This study evaluates the second-quadrant demagnetization curve which is essential for predicting the performance of Nd-Fe-B permanent magnets. It analyses the two-line geometric intersection method that reconstructs the main features of the demagnetization curve from only four points of the measured intrinsic curve (J-H). A reversible line, anchored at 0.2Hk and 0.7Hk, approximates the recoil-dominated region, while an irreversible line, anchored at 0.1Br and 0.5Br, captures the nucleation-dominated region; their intersection (Hψ, Jψ) and opening angle α define a compact set of descriptors, including a dimensionless form factor FF = 90°/α. The method was applied to four sintered Nd-Fe-B-based magnets spanning a squareness factor from 0.27 to 0.94 and a nearly fourfold range of intrinsic coercivity. The reconstructed remanence and intrinsic coercivity agree with experiment within 0.7% and 0.9%, respectively, and the enclosed curve area within 2.2%. The form factor correlates linearly with the experimental squareness factor (R2 = 0.99), offering a computationally inexpensive geometric proxy for the switching-field distribution that governs loop squareness, and the recoil permeability obtained from the reversible-line slope agrees with an independent estimate derived from Br and (BH)max within 1–7%. An efficiency metric ηmod = 1/μr, rising from 53.5% to 95.6% with squareness, links the reversible response directly to energy-product utilization. The knee field itself is not determined independently of prior experimental values. Keywords Magnetic propertiesKnee fieldMagnetsPowder metallurgyRare earthGeometric intersection
