A formula in a protected sheet doesn't work for unauthorized people

Hi experts,

We have a google sheet with formulas in some column. The formulas are important to the whole functioning of the sheet. So in order to protect those columns from unauthorized changes we protected them.

Those columns calculate stuff based on input from other columns. Now when users input stuff into those stuff, the protected columns with the formula doesn't get executed for those people. Only for people who have edit permissions.


How can we solve this?
The formulas in the protected colums should work for unauthorized people. But the protection should prevent people at the same time for changing the formulas in those protected columns.