As a general statement spackle will not fill holes that are larger than 1.5 inches.  The reason being that the spackle cannot support itself.

There are hole patch kits available, however these are usually a self adhesive mesh that sits above the surface of the drywall and hence after adding either joint compound or spackle it is necessary to feather the seam out for at least 12 inches or it will be very noticeable.  It takes a lot of practice to feather out drywall compound so that you cannot see the repair.

The better way of repairing a large hole is to place a piece of drywall in the hole and use joint compound to fill the gap.  Although this may sound obvious the problem is how to support the piece of drywall in the hole.  The most convenient method is to mount the piece of drywall to a wood support.

The following pictures and text outline the method for repairing a large hole in drywall.  This method can be used on walls as well as ceilings.  The repair will stay in place indefinitely and if some patience is taken when sanding the joint compound or spackle between the drywall pieces will be unnoticeable.

Before inserting the piece of wood, make sure that all loose pieces of drywall and any loose pieces of paper have been removed from the hole.

If you have a problem cutting a piece of drywall to fit, there are 2 methods that you can use.

1. The first method is to make the hole square by using a drywall saw.

2. The second method is to place chalk on the edge of the hole and push a piece of drywall against the hole.  The chalk will leave a layout mark of the cut to be made.

Use joint compound to cover the screw heads and sand.