  In one dimension very general results from conformal field theory and exact
calculations for certain quantum spin systems have established universal
scaling properties of the entanglement entropy between two parts of a critical
system. Using both analytical and numerical methods, we show that if particle
number or spin is conserved, fluctuations in a subsystem obey identical scaling
as a function of subsystem size, suggesting that fluctuations are a useful
quantity for determining the scaling of entanglement, especially in higher
dimensions. We investigate the effects of boundaries and subleading corrections
for critical spin and bosonic chains.
