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Torque as a tightening method is a simple technique that can be used to tighten a bolt to a given pre-load. Therefore, it is important to theoretically derive an accurate torque vs tension relationship for threaded fasteners as this would enable the industry to achieve a reliable pre-load. Various attempts were made to develop a complete theoretical relationship between torque and tension. Due to the thread angle there exists a nut dilation force causing the nut to expand radially out wards. This effect is more prominent in nuts with smaller height (Style 0 hex nut, refer ISO 4035 1 ). This nut dilation force creates a combined frictional effect with the drive torque thus affecting the torque tension relationship. This paper proposes a novel 3D formulation for torque tension relationship taking into consideration the nut dilation effect. This paper further develops new formulae for tightening and loosening torque, retaining torque, tension vs nut rotational angle relationship as well as formula for nut dilation force for both tightening and loosening.