A modified expression of Byram's convective number is proposed to account for the effect of slope in wildland fires. Instead of decomposing the forces of wind and buoyancy, as is done for fire propagating over flat terrain, both forces are projected in directions parallel and perpendicular to the ground. For steep slopes, this correction results in a convective number that is significantly different from the formulation proposed by Nelson Jr (Int J Wildland Fire 24:1001-1007, 2015. 10.1071/ WF14155). A database consisting of 11 experimental fires carried out in shrublands was used to support the use of the new convective number formula. In addition, 14 numerical simulations were carried out to better highlight the action of induced wind on wildfires behaviour.