We use high-resolution N-body simulations to study the equilibrium den
sity profiles of dark matter halos in hierarchically clustering univer
ses. We find that all such profiles have the same shape, independent o
f the halo mass, the initial density fluctuation spectrum, and the val
ues of the cosmological parameters. Spherically averaged equilibrium p
rofiles are well fitted over two decades in radius by a simple formula
originally proposed to describe the structure of galaxy clusters in a
cold dark matter universe. In any particular cosmology, the two scale
parameters of the fit, the halo mass and its characteristic density,
are strongly correlated. Low-mass halos are significantly denser than
more massive systems, a correlation that reflects the higher collapse
redshift of small halos. The characteristic density of an equilibrium
halo is proportional to the density of the universe at the time it was
assembled. A suitable definition of this assembly time allows the sam
e proportionality constant to be used for all the cosmologies that we
have tested. We compare our results with previous work on halo density
profiles and show that there is good agreement. We also provide a ste
p-by-step analytic procedure, based on the Press-Schechter formalism,
that allows accurate equilibrium profiles to be calculated as a functi
on of mass in any hierarchical model.