The scale factor R at time t for the size of the universe Eric Weisstein's World of Astronomy is related to the scale factor at time by
where a is called the expansion parameter. Then the speed of expansion is
Rearranging gives
which is just the Hubble law with Hubble constant.
The ratio is related to the redshift z by th equation.
Deceleration Parameter, Expansion of the Universe, Expansion Rate, Hubble Constant, Hubble Law, Luminosity Distance, Redshift