California Real Estate Exam Math: Formulas and Practice Problems

Real estate math scares a lot of exam candidates — but it shouldn't. Math questions make up 10–15% of the California exam (roughly 15–22 questions out of 150), and every single one is formula-based. Once you know the formulas, math questions are the most reliable points on the exam.

This guide covers every math formula you need, with worked examples for each.

The Golden Rule of Real Estate Math

Almost every real estate math problem can be solved with one of three variations of the same relationship:

Part = Whole × Rate Rate = Part ÷ Whole Whole = Part ÷ Rate

Memorize this triangle: put the "Whole" on top, "Part" and "Rate" on the bottom. Cover the variable you're solving for, and the remaining two show you the operation.

1. Commission Calculations

Commission is the most common math topic on the exam.

Formula: Commission = Sale Price × Commission Rate

Example 1: A home sells for $850,000. The total commission is 5%. How much is the commission? - $850,000 × 0.05 = $42,500

Example 2 — Split commission: A home sells for $650,000. Total commission is 6%, split equally between listing and buyer's brokers. The listing agent receives 55% of their broker's commission. How much does the listing agent earn? - Total commission: $650,000 × 0.06 = $39,000 - Each broker's side: $39,000 ÷ 2 = $19,500 - Listing agent's share: $19,500 × 0.55 = $10,725

Example 3 — Find the price from commission: An agent earns $18,000 on a 4% commission. What did the property sell for? - Price = Commission ÷ Rate = $18,000 ÷ 0.04 = $450,000

2. Loan-to-Value (LTV) Ratio

Formula: LTV = Loan Amount ÷ Property Value

Example 1: A buyer puts 15% down on a $400,000 home. What is the LTV? - Down payment: $400,000 × 0.15 = $60,000 - Loan: $400,000 − $60,000 = $340,000 - LTV: $340,000 ÷ $400,000 = 85%

Example 2 — Find the loan amount from LTV: A property is valued at $500,000. The lender approves an 80% LTV loan. What is the loan amount? - $500,000 × 0.80 = $400,000

Example 3 — Find the value from loan amount: A buyer gets an 85% LTV loan for $425,000. What is the purchase price? - Value = Loan ÷ LTV = $425,000 ÷ 0.85 = $500,000

3. Capitalization Rate (Cap Rate)

The income approach to appraisal uses this formula.

Formula: Value = NOI ÷ Cap Rate (Alternatively: Cap Rate = NOI ÷ Value)

NOI (Net Operating Income) = Gross Income − Vacancy − Operating Expenses (Do NOT subtract mortgage payments — NOI is before debt service)

Example 1: An apartment building has a NOI of $120,000. The local cap rate is 8%. What is the estimated value? - Value = $120,000 ÷ 0.08 = $1,500,000

Example 2 — Find cap rate: A building sells for $2,000,000 and has a NOI of $160,000. What is the cap rate? - Cap Rate = $160,000 ÷ $2,000,000 = 8%

Example 3 — Find NOI: A property sells at a 7% cap rate for $1,200,000. What is the NOI? - NOI = Value × Cap Rate = $1,200,000 × 0.07 = $84,000

4. Gross Rent Multiplier (GRM)

A simpler valuation shortcut often used for residential income property.

Formula: GRM = Price ÷ Monthly Rent Value = GRM × Monthly Rent

Example 1: A duplex sells for $480,000. Monthly rent is $2,400. What is the GRM? - GRM = $480,000 ÷ $2,400 = 200

Example 2 — Estimate value using GRM: Comparable properties have a GRM of 175. The subject property rents for $3,000/month. Estimate the value. - Value = 175 × $3,000 = $525,000

5. Prorations

Prorations divide recurring costs (property taxes, HOA fees, prepaid rent) between buyer and seller at closing. The key is knowing who has paid for a period they won't own, and who owes for a period they will own.

Standard proration method (exams typically use 360-day year, 30-day months): - Daily rate = Annual amount ÷ 360 - Days seller owned = count from Jan 1 to closing date - Taxes paid in arrears → seller OWES buyer for days seller owned - Taxes prepaid → seller is OWED by buyer for days seller won't own

Example — Property taxes paid in arrears: Closing date: September 15. Annual property taxes: $3,600. Calculate the seller's proration credit to buyer.

• Daily rate: $3,600 ÷ 360 = $10/day
• Seller's days (Jan 1 – Sep 15): 8 months × 30 = 240 days + 15 = 255 days
• Seller owes buyer: 255 × $10 = $2,550

Example — Prepaid rent (tenant in place): Closing date: July 10. Monthly rent is $1,800. Seller already collected July's rent. Buyer gets credit for days they'll own in July.

• Daily rate: $1,800 ÷ 30 = $60/day
• Buyer owns July 10 onward: days 10–30 = 21 days (depends on how exam counts: usually days remaining starting from day after closing)
• Buyer credit: 21 × $60 = $1,260

6. Depreciation (Cost Approach)

Straight-line depreciation formula: Annual Depreciation = (Building Value − Salvage Value) ÷ Useful Life

Example: A building has a replacement cost of $500,000. Salvage value is $0. Estimated useful life is 40 years. What is the annual depreciation? - $500,000 ÷ 40 = $12,500/year

Accrued depreciation example: The same building is 10 years old. What is its depreciated value? - Total depreciation: $12,500 × 10 = $125,000 - Depreciated value: $500,000 − $125,000 = $375,000 - Add land value (land does not depreciate) for total property value

7. Transfer Tax

California counties charge a documentary transfer tax on property conveyances.

Formula: Transfer Tax = (Sale Price ÷ $500) × Tax Rate

In most California counties: $1.10 per $500 (or fraction thereof) of value.

Example: A property sells for $750,000. What is the documentary transfer tax? - $750,000 ÷ $500 = 1,500 units - 1,500 × $1.10 = $1,650

8. Area and Square Footage

Real estate math sometimes involves calculating square footage of rooms or lots.

• Rectangle: Length × Width
• Triangle: (Base × Height) ÷ 2
• Lot size conversion: 1 acre = 43,560 sq ft

Example: A rectangular lot is 125 feet deep and 60 feet wide. How many acres is it? - Area: 125 × 60 = 7,500 sq ft - Acres: 7,500 ÷ 43,560 = 0.172 acres

Common Exam Math Mistakes to Avoid

Not converting percentages: Always convert percentages to decimals before calculating (5% = 0.05, not 5).

Confusing annual vs. monthly figures: Cap rate and NOI are typically annual; GRM uses monthly rent. Keep units consistent.

Forgetting to exclude mortgage payments from NOI: Net Operating Income is before debt service. Don't subtract loan payments when calculating NOI.

Using calendar days instead of 360/30 convention: Unless the exam question specifies otherwise, use 360 days/year and 30 days/month for prorations.

Rounding too early: On multi-step problems, carry extra decimal places through the calculation and round only at the final answer.

Quick Reference: Formula Sheet

• Commission = Price × Rate
• LTV = Loan ÷ Value
• Value (income) = NOI ÷ Cap Rate
• GRM = Price ÷ Monthly Rent
• Daily Proration Rate = Annual Amount ÷ 360
• Annual Depreciation = Building Value ÷ Useful Life
• Transfer Tax = (Price ÷ 500) × $1.10

Print this list and drill each formula until you can apply it without looking. Ten practice problems per formula type is enough to make them automatic.

Our quiz at CARealestate.com has a dedicated math section with 50+ worked problems. Use it to confirm you've got every formula type mastered before exam day.