Home Affordability Calculator

You’re scrolling listings on a Sunday night and see a place that looks perfect—good schools, short commute, and a kitchen you won’t immediately want to rip out. The price, though, makes you pause. Before you fall in love with a house you can’t comfortably pay for, it helps to translate your income, debts, down payment, and interest rate into a realistic maximum purchase price. That’s exactly what a home affordability calculation does: it turns “I think we can handle it” into a number you can sanity-check.

What Is a Home Affordability Calculator?

A home affordability calculation estimates the maximum home price you can buy based on (1) what lenders typically allow you to spend each month on housing and total debt, and (2) what loan size that monthly payment can support at a given interest rate and term. The logic here follows two widely used lending guidelines:

- Housing ratio (front-end): housing costs up to 28% of gross monthly income - Total debt ratio (back-end): all monthly debt (housing + other debts) up to 36% of gross monthly income

These ratios are commonly referenced in mortgage underwriting as “28/36.” Actual approvals vary by loan type and lender; for example, the CFPB’s Qualified Mortgage (QM) general standard historically used a 43% debt-to-income threshold for certain QM categories (context for why DTI matters). See the Consumer Financial Protection Bureau for QM/DTI background (Gold: consumerfinance.gov).

Key inputs: - Annual household income (gross) - Monthly debt payments (car loans, student loans, minimum credit card payments, etc.) - Down payment saved - Interest rate - Loan term (e.g., 15 or 30 years)

Key outputs: - Maximum home price - Maximum loan amount - Maximum monthly payment (principal + interest in this simplified model) - DTI (debt-to-income ratio) - Down payment percent

The Formula (28/36 Rule + Mortgage Payment Math)

The calculation works in two stages: (A) find the maximum affordable monthly mortgage payment, then (B) convert that payment into a maximum loan using standard amortization math.

1) Convert income to monthly monthlyIncome = annual_income / 12

2) Compute the two affordability caps maxHousing = monthlyIncome * 0.28 maxTotal = monthlyIncome * 0.36

3) Subtract existing monthly debts from the total-debt cap, then take the stricter limit maxPayment = min(maxHousing, maxTotal - monthly_debts)

Plain English: you’re limited by whichever is smaller—(a) 28% of income for housing, or (b) what’s left for housing after keeping total debt at or below 36%.

4) Convert interest rate and term to monthly rate and number of payments mr = rate / 100 / 12 n = loan_term * 12

5) Convert maximum payment to maximum loan (amortization) maxLoan = maxPayment * ( (1 + mr)^n - 1 ) / ( mr * (1 + mr)^n ) (when mr > 0) maxLoan = maxPayment * n (when mr = 0)

This is the standard present-value formula for a fixed-rate mortgage: it answers, “What principal can be financed if the payment is capped at maxPayment?”

6) Add down payment to get maximum home price maxHome = maxLoan + down_payment

7) Compute DTI for context DTI = ((maxPayment + monthly_debts) / monthlyIncome) * 100

Pro Tip (Common Mistake): The maxPayment here is a principal-and-interest estimate. Real housing payment often includes property taxes, homeowners insurance, HOA dues, and possibly mortgage insurance—so the purchase price that “fits” in practice may be lower unless you explicitly budget for those items.

Step-by-Step Worked Examples (Real Numbers)

Below are three examples showing the math end-to-end. (Rounding is to the nearest dollar for readability.)

### Example 1: Moderate income, moderate debts, 30-year loan - Annual income = $120,000 - Monthly debts = $800 - Down payment = $60,000 - Interest rate = 6.5% - Term = 30 years

1) monthlyIncome = 120,000 / 12 = $10,000 2) maxHousing = 10,000 * 0.28 = $2,800 3) maxTotal = 10,000 * 0.36 = $3,600 4) maxTotal - debts = 3,600 - 800 = $2,800 5) maxPayment = min(2,800, 2,800) = $2,800

Now convert payment to loan: - mr = 0.065 / 12 = 0.0054167 - n = 30 * 12 = 360 - (1 + mr)^n ≈ (1.0054167)^360 ≈ 6.99 - maxLoan = 2,800 * (6.99 - 1) / (0.0054167 * 6.99) - maxLoan ≈ 2,800 * 5.99 / 0.03785 ≈ 2,800 * 158.3 ≈ $443,000 (approx.)

Max home price: - maxHome = 443,000 + 60,000 = $503,000 (approx.)

