The active phase of the catalyst is a component of a heterogeneous catalyst that is directly involved in the catalytic reaction. For example, the catalyst platinum will be the active phase when hydrogenated. Carrier, promoter, activator - the rest.
The calculation can be found in the links
Article Evidence for the Active Phase of Heterogeneous Catalysts thr...
Article Evidence for the Active Phase of Heterogeneous Catalysts thr...
If you are using supported metal catalyst, you can calculate the dispersion of active centers (metal nanoparticles) using CO or H2 pulse chemisorption experiment.
Metal dispersion = ((Vadsorbate * SF * MW)/(W*22414)) *100
where, Vadsorbate is volume of CO or H2 adsorbed on surface of your material, SF is stoichiometric factor, MW is atomic weight of your active phase in g/mol and W is weight of your catalyst in g.
Heterogeneous catalyst is composed of an active phase dispersed onto support. By the nature active centers can be classified as metallic, acidic, and basic can be characterized by temperature-programed desorption or adsorption (TPD, TPA) or pulse chemisorption.