Electromagnetic core–mantle coupling is one candidate for explaining length of day (LOD) variations on decadal time scales. This coupling has traditionally been calculated from models of core surface flow U → , but core flow inversions are not unique. Unfortunately, the main torque contribution depends on the toroidal part ∇× r → Φ of the vector field ( U → B r ), which is left undetermined by the radial induction equation that links core flows to magnetic field data under the frozen-flux hypothesis. ( B r is the radial magnetic field at the core surface.) We have developed a new method that bypasses flow inversions. Using the vector field ( U → B r ) directly, we estimate its toroidal part by imposing that ( U → B r ) vanishes where B r=0. The calculation of the electromagnetic torque is also hindered by the uncertainty in the conductivity structure of the lower mantle. However, we conclude that the conductivity of the lower mantle has to be much larger than current estimates derived from diamond anvil cell experiments to make the electromagnetic torque significant. The region beneath Africa and the mid-Atlantic (where there is the most significant ( B r=0) curve apart from the magnetic equator) is particularly important. Here, the field Φ is relatively well constrained, and this is the single region that contributes most to the torque. Following Holme [Holme, R., 1998a. Electromagnetic core–mantle coupling 1: explaining decadal changes in the length of day. Geophys. J. Int. (132) 167–180.], we show nevertheless that small changes to Φ suffice to recover the torque Γ LOD required to explain LOD variations provided that the lower mantle conductivity is high enough. We find a value similar to Holme [Holme, R., 1998b. Electromagnetic core–mantle coupling 2: probing deep mantle conductance. In: Gunis, M., Wysession, M.E., Knittel, E., Buffett, B.A. (Eds.), The Core–Mantle Boundary Region. AGU, pp. 139–151.] for the minimum conductance (10 8 S). However, we were not able to simultaneously recover Γ LOD and constrain U → to be tangentially geostrophic.