Maps of semi-major axis evolution timescale for different planetary masses and semi-major axis for a 1 M_⊙ star (top) and for a 0.1 M_⊙ star (bottom), assuming a low-viscosity disc (α = 10⁻⁴) with gas surface density and aspect ratio profiles described in Eqs. (1) and (2), assuming s = 0.5 (f = 0) in the inner disc and s = 1 (f = 0.25) in the outer disc. The transition was set at r_trans = 0.3 au for M_★ = 0.1 M_⊙, and at r_trans = 2 au for M_★ = 1 M_⊙. We assumed r₀ = r_tran, and characterised both the inner and outer disc by Σ₀ = 4 × 10⁻⁴ M_⊙/au² and h₀ = 0.03, simulating the conditions of a disc at 1–2 Myr with a high gas disc mass ~10% M_★. Limits for inward and outward migration are overplotted (dashed grey lines). Right: timescales calculated applying only the fitting function from K18 (see Eq. (5)). Left: timescales calculated combining the fitting function from K18 for K < 10⁴ and q < 0.002, and the fitting functions propose in this work (see Eq. (6)), for 0.002 < q < 0.02 and K < 2 × 10⁷, relating the surface density Σ(r) to Σ₀ = 10⁻⁵ M_★/r² (dotted grey line).