The effective thermal conductivity of snow, k_eff, is a crucial climatic and environmental variable. Here, we test the intuition that k_eff is linked to microstructural and mechanical properties by attempting to relate k_eff to density ρ_snow, and to shear strength σ measured with a handheld shear vane. We performed 106 combined measurements of k_eff, ρ_snow and σ in the Alps, Svalbard, Arctic Alaska, and near the North Pole, covering essentially all snow types. We find a good correlation between k_eff and ρ_snow which is not significantly different from that of Sturm et al. (1997). The correlation between k_eff and a combination of σ and ρ_snow is stronger than with density alone. We propose an equation linking k_eff, (W m^-1 K^-1) ρ_snow (kg m^-3) and σ (Pa): k_eff = 7.114 10^-5 ρ_snow σ^0.333 + 2.367 10^-2. This equation places constraints on the calculation of k_eff, ρ_snow and σ in avalanche warning models where σ is a key variable. For our samples, we calculate σ from measured values of k_eff and ρ_snow using our equation and compare the value to that predicted by the French MEPRA avalanche warning model, which uses density and grain type as input data. MEPRA and the prediction of σ based on k_eff and ρ_snow agree within 8%. MEPRA agrees with observations within 11%. Calculating σ from density only yields values 55% lower than measured, showing the interest of using additional data to predict σ.