The Hubble constant has been added in addition to the three fundamental constants (speed of light, gravitational constant and Planck constant) used by Max Planck, for derivation of the Planck mass by dimensional analysis. As a result, a general solution is found for the mass dimension expression m = γ p m 0, where m 0 ≡ m p is the Planck mass, γ =
1.23×10−61 is a small dimensionless quantity and p is an arbitrary parameter in the interval [-1, 1]. The Planck mass m p = 2.17×10 -8 kg, mass of the Hubble sphere M H ~ 10 53 kg, minimum quantum of mass/energy m G = 2.68×10-69 kg,Weinberg mass m W = 1.08×10 -28 kg, mass of hypothetical quantum gravity atom M G = 3.8×10 12 kg, Eddington mass limit of stars M E = 6.6×10 32 kg and some more masses potentially important for the physics and astrophysics represent particular solutions for values of p, expressed as fractions with small numerators and nominators.