The Department of Finance is being forced back to the drawing board after the city’s Law Department ordered the agency to recalculate the math it used in determining the value of rental apartments, co-ops and condos.

As a result of the order, the assessment notices sent out last month to residential owners are moot, and hundreds of thousands of “changes by notice” are expected to be mailed over the next few days.

It is expected that rental apartment assessments will go up, while co-ops and condos will get a break.

Sources tell The Post the snafu is the result of Finance Commissioner Martha Stark using two different calculations – called “gross rent multipliers” – to come up with January’s tentative assessments for all apartments.

Long-established state law required that co-ops and condominiums be valued as if they were rental buildings.

However, this time around the Finance Dept. used one methodology to calculate the assessments of rental apartments and another to tabulate the value of condos and co-ops.

“We were using two and are now using one,” Finance spokesman Owen Stone confirmed.

Industry groups protested the use of the GRM, which is a number multiplied by the total rent roll to come up with a “down and dirty” valuation figure.

Jack Freund from the Rent Stabilization Association said using the new calculation hurts low-income buildings with high operating expenses and low margins because the expenses don’t get factored into the final number.

“They will get socked with a value that is higher than the income capitalization approach, and it is destructive of the city’s affordable housing stock,” Freund said.

As a result of the change, condo owners and residential multi-family property owners will be mailed a new assessment notice that will affect the taxes the owner pays. July 1 is the deadline for paying property taxes.