House rent allowance is only partly tax-free, and the exempt part depends on your basic salary, your rent and your city. Pick your basic to see the exemption across a range of rents.
The exemption is the least of three figures: HRA received, rent minus 10% of basic, and 50% of basic in a metro (40% elsewhere). Because two of the three scale with basic, your basic salary is the biggest lever on how much HRA stays tax-free. These pages fix the basic and vary the rent so you can find your case quickly.
Remember that HRA exemption applies only under the old tax regime and only if you actually pay rent. For an exact figure, open the HRA calculator.
A quick rule of thumb: your exemption is nil until rent crosses 10% of basic, then rises with rent up to a ceiling of 50% of basic in the metros of Delhi, Mumbai, Kolkata and Chennai, or 40% of basic everywhere else. Because both the ceiling and the 10% deduction move with basic salary, a higher basic gives more room to shelter rent, which is one reason employees negotiate the basic component and not just the headline CTC. The pages here fix the basic and vary the rent so you can see exactly where your own case lands. Keep in mind that only the four cities of Delhi, Mumbai, Kolkata and Chennai count as metros for the 50% rule; every other city, including Bengaluru, Hyderabad and Pune, uses the 40% figure, which quietly lowers the exemption for the same rent and basic.