How can I write the formula for calcium nitride?

The correct answer is #Ca_3N_2#.

Let us see how we got the answer; Look at the electronic arrangement of Ca and N atom.

Ca ( Z= 20) has 20 electrons with following electronic configuration. 1#s^2#2#s^2#2#p^6#3#s^2#3#p^6#4#s^2#.

It loses two electron in its 4s subshell to achieve stability and forms ion #Ca^(2+)#.

#Ca^(2+)# = 1#s^2#2#s^2#2#p^6#3#s^2#3#p^6#

N ( Z=7) on the other hand has seven electrons and wants to gain three electrons to achieve stable noble gas configuration.Nitrogen atom on gaining three electrons forms negative nitride ion, #N^(3-)# ion.

N ( Z=7) = 1#s^2#2#s^2#2#p^3#

#N^-3# = 1#s^2#2#s^2#2#p^6#

Two Nitrogen atoms gains three electrons each ( total of six) from three Ca atoms, each Ca atom loses two electrons (total of six) to two Nitrogen atom , in this process each Ca atom becomes #Ca^(2+)# ion and nitrogen atom after gaining three electrons becomes #N^(3-)# ion.

so in all we have three #Ca^(2+)# ions and two nitride #N^(3-)# ions.
so the formula becomes #Ca_3N_2#.