DTI: - DTI = ((2,800 + 800) / 10,000) * 100 = 36%

### Example 2: Higher income, higher debts, 30-year loan - Annual income = $180,000 - Monthly debts = $2,200 - Down payment = $100,000 - Interest rate = 7.0% - Term = 30 years

1) monthlyIncome = 180,000 / 12 = $15,000 2) maxHousing = 15,000 * 0.28 = $4,200 3) maxTotal = 15,000 * 0.36 = $5,400 4) maxTotal - debts = 5,400 - 2,200 = $3,200 5) maxPayment = min(4,200, 3,200) = $3,200 Here, existing debt forces the payment down.

Loan math: - mr = 0.07 / 12 = 0.0058333 - n = 360 - (1 + mr)^n ≈ (1.0058333)^360 ≈ 8.11 - maxLoan = 3,200 * (8.11 - 1) / (0.0058333 * 8.11) - maxLoan ≈ 3,200 * 7.11 / 0.0473 ≈ 3,200 * 150.3 ≈ $481,000 (approx.)

Max home price: - maxHome = 481,000 + 100,000 = $581,000 (approx.)

DTI: - DTI = ((3,200 + 2,200) / 15,000) * 100 = 36%

### Example 3: Same income, shorter term (15-year) changes the price - Annual income = $120,000 - Monthly debts = $500 - Down payment = $80,000 - Interest rate = 6.0% - Term = 15 years

1) monthlyIncome = 120,000 / 12 = $10,000 2) maxHousing = 10,000 * 0.28 = $2,800 3) maxTotal = 10,000 * 0.36 = $3,600 4) maxTotal - debts = 3,600 - 500 = $3,100 5) maxPayment = min(2,800, 3,100) = $2,800 Front-end ratio limits you.

Loan math: - mr = 0.06 / 12 = 0.005 - n = 15 * 12 = 180 - (1 + mr)^n ≈ (1.005)^180 ≈ 2.45 - maxLoan = 2,800 * (2.45 - 1) / (0.005 * 2.45) - maxLoan ≈ 2,800 * 1.45 / 0.01225 ≈ 2,800 * 118.4 ≈ $331,000 (approx.)

Max home price: - maxHome = 331,000 + 80,000 = $411,000 (approx.)

Context fact: A 15-year mortgage often has a lower interest rate than a 30-year, but the shorter term dramatically increases the payment per dollar borrowed—so affordability by purchase price usually drops even if the interest rate is slightly better.

Common Mistakes to Avoid (and a Pro Tip)

Common Mistake #1: Forgetting taxes and insurance. Many households pay hundreds to over a thousand dollars monthly for property taxes and homeowners insurance depending on location and home value. If you only budget principal + interest, you may overshoot.

Common Mistake #2: Using net (take-home) income instead of gross. The 28/36 ratios are based on gross income. Using net income will produce a much lower number and can confuse comparisons with lender pre-approvals.

Common Mistake #3: Leaving out recurring debts. Include minimum credit card payments, personal loans, child support, and any installment debt. Understating monthly debts inflates maxPayment.

Common Mistake #4: Assuming approval equals comfort. A lender limit isn’t a lifestyle limit. If you’re also saving for retirement, childcare, or irregular expenses, you may want a lower target DTI than 36%.

Pro Tip: If you want a quick “stress test,” rerun the math with the interest rate 1% higher. If the max home price drops below what you’re shopping for, you’re rate-sensitive and may want more down payment or a lower price band.

When to Use This Calculator vs. Doing It Manually

Use a home affordability calculation when you’re (1) setting a realistic search price range, (2) deciding whether to pay down debt or save more down payment, (3) comparing a 15-year vs. 30-year term, or (4) checking how a rate change affects buying power. Manual calculation is fine for rough estimates, but the amortization step (turning a payment into a loan amount) is where people most often slip—especially when comparing multiple rates and terms quickly. For a one-off back-of-the-napkin check, the 28/36 caps get you close; for shopping decisions, the full payment-to-loan math is worth using every time.

maxPayment = min(0.28 × (annual_income/12), 0.36 × (annual_income/12) − monthly_debts)

This Home Affordability method estimates a “safe” maximum monthly mortgage payment using the common 28/36 guideline: spend up to 28% of gross monthly income on housing, and up to 36% on total debt (housing plus other monthly debts). The calculator first converts annual household income to a monthly figure, then computes two caps. The housing-only cap is maxHousing = 0.28 × monthlyIncome. The total-debt cap is maxTotal = 0.36 × monthlyIncome, but because you already have other obligations (car loans, student loans, credit cards), the room left for a mortgage payment is maxTotal − monthly_debts. The maximum affordable mortgage payment is the smaller of those two numbers, because you must satisfy both constraints.

monthlyIncome = annual_income / 12

Here, annual_income is gross household income per year, typically in dollars/year (or your local currency/year). monthly_debts is the sum of required minimum monthly debt payments in dollars/month. down_payment is cash saved toward the purchase, in dollars. rate is the annual interest rate as a percent (for example, 6.5 for 6.5%). loan_term is the mortgage length in years (commonly 15, 20, 30).

