A CPM schedule is not a chart. It is the output of an arithmetic procedure you could run on the back of an envelope: two passes over a list of tasks and the links between them. The bars you end up looking at are just a drawing of the answer. I think most of the confusion around the term starts there — people are shown the picture and told it is the method.
So here is the method itself, worked end to end on a real plan: a 21-task house renovation, five trades, no invented numbers. Every figure below came out of the same file, and you can run it yourself in a minute.




