Appraisal Math Calculator
Master the 7 essential appraisal math formulas. Calculate NOI, cap rate, GRM, GIM, depreciation, cost approach value, and sales comparison adjustments with step-by-step explanations.
How it works
Net Operating Income (NOI) = Potential Gross Income - Vacancy Loss - Operating Expenses. NOI is the income a property generates after deducting vacancy and operating expenses, but before debt service.
Example
A 10-unit building rents at $1,200/month each. PGI = $144,000. With 5% vacancy ($7,200) and $48,000 expenses, NOI = $144,000 - $7,200 - $48,000 = $88,800.
Appraisal Math Formulas Every Appraiser Must Know
The real estate appraiser exam tests your ability to apply mathematical formulas across all three approaches to value: the income approach, the cost approach, and the sales comparison approach. Understanding these formulas is not just about memorization — you need to know when and how to apply them in real appraisal scenarios.
Income Approach Formulas
The income approach relies on Net Operating Income (NOI) as the foundation. PGI minus vacancy and collection loss gives you Effective Gross Income (EGI). Subtract operating expenses (but never debt service or income taxes) to get NOI. The capitalization rate converts NOI into value: Value = NOI / Cap Rate. For quick estimates, the Gross Rent Multiplier (GRM) and Gross Income Multiplier (GIM) provide market-derived multipliers.
Cost Approach Formula
The cost approach is especially important for unique or special-purpose properties. Start with the replacement cost new (what it would cost to build a substitute with equal utility), subtract accrued depreciation from all causes (physical deterioration, functional obsolescence, and external obsolescence), then add land value.
Sales Comparison Adjustments
In the sales comparison approach, you always adjust the comparable, never the subject. The key rule: if the comparable is superior, subtract; if the comparable is inferior, add. A popular mnemonic is "CBS" — Comp Better, Subtract.
How to Use This Calculator: Step-by-Step Exam Examples
Appraisal math questions make up roughly 15% of the appraiser exam. The key to answering them correctly is knowing which formula to apply and plugging in the numbers in the right order. Below are four worked examples using the calculator above — practice each one until the process feels automatic.
Example 1: Net Operating Income (NOI)
Scenario: A 10-unit apartment building generates $1,200/month per unit. Market vacancy is 5%. Annual operating expenses total $62,000.
Formula: NOI = (PGI - Vacancy) - Operating Expenses
Calculation: PGI = 10 units x $1,200 x 12 months = $144,000. Vacancy = $144,000 x 5% = $7,200. EGI = $144,000 - $7,200 = $136,800. NOI = $136,800 - $62,000 = $74,800.
Tip: Select "Net Operating Income (NOI)" in the calculator, enter PGI as $144,000, vacancy rate as 5%, and operating expenses as $62,000. The result matches instantly.
Example 2: Capitalization Rate
Scenario: A comparable property sold for $950,000 and had a verified NOI of $76,000 at the time of sale. What is the cap rate?
Formula: Cap Rate = NOI / Sale Price
Calculation: Cap Rate = $76,000 / $950,000 = 0.08 = 8.0%.
Tip: If you know the cap rate and NOI, you can also solve for value: Value = $76,000 / 0.08 = $950,000. On the exam, the question may ask you to find any one of the three variables (NOI, cap rate, or value) given the other two.
Example 3: Gross Rent Multiplier (GRM)
Scenario: Three comparable properties sold at the following prices with monthly rents: Comp A — $285,000 / $1,900, Comp B — $310,000 / $2,050, Comp C — $298,000 / $2,000. What is the indicated GRM, and what is the value of a subject property renting for $2,100/month?
Formula: GRM = Sale Price / Monthly Rent; Value = Monthly Rent x GRM
Calculation: GRM_A = $285,000 / $1,900 = 150.0. GRM_B = $310,000 / $2,050 = 151.2. GRM_C = $298,000 / $2,000 = 149.0. Average GRM = 150.1 (round to 150). Subject Value = $2,100 x 150 = $315,000.
Example 4: Straight-Line Depreciation (Cost Approach)
Scenario: A building has a replacement cost new of $400,000, an economic life of 50 years, and an effective age of 15 years. The land is worth $120,000. What is the property value by the cost approach?
Formula: Value = (Replacement Cost - Accrued Depreciation) + Land Value
Calculation: Annual Depreciation = $400,000 / 50 = $8,000/year. Accrued Depreciation = $8,000 x 15 = $120,000. Depreciated Value = $400,000 - $120,000 = $280,000. Property Value = $280,000 + $120,000 = $400,000.
Tip: Use the "Cost Approach" mode in the calculator. Enter replacement cost, economic life, effective age, and land value. The calculator shows both annual depreciation and the final indicated value.
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