A week after principals were required to submit their budgets for next year, the city still doesn’t have an answer to the question of how many teachers are losing their positions because of budget cuts.

That question is essential for the counterintuitive reason that positions cut at schools actually don’t save the system any money. If a principal can’t pay for a teacher, the teacher goes into a pool of “excessed” teachers whose salaries are paid by the department. That pool already contains more than 1,700 people and has been criticized as a burden on the city’s budget. If the size of the pool swells because of the budget cuts, the department could end up shouldering thousands of teachers’ salaries — all while the teachers aren’t officially on a school’s staff.

Department of Education staff are still crunching the budget numbers, officials say. The department’s chief operating officer, Photeine Anagnastopoulos, told me on Tuesday that the excess situation was shaping up to be “not as bad” as she and others had anticipated, particularly considering that principals haven’t yet launched the bulk of their hiring for the fall.

But a source familiar with the budget process says the numbers have been delayed because the department is “scrambling” to check principals’ math about whether they need to cut positions. Staff at the department’s service centers are “going over budgets in high-excess schools trying to negotiate fewer excesses,” the source said.

An added complication, the source said, is that a reorganization within the department means that the service centers are short-staffed right now.

The teachers union is also reviewing cuts that union representatives at each school flag as being unnecessary, vice president Michael Mulgrew told me. “They’re reviewing every school and we’ve been investigating and will continue to monitor very closely,” he said.

Whatever number of excessed teachers is announced in the coming days, it is certain to decrease over the summer, Anagnastopoulos said. “The hiring hasn’t started yet, only the excessing,” she said. Hiring restrictions currently in place mean that principals will have to turn to the pool of excessed teachers first when filling most open positions.

“Right now I’m pretty confident that we’ll be able to manage it,” she said. 

Principals are reporting having to excess large numbers of teachers because of the budget cuts, according to GothamSchools’ interactive budget map and other sources. In addition to the teachers whose jobs are budget cut casualties, some teachers are winding up in the pool because the department is closing or phasing out their schools. At PS 27 in Brooklyn, which is shedding 10 grades, 72 teachers are slated to join the excess pool, for example.