I remember one of Akin's Laws of Spacecraft Design being something like: take your original estimates, multiply the time by π and shift the decimal on cost one place to the right.
What happens is that the difference between the estimate that management will psychologically accept to begin the project (and then commit to due to sunk cost fallacy) and the actual schedule is about a factor of 3.
There's a paper that gives an exact number: 1.7x. This is the average time it goes over estimates, for code and writing tasks. The other numbers seem better, but you should not go below 1.7.
If I had a bad case of managers, I would probably multiply by four.