We study the spin Hall (SH) effect for the Dirac electrons in terms of the spin and magnetic moment accumulation coefficients −Γ[00]gs(m)zxy. We take short-range nonmagnetic impurities into account within the self-consistent T -matrix approximation. Similarly to the universal scaling for the anomalous Hall (AH) effect, we find three distinct regimes by changing the electric conductivity σ[yy]; the superclean regime with −Γ[00]gs(m)zxy ∝ σ[yy] owing to the skew scattering, moderately dirty regime with almost constant −Γ[00]gs(m)zxy, and dirty regime with a new scaling relation −Γ[00]gs(m)zxy ∝ (σ[yy])[0.6] whose exponent differs from that of the AH conductivity. Our results construct a unified theory of the SH effect without any ambiguity of spin current.