The structural, magnetic, and electronic properties of NdFe_0.5Mn_0.5O₃ have been studied in a comprehensive manner using various experimental and theoretical methods. Mn/Fe sublattice of the compound orders into a G-type antiferromagnetic phase close to 250 K where the magnetic structure belongs to Γ₁ irreducible representation (G_y) unlike Γ₄ (G_x) representation observed in most of the orthoferrites and orthochromites. The magnetic structure undergoes a complete spin reorientation transition with temperature between 75 and 25 K where the magnetic structure exists as a sum of two irreducible representations (Γ₁ + Γ₂). At 1.5 K, the antiferromagnetic structure belongs entirely to Γ₂ representation (G_z) with a small ferromagnetic component (F_x) due to Nd. The unusual spin reorientation and correlation between magnetic ground state and electronic structure have been investigated using phenomenological theory and first-principles calculations within GGA+U and GGA+U+SO formalisms.