase Price × Down Payment %.
Debt-to-Income Ratio (DTI)
Total Monthly Debt ÷ Gross Monthly Income
Example
$2,000 debt ÷ $6,000 income = 33% DTI
Most conventional loans require DTI below 43–45%.
Discount Points
1 point = 1% of loan amount
Example
2 points on $320,000 = $6,400 cost
Each point typically reduces interest rate by ~0.25%.
Simple Interest
Principal × Annual Rate × Time (years)
Example
$100,000 × 6% × 1 = $6,000/year
Mortgage interest is typically calculated monthly: P × (rate ÷ 12).
Property Valuation
Capitalization Rate (Cap Rate)
NOI ÷ Property Value
Example
$30,000 NOI ÷ $400,000 = 7.5% cap rate
Used for income-producing properties. Higher cap rate = higher risk/return.
Property Value from Cap Rate
NOI ÷ Cap Rate
Example
$30,000 ÷ 0.075 = $400,000
The income approach to valuation.
Net Operating Income (NOI)
Gross Income − Vacancy & Credit Loss − Operating Expenses
Example
$50,000 − $2,500 − $17,500 = $30,000 NOI
Does NOT include mortgage payments (debt service).
Gross Rent Multiplier (GRM)
Property Price ÷ Gross Annual Rent
Example
$400,000 ÷ $40,000 = GRM of 10
Lower GRM = better value. Used for quick comparison, not precise valuation.
Assessed Value
Market Value × Assessment Ratio
Example
$400,000 × 80% = $320,000 assessed value
Assessment ratio varies by jurisdiction.
Appreciation / Future Value
Current Value × (1 + Annual Rate)^Years
Example
$300,000 × (1.04)^5 = $364,996
For simple annual appreciation: Current Value × (1 + Rate × Years).
Property Tax & Proration
Annual Property Tax
Assessed Value × Tax Rate (or Mill Rate ÷ 1,000)
Example
$320,000 × 0.015 = $4,800/year
1 mill = $1 per $1,000 of assessed value. 15 mills = 1.5% = $0.015.
Mill Rate Conversion
Mills ÷ 1,000 = Tax Rate (decimal)
Example
15 mills ÷ 1,000 = 0.015 (1.5%)
Tax = Assessed Value × (Mills ÷ 1,000).
Proration — Daily Rate (365-day method)
Annual Amount ÷ 365
Example
$4,800 ÷ 365 = $13.15/day
Most common method. Some use 360-day banker's year.
Proration — Monthly (360/30 method)
Annual Amount ÷ 12 ÷ 30
Example
$4,800 ÷ 12 ÷ 30 = $13.33/day
Used in banker's year calculations.
Seller's Tax Credit at Closing
Daily Rate × Days Seller Owned (Jan 1 to Closing Date)
Example
Closing May 15: 135 days × $13.15 = $1,775 seller credit
Seller credits buyer for taxes owed but not yet paid.
Transfer Tax
(Sale Price ÷ Unit Value) × Tax Rate
Example
($400,000 ÷ $500) × $1.65 = $1,320 transfer tax
Rates vary by state and county. Unit is commonly per $500 or $1,000.
Area & Measurements
Rectangle Area
Length × Width
Example
50 ft × 30 ft = 1,500 sq ft
Most common area calculation on the exam.
Triangle Area
(Base × Height) ÷ 2
Example
(60 × 40) ÷ 2 = 1,200 sq ft
Used for irregular lot shapes.
Acres Conversion
1 acre = 43,560 sq ft
Example
87,120 sq ft ÷ 43,560 = 2 acres
Must memorize: 43,560 sq ft per acre.
Section of Land
1 section = 640 acres = 1 square mile
Example
½ section = 320 acres; ¼ section = 160 acres
Township = 36 sections. Range lines run N–S; Township lines run E–W.
Square Footage to Price per Sq Ft
Price ÷ Square Footage
Example
$400,000 ÷ 2,000 sq ft = $200/sq ft
Depreciation & Investment
Straight-Line Depreciation
(Cost − Land Value) ÷ Useful Life
Example
($500,000 − $100,000) ÷ 27.5 years = $14,545/year
IRS useful life: 27.5 years (residential), 39 years (commercial). Land is NOT depreciated.
Accumulated Depreciation
Annual Depreciation × Years Held
Example
$14,545 × 5 = $72,725
Adjusted Basis
Original Cost + Capital Improvements − Accumulated Depreciation
Example
$500,000 + $20,000 − $72,725 = $447,275
Used to calculate taxable gain on sale.
Capital Gain on Sale
Sale Price − Adjusted Basis − Selling Costs
Example
$600,000 − $447,275 − $30,000 = $122,725 taxable gain
Return on Investment (ROI)
Annual Net Income ÷ Total Investment × 100
Example
$30,000 NOI ÷ $100,000 down payment = 30% ROI
Also called cash-on-cash return when using equity invested.
Quick Reference — Most Tested Formulas
These appear on virtually every state exam. Know all of them cold.
| Formula | Equation |
|---|---|
| Gross Commission | Sale Price × Commission % |
| Required Listing Price | Net ÷ (1 − Commission %) |
| Loan-to-Value (LTV) | Loan Amount ÷ Property Value |
| Daily Proration Rate | Annual Amount ÷ 365 |
| Property Tax | Assessed Value × (Mill Rate ÷ 1,000) |
| Assessed Value | Market Value × Assessment Ratio |
| Cap Rate | NOI ÷ Property Value |
| Property Value (income) | NOI ÷ Cap Rate |
| GRM | Price ÷ Annual Gross Rent |
| Straight-Line Depreciation | (Cost − Land) ÷ Useful Life |
| Rectangle Area | Length × Width |
| Triangle Area | (Base × Height) ÷ 2 |
| Acres | Square Feet ÷ 43,560 |
| Discount Points | 1 pt = 1% of Loan Amount |
Real Estate Math — FAQ
Practice math questions for your state
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