base cabinet against vertically sloping wall

Probably be easier to chop the wall out

you could could scribe the back of the cabinets, much of a muchness really

 

It depends on your worktop and whether you are having an upstanding or are tiling.
If your worktop is tight for overhang you will have to bring it away from the wall at the back - not a problem if you're using an upstand as that will give you 20mm or so to play with. If you're tiling though......
Edit:. The above assumes you don't scribe or chop out. I would scribe.

 

Get two offcuts of 18mm board.

Plumb and level the cabinet with one 18mm offcut between the top of the cabinet and the wall.

Then run the other offcut down the wall with a pencil lead hard up against it.

Cut down the line and screw the cabinet to the wall.

The back line will follow the wall and the front edge will be plumb.

15mm off should affect any undermounted appliances

 

No, the opposite, depending on the shape of the wall the worktop goes against you should have a decent overhang.

 

This may help. https://www.google.com/url?sa=t&sou...FjAUegQIARAB&usg=AOvVaw0kIkZMvoHS3cLxMhhUt-4T
The method GB has suggested is just like having the compasses set to 18mm (and much easier) but hopefully explains it for you.

 

No the very top of the cabinet should be the original width.

 

Have you checked for level and plumb? If the front edge is leaning forward that will cause it to be out.

 

The joys of kitchen fitting. On paper dead easy, in reality the walls are never straight square or plumb and the trick is to work out where to hide the discrepancies so it all works. The trick is to lose the errors so no-one notices. As others have said, you need the top/front edge to be level, straight and the correct distance off the wall for the worktop depth - get this by trimming or setting off the backs to fit.

Rather than use a spirit level, go and get a little laser level https://www.screwfix.com/p/stanley-cubix-self-levelling-laser-level/256fg.

Now you can accurately set out all the levels and verticals and see what they look like before you start fitting.

When fitting cabinets, set a little block on each corner with a datum line on it (or use 4 lego bricks) - you can now set your laser and adjust the cabinet legs so the top of the cabinet is perfectly flat and level in all planes.

Cabinets will twist if you tighten them up to a twisted wall!

 

I had the reverse problem on a recent kitchen - I couldn't get one of the doors to close no matter how much I adjusted everything even trying with twisting the cabinet out of square against the uneven wall.
In desperation I decided to swap the hinges which is when I found one of the clear rubber button door buffers had become detached from its backing and hidden inside the hinge. A mixture of 'phew' and 'Grrrrr' in equal measure!

 

The method i use every monday morning is as follows:

Build the cabs, then from about 2 inches below the top of the cabs using a jigsaw, cut the gable end about 30mm all the way down to the bottom of the cabs within the service void (forget this if it's an Ikea kitchen )
Start with a corner cab first, position and completely level it. Then check with a straight edge and a 1m cab shelf from the corner cab along both walls if the walls are actually at 90 degrees to each other (they very rarely are). Place and level all the other base cabs and screw them together. Using a long straight edge (a length of plinth) bridge any appliances to the next base cab and continue. Once done, fix all the base cabs to the walls.

If the walls have loads of bows in them, this will show itself when using the plinth as a long straight edge. As long as any gaps at the back of the worktop can be hidden by upstand or tiles, you are good to go.