For which infinite cardinals κ is there a partition of the real line R into precisely κ Borel sets? Work of Lusin, Souslin, and Hausdorff shows that R can be partitioned into ℵ1 Borel sets. But other than this, we show that the spectrum of possible sizes of partitions of R into Borel sets can be fairly arbitrary. For example, given any A⊆ω with 0,1∈A , there is a forcing extension in which A={n:there is a partition of R into ℵn Borel sets} . We also look at the corresponding question for partitions of R into closed sets. We show that, like with partitions into Borel sets, the set of all uncountable κ such that there is a partition of R into precisely κ closed sets can be fairly arbitrary.