What this calculator does
Find out how much house you can afford. This calculator finds the highest home price whose monthly payment fits the limits lenders commonly use. It starts from your income, other debts and down payment. Then it adds your mortgage rate, property tax, insurance, HOA dues and PMI (mortgage insurance). You'll also see the monthly payment at that price, which limit is holding you back, and how the answer changes with more careful or more generous limits.
Lenders often look at two numbers when you apply for a mortgage. The first is the share of your monthly income before tax (your gross income) that goes to housing. The second is the share that goes to housing plus all your other debt payments. These are called debt-to-income ratios. A widely used guideline caps them at 28% and 36%, though real limits vary by loan type and borrower.
The calculator works backward from the lower of those two limits to a home price. Use the result as a guide for planning, not a promise that you'll be approved.
Where it's used
Why this math matters outside the classroom:
- Housing budget. A household earning $90,000 a year that keeps housing to 28% of gross income has $2,100 a month to spend on it.
- Working back to price. Buyers convert that monthly budget, after taxes, insurance and dues, into a loan amount and then a home price.
- Rate sensitivity. Shoppers see how the price range shrinks when mortgage rates rise while the monthly budget stays the same.
- Existing debts. Adding a car payment to the debt side shows how other debts reduce the room left for housing.
Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter your yearly income before tax and the monthly payments on your other debts.
- Enter your down payment, the interest rate you expect and the loan term.
- Enter a property tax rate, your yearly insurance, and any HOA dues or PMI rate.
- Keep the 28% and 36% limits or set your own. Then read the highest price and the payment that goes with it. The table repeats the math at 25%/33%, 28%/36% and 31%/43%. That lets you compare a careful, a typical and a stretch budget side by side.
What the inputs mean
- Gross annual income
- Income before tax for everyone on the loan. Lenders use this gross income for these ratios.
- Other monthly debt payments
- The minimum monthly payments on car loans, student loans, credit cards and similar debts. Leave out rent you'll stop paying and everyday living costs.
- Property tax rate
- Yearly property tax as a percent of the price. Because it's based on the price, it grows with the home you choose.
- PMI rate
- A yearly percent of the amount you borrow. If you enter it, it's included for the whole calculation.
- Housing cost limit (front-end ratio)
- The share of your monthly income before tax that can go to housing. Housing here means the loan payment (principal and interest), tax, insurance, HOA dues and PMI.
- Total debt limit (back-end ratio)
- The share of your monthly income before tax that can go to housing plus all your other debt payments.
Formula and method
monthly income M = income ÷ 12 front limit = M × front ratio; back limit = M × back ratio − debts H = the smaller of the two limits a = i ÷ (1 − (1 + i)^(−n)) + PMI ÷ 12; b = tax rate ÷ 12 H = a × (price − down) + b × price + insurance ÷ 12 + HOA price = (H − insurance ÷ 12 − HOA + a × down) ÷ (a + b)
In the formulas, M is your monthly income before tax and H is the most you can spend on housing each month. The letter a is how much each $1 you borrow adds to your monthly payment, including PMI. The letter b is how much each $1 of price adds in property tax each month. In the loan part of a, i is the monthly interest rate (the yearly rate ÷ 12) and n is the number of monthly payments.
Your housing payment rises in a straight line as the price goes up. Each dollar you borrow adds a, and each dollar of price adds b in tax. Because of that, the calculator can solve for the price directly, with no trial and error.
If your down payment is bigger than the price your budget could support with a loan, the result switches to a price with no loan at all. Then only tax, insurance and dues limit it.
Worked example
You earn $110,000 a year and pay $600 a month on other debts. You have $60,000 down and expect 6.5% over 30 years. Property tax is 1.1%, insurance is $1,800 a year, and there's no HOA or PMI. The limits are 28%/36%.
- Monthly income: $110,000 ÷ 12 = $9,166.67.
- Housing limit: 28% × $9,166.67 = $2,566.67. Total debt limit: 36% × $9,166.67 − $600 = $2,700.00. The housing limit is lower, so it applies.
- a = 0.00632068 per dollar borrowed; b = 1.1% ÷ 12 = 0.00091667 per dollar of price.
- Price = ($2,566.67 − $150.00 + 0.00632068 × $60,000) ÷ (0.00632068 + 0.00091667) ≈ $386,316.63.
Result: The highest price is about $386,316.63, with a loan of $326,316.63. The housing payment is $2,566.67: $2,062.54 principal and interest, $354.12 tax and $150.00 insurance. Total debt-to-income is about 34.5%. The $60,000 down payment is about 15.5% of the price, so a conventional lender would likely add PMI. With 25%/33% limits the price falls to about $348,319.28. With 31%/43% it rises to about $424,313.98.
Understanding the result
The result is the most you could spend under the limits you chose. It's a ceiling, not a target. Many households like to stay below it. That leaves room for savings, repairs and other goals these ratios don't count.
The 'limit that applies' result tells you which ratio is holding you back. If it's the total debt (back-end) ratio, paying down other debts will raise your price more than a higher housing limit would.
The comparison table gives you a quick range. The conservative row is a price that leaves breathing room in your budget. The stretch row is close to the most some loan programs allow, so it isn't a comfortable target.
Assumptions and limitations
- A fixed-rate loan, paid monthly at the end of each month, with interest charged at the yearly rate ÷ 12.
- The ratios use income before tax. The 28%/36% defaults are a common guideline, not a lender rule. The 25%/33% and 31%/43% rows in the table are example careful and stretch limits.
- Property tax goes up with the price. Insurance and HOA dues are fixed amounts.
- Closing costs and cash you keep in reserve aren't taken out of the down payment.
- Lenders also look at your credit history, savings in reserve, job and the rules of each loan program. They may allow higher ratios.
- Debt-to-income ratios don't include living costs, childcare or savings goals.
- Results are estimates for planning, not a pre-approval.
Frequently asked questions
What is the 28/36 rule?
It's a common guideline. Housing costs should be no more than 28% of your monthly income before tax. All your debt payments together, housing included, should be no more than 36%. Some loan programs allow higher ratios, and some people choose lower ones.
Why is my maximum lower than a lender's pre-approval?
Lenders may use higher ratios than the defaults here. They may also leave out tax and insurance estimates at the pre-approval stage. A lower, comfortable budget is often wiser than the most a lender will approve.
Does a bigger down payment raise the price I can afford?
Yes, by roughly the extra amount and a little more, because the same monthly payment now supports a higher price. Property tax on the higher price limits how far it goes.
How much house can I afford on a $100,000 salary?
Keep the other defaults on this page: $600 of monthly debts, $60,000 down, 6.5% for 30 years, 1.1% property tax and $1,800 of insurance. With 28%/36% limits, the highest price is about $354,076. Change the rate, down payment or debts and the answer moves a lot. That's why a single rule of thumb such as "three times your income" is only a rough start.
How do interest rates change what I can afford?
A higher rate raises the payment on every dollar you borrow, so the same budget supports a smaller loan. With the default inputs, moving the rate from 6.5% to 7.5% lowers the highest price from about $386,317 to about $358,612. Try the rates you're being quoted to see your own range.
Should I include my car payment?
Yes. Include any regular debt payment that will continue after you buy, at its required monthly minimum.
How this calculator is checked
Method: Debt-to-income limits converted to a housing budget, then solved for price using the standard level-payment factor plus tax, insurance, HOA and PMI. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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