The formula
How to calculate payment to price
The usual mortgage calculator runs forward — loan amount in, monthly payment out. This runs the same formula backward: start from a monthly payment you know you can comfortably afford, and see the loan amount and purchase price that payment actually supports at a given rate and term.
This is the standard amortization formula rearranged to solve for the loan amount rather than the payment. At the defaults — an $1,800 payment, 6.5% over 30 years — it supports a loan of roughly $284,000, which becomes a maximum purchase price of about $324,000 once the $40,000 down payment is added back on top.
The calculator asks for:
- Desired monthly payment — principal and interest only — see the note below on taxes, insurance and country-specific costs
- Interest rate (%)
- Loan term (years)
- Down payment / deposit
Everything recalculates as you type, and the numbers in the address bar update with it, so a link to this page carries your figures with it.
Where a figure is not immediately to hand — a precise interest rate, an exact balance — a reasonable estimate is a perfectly good starting point. Because every result updates instantly, refining a rough guess into the real figure once you have it takes a moment, and nothing about the calculation depends on getting it exactly right on the first attempt.
Why payment to price matters
The formula behind payment to price is standard and has not changed in decades; what changes is the situation it gets applied to. Two households can run the identical calculation and land on very different conclusions once their own numbers — income, rate, term, balance — are dropped in, which is why a generic textbook example is less useful than a calculator you can adjust to match your own circumstances.
Beyond a one-off check, the same calculation is worth revisiting whenever the underlying numbers change — a new interest rate, a change in income, a different term. Because the figures live in the page's own web address, coming back to update just one field and compare the new result against the old one takes seconds rather than starting again from a blank page.
It is also worth being clear about what a single figure like this can and cannot settle on its own. It answers the specific question the formula was built to answer, and nothing more — a favourable payment to price result does not automatically mean a decision is a good one overall, since plenty of other factors that a formula cannot capture, from personal circumstances to how comfortable a commitment feels, usually matter just as much as the arithmetic. Use the number as one solid input among several rather than the whole of the decision.
In practice, most people arrive at a page like this one having already tried a version of the calculation by hand or in a spreadsheet, and use the calculator here to confirm it rather than replace it. That is a reasonable way to use it — the two should agree to the last decimal place if the same inputs and the same formula are used, and if they do not, the formula shown above is the one to check your own working against first.
Worked example
Take the figures the calculator starts with:
- Desired monthly payment: 1,800
- Interest rate: 6.5 %
- Loan term: 30 years
- Down payment / deposit: 40,000
That gives:
- Loan amount this payment supports: 284,779.48
- Maximum purchase price: 324,779.48
These figures are only the calculator's own starting values, included so the working is visible rather than hidden inside the tool above. Replace them with your own numbers and the same arithmetic applies — nothing about the method changes, only the inputs feeding it.
Reading the result
The figure this calculator returns is principal and interest only — the same limitation as the forward mortgage-payment calculator. Property tax, buildings insurance, and (below a 20% down payment in the US) mortgage insurance all sit on top of this and reduce how much loan the same total housing budget actually supports.
Where this goes wrong. Treating this as a country-neutral figure. What gets added on top of principal and interest — and how big it is — varies a lot by country: US buyers see property tax and, often, mortgage insurance escrowed into the payment; UK buyers face Stamp Duty Land Tax as an upfront cost (not part of the monthly payment) and lenders apply their own affordability stress tests on top of the raw payment-to-loan maths here; Belgian buyers face registration duties (droits d'enregistrement / registratierechten) of several percent of the price, again upfront rather than monthly, plus notary fees. This calculator gives the loan-to-payment arithmetic only — check the taxes and costs that apply in your own country before treating the price figure as a real budget.
A useful check on any unfamiliar result is to compare it against a rough mental estimate first — round the inputs to convenient numbers and see whether the calculator's answer lands in roughly the same territory. A wildly different figure usually means one of the fields was entered in the wrong unit, most often a percentage typed as a whole number where a decimal was expected, or the reverse.
Because the down payment is added back on top of the loan amount this calculator solves for — the loan only needs to cover the part of the price not already covered by the deposit.
No. Those are one-off costs paid on top of the purchase price, not part of the recurring monthly payment this calculator solves from, and they vary too much by country and region to build into a single formula. Budget for them separately.
It returns loan amount this payment supports. With 1,800 desired monthly payment, 6.5 % interest rate and 30 years loan term, that comes to 284,779.48. Change any field and the figure moves with it.
Whenever one of the underlying figures changes — a new interest rate, a different balance, an updated term — since the result only reflects what is currently in the fields. There is no need to keep a separate record of past results; the web address for a filled-in version already carries the figures used to produce it.
Not unless a tax rate or a fee is explicitly one of the inputs above. Where it is not, the figure shown is a gross calculation, and any tax due depends on your personal circumstances and current tax rules, which are worth checking separately.
The arithmetic itself is exact — the calculator applies the formula shown above precisely, with no rounding until the final figure is displayed. The uncertainty, where it exists, is entirely in the inputs: an estimated rate or an approximate balance carries that same approximation through to the result.