Planar zeros are a peculiar feature of certain scattering amplitudes with one or more gauge bosons radiated, consisting in the vanishing of the amplitude for configurations where all momenta lie on a single plane. In this talk I shall study these planar zeros in the context of the five-point scattering amplitude for gauge bosons, gravitons, and scalars. For gauge theories, planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. The coefficients of the curve depend on the values of the independent color structures. In the case of gravity, we find that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. This fact can be explained using the BCJ double-copy structure of gravity amplitudes.