Adding/Combining Cylinder Powers

Hello Everyone,

I was trying to build an excel spreadsheet to do vertex, wrap, & panto tilt compensation and I've gotten through calculating vertex, and the new sphere powers using Darryl's formula on pdf pg.74 of Intro to Ophthalmic Optics , but his formula only gives the induced cylinder power and not the "new" cylinder power that must be ordered.

So the next thing I need to do is take the induced cylinder & axis(180 for panto & 90 for wrap) and add it to the patients cylinder and axis. I'm struggling to find the formula on how to do this.

Example: Patients Cyl is -0.50 @135 and the induced cyl from panto tilt is -0.50 @ 180Any help would be appreciated.