We report a comprehensive experimental investigation of the magnetic structure of the cycloidal phase in Ca3Ru2O7, which mediates the spin reorientation transition, and establishes its magnetic phase diagram. In zero applied field, single-crystal neutron diffraction data confirms the scenario deduced from an earlier resonant x-ray scattering study: between 46.7~K <T<49.0~K the magnetic moments form a cycloid in the a−b plane with a propagation wavevector of (δ,0,1) with δ≃0.025 and an ordered moment of about 1 μB, with the eccentricity of the cycloid evolving with temperature. In an applied magnetic field applied parallel to the b-axis, the intensity of the (δ,0,1) satellite peaks decreases continuously up to about μ0H≃5 T, above which field the system becomes field polarised. Both the eccentricity of the cycloid and the wavevector increase with field, the latter suggesting an enhancement of the anti−symmetric Dzyaloshinskii−Moriya interaction via magnetostriction effects. Transitions between the various low-temperature magnetic phases have been carefully mapped out using magnetometry and resistivity. The resulting phase diagram reveals that the cycloid phase exists in a temperature window that expands rapidly with increasing field, before transitioning to a polarised paramagnetic state at 5 T. High-field magnetoresistance measurements show that below T≃70 K the resistivity increases continuously with decreasing temperature, indicating the inherent insulating nature at low temperatures of our high-quality, untwinned, single-crystals. We discuss our results with reference to previous reports of the magnetic phase diagram of Ca3Ru2O7 that utilised samples which were more metallic and/or poly-domain
