How Much House Can I Afford? The Actual Math
The exact debt-to-income math lenders use to determine how much house you can afford, with a full worked example.
"How much house can I afford" isn't one formula — it's two debt-to-income checks run at the same time, and whichever one is stricter sets your actual limit.
Step 1: Two DTI caps, checked separately
- Front-end DTI: housing payment ÷ gross monthly income, conventionally capped around 28%.
- Back-end DTI: (housing payment + all other debts) ÷ gross monthly income, conventionally capped around 36%.
Step 2: Find the max allowed housing payment
Multiply gross monthly income by each cap to get two candidate housing-payment limits, then subtract existing monthly debts from the back-end one (debts don't affect the front-end number). The smaller of the two candidates is your real limit.
Step 3: Convert the payment limit into a home price
The max housing payment has to cover principal, interest, property tax, insurance, and HOA — and since property tax is usually a percentage of the home price itself, solving for the actual home price takes a bit of algebra, not just plugging numbers into a mortgage formula.
Worked example: $90,000 income, $400 monthly debts, $60,000 down, 6.5% rate, 30-year term. Back-end allows a $2,300 payment; front-end allows only $2,100 — front-end wins, landing on a $328,745 max home price.
The House Affordability Calculator runs this full calculation instantly, including the property tax algebra.