Rent vs. buy is mostly a timeline question.
Buying can build equity, but ownership also introduces transaction costs and recurring expenses. The break-even point is the time when the modeled economic cost of buying catches up with or beats the modeled cost of renting.
Buying has entry and exit costs
Closing costs at purchase and selling costs later can make short ownership periods expensive even when the monthly mortgage payment looks competitive with rent.
Equity matters
Mortgage principal repayment and home-price changes affect the owner's ending equity. That is different from simply adding up monthly payments.
Ownership costs matter too
Property taxes, insurance, maintenance, HOA dues, mortgage insurance, and financing costs can materially change the result.
Rent changes over time
A meaningful comparison should also make an explicit assumption about future rent rather than holding one side of the decision static.
There is no universal number of years.
The break-even horizon changes with the purchase price, mortgage rate, rent, closing costs, appreciation, maintenance, selling costs, and how long you expect to stay.
That is why a calculator is more useful than a rule such as “buy if you will stay five years.” A five-year result in one market can look very different from another.