Once maxPayment is found, the calculator converts that affordable payment into a maximum loan amount using the standard amortizing loan present value formula. It uses the monthly interest rate mr = (rate/100)/12 and the number of payments n = loan_term × 12.

maxLoan = maxPayment × ((1+mr)^n − 1) / (mr × (1+mr)^n)

This is the present value of an annuity: a fixed payment made n times, discounted at mr per month. If mr = 0 (a zero-interest edge case), the formula would divide by zero, so the method correctly falls back to maxLoan = maxPayment × n.

Finally, it estimates the maximum home price as the loan plus your down payment (rounded): maxHome = maxLoan + down_payment. It also reports a back-end debt-to-income ratio: dti = ((maxPayment + monthly_debts) / monthlyIncome) × 100, expressed as a percent, and the down payment percent: down_pct = (down_payment / maxHome) × 100.

Because these inputs are financial, there’s no imperial/metric conversion in the physics sense, but you may still need currency and time consistency. Keep everything in the same currency, and ensure income is annual while debts and payment are monthly. If you’re paid weekly, convert to annual first (weekly_income × 52), then divide by 12. If you’re paid biweekly, use × 26. If you only know hourly pay, annual_income = hourly_rate × hours_per_week × 52.

Example 1 (moderate debts, 30-year loan): annual_income = 120,000; monthly_debts = 800; down_payment = 60,000; rate = 6.5; loan_term = 30. monthlyIncome = 120,000/12 = 10,000. maxHousing = 0.28×10,000 = 2,800. maxTotal = 0.36×10,000 = 3,600, so maxTotal − debts = 3,600 − 800 = 2,800. maxPayment = min(2,800, 2,800) = 2,800. mr = 0.065/12 = 0.0054166667. n = 30×12 = 360. (1+mr)^n ≈ (1.0054166667)^360 ≈ 6.99. Then maxLoan = 2,800 × (6.99−1) / (0.0054166667×6.99) = 2,800 × 5.99 / 0.03786 ≈ 2,800 × 158.2 ≈ 443,000. maxHome ≈ 443,000 + 60,000 = 503,000. dti = ((2,800+800)/10,000)×100 = 36.0%. down_pct ≈ 60,000/503,000×100 ≈ 11.9%.

Example 2 (higher debts, 15-year loan): annual_income = 90,000; monthly_debts = 1,200; down_payment = 100,000; rate = 5.0; loan_term = 15. monthlyIncome = 90,000/12 = 7,500. maxHousing = 0.28×7,500 = 2,100. maxTotal = 0.36×7,500 = 2,700, so maxTotal − debts = 2,700 − 1,200 = 1,500. maxPayment = min(2,100, 1,500) = 1,500 (debts are the binding constraint). mr = 0.05/12 = 0.0041666667. n = 15×12 = 180. (1+mr)^n ≈ (1.0041666667)^180 ≈ 2.11. maxLoan = 1,500 × (2.11−1) / (0.0041666667×2.11) = 1,500 × 1.11 / 0.00879 ≈ 1,500 × 126.3 ≈ 189,000. maxHome ≈ 189,000 + 100,000 = 289,000. dti = ((1,500+1,200)/7,500)×100 = 36.0%. down_pct ≈ 100,000/289,000×100 ≈ 34.6%.

Limitations matter. This method treats “monthly payment” as a single number, but real housing costs often include property taxes, homeowners insurance, HOA dues, and mortgage insurance; if those aren’t included in monthly_debts, you should subtract them from maxPayment before computing maxLoan. It also assumes a fixed-rate, fully amortizing loan; adjustable-rate mortgages, interest-only periods, or balloon loans change the payment-to-loan relationship. Rounding can shift results slightly. Finally, the 28/36 guideline is a rule of thumb, not a guarantee of approval; lenders may use different DTI thresholds, and underwriting also depends on credit score, cash reserves, and the specific loan program.

• HUD — Housing and Urban Development
• Federal Reserve — Economic Data
• CFPB — Owning a Home
• Consumer Financial Protection Bureau
• Investopedia