The kinematic time and maximum spreading time for the impact of nanodroplets of different types of fluids on solid surfaces with different wettability are investigated. It shows that the capillary regime still exits for the nanodroplet impact, even if viscous dissipation increases significantly when the droplet size reduces to the nanoscale. By taking into account the influence of liquid types and surface wettability, we first obtain scaling laws of the maximum spreading time for the capillary and viscous regimes. We further propose a universal scaling law by interpolating the scaling laws in the two asymptotic regimes. The universal scaling law is in excellent agreement with molecular dynamics simulations for various liquids and surface wettability.