You can put away up to the annual maximum amount as determined by the Internal Revenue Service. The maximum contribution amounts for 2023 are $3850 for self-only and $7750 for families.
The annual “catch-up” contribution amount for individuals age 55 or older is $1000. A catch-up contribution is a little “extra” that you can add to your HSA if you are 55 or older. Keep in mind that you can’t contribute to an HSA if you are on Medicare.