No, you cannot use a metrc socket on a standard socket wrench. These are two different systems of measurement and are not interchangeable.

The socket wrench is one among the system of wrenches that departs the wrench handle from the wrench that engages the fastener. Whereas, the torque wrench are the torque indicating socket wrench handle. When it is used properly, that could help you calculate the torque amount while fastening using the wrench. It also limits the amount of torque which is applied on material.

A socket wrench can drive sockets that totally encompass a nut or bolt head, thus getting a much better grip of it than a wrench.

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The function of a socket wrench is to tighten or loosen nuts and bolts. It does this better by completely encompassing all sides of the nut.