RpnCalc is the best RPN calculator on the App Store.

It has an interface that users of the HP calculator line will be completely at home with, including these features:

Scientific mode
Basic (large key) mode
20 Memories
Key click (haptic feedback)
Continouous memory
16-level stack (configurable)
Front four stack elements displayed

RpnCalc has a sixteen-level stack to hold more data. The front four elements on the stack are visible at all times, making it much easier to keep track of where you are in your calculations.

“Calculator tape” records your calculations and can be shared via email, bluetooth, etc.

See http://www.efalk.org/RpnCalc/ for manual

Oh, and here’s the privacy policy: RpnCalc never collects any private data of any sort. It never connects to the internet. It doesn’t even run ads.