We know of an ancient radiation
That haunts dismembered constellations
A faintly glimmering radio station

Cake, Frank Sinatra

This page has a calculator useful for answering those questions that come up when you're in talks or writing telescope proposals, like How many kpc correspond to 1 arcminute at redshift 3?, How bright is an L* galaxy at redshift 1.5? or What is the lookback time to redshift 2?.

For a nice introduction to calculating useful cosmological quantities see Hogg (1999). The default parameters below are taken from the WMAP7 results (ADS). A flat cosmology is assumed.

w H0 km/s/Mpc zmin zmax
Ωm ΩΛ= , Ωk = 0

Comoving distance to zmin = Mpc
Comoving distance to zmax = Mpc

Distance (Mpc) per arcmin Hubble parameter (km/s/Mpc)
z z
Elapsed time since the emission of a
photon with redshift z (Gyr)
Rest-frame apparent b magnitude
of a Mb = -21 galaxy
z z

Mb = -21 roughly corresponds to the L* value of the Schechter luminosity function fitted at z = 0–1 by Faber et al. (2007).

Take a look at some other popular cosmology calculators.