An assembly, intercalated between a torque tool and a fastening element, for measuring torques and angular displacements of fasteners comprising, in combination: - a socket subassembly having an unitary elongated body, including at one extremity a first engaging cavity, at an opposite extremity, a second engaging cavity; and incorporating an externally open, annular channel provided between said extremities of said socket subassembly; - a strain transducer subassembly, for measuring torsional strains on said socket subassembly, mounted in said externally open, annular channel; - a circular cover attached to said socket subassembly for enclosing said externally open, annular channel; and - an electronic subassembly for converting said torsional strains on said socket subassembly to standard torque values and for determining tightening angular displacements; said electronic subassembly being interconnected to said strain transducer subassembly and mounted on said circular cover to face said strain transducer subassembly; said socket subassembly including said first engaging cavity, shaped to conform to and engage with said torque tool exit shaft, usually of square drive type; said second engaging cavity being shaped to conform to and engage with said fastening element, of a specific size; said externally open, annular channel being provided with a circular bottom surface for mounting said strain transducer subassembly; said strain transducer subassembly comprises four strain gages, equally spaced from each other on said circular bottom surface, intended for measuring torsional strains; each of said four strain gages being of the 45 degree dual grid shear pattern and being made of constantan comprising a pair of parallel, juxtaposed strain elements, so arranged that a convergence line of said parallel, juxtaposed strain elements is parallel to the longitudinal axis of symmetry of said socket subassembly, for measuring torsional strains, only; said strain transducer subassembly being wired in a Wheatstone bridge to produce analog voltage signals, proportional to only torsional strains in said socket assembly, and therefrom in said fastening element; said circular cover subassembly comprising a first and second semicircular segments (305, 310); said first semi-circular segment incorporating an axial protrusion and diametrically opposed threaded openings; said second semi-circular segment incorporates a pair of fastening openings, corresponding to said diametrically opposed threaded openings; said diametrically opposed threaded openings and said pair of fastening openings being used for attachment of said first and second semi-circular segments (305, 310) by fasteners; said electronic subassembly comprising a processing unit, a user interface unit and a power supply unit; said processing unit including a microcontroller for digital and analog signal processing, mounted on said first semi-circular segment and connected to said strain transducer subassembly for converting the torsional strain into standard engineering units of torque, for measuring angular displacement by means of a sensor for providing date/time function to time stamp tightening cycles and measured parameters, and for parameter and configuration memory storage; said user interface unit including a display, mounted on said first semi-circular segment and interconnected to said microcontroller, for showing the selected imposed parameters, and for showing the running and final measured parameters; a connection port, mounted to said first semi-circular segment and interconnected to said processing unit for communication to an external device or for the purpose of controlling said torque tool shut-off at the imposed parameter; a keypad, interconnected to said processing unit for selecting the desired parameter for verification, or for selecting the parameter at which to signal said torque tool's own controller to shut- off at the imposed parameter; a pass/fail indicator, interconnected to said processing unit, for showing if the measured parameter, is within the pre-established upper parameter limit and lower parameter limit as defined by the user; and said power supply unit including a power source in the form of a battery and a battery charging and protection circuit. - a socket subassembly having an unitary elongated body, including at one extremity a first engaging cavity, at an opposite extremity, a second engaging cavity; and incorporating an externally open, annular channel provided between said extremities of said socket subassembly; - a strain transducer subassembly, for measuring torsional strains on said socket subassembly, mounted in said externally open, annular channel; - a circular cover attached to said socket subassembly for enclosing said externally open, annular channel; and - an electronic subassembly for converting said torsional strains on said socket subassembly to standard torque values and for determining tightening angular displacements; said electronic subassembly being interconnected to said strain transducer subassembly and mounted on said circular cover to face said strain transducer subassembly;