The total required torque, MT, is to a large extent determined by frictional losses. It can, however, be shown that it is directly proportional to the axial force in the bolt, F.

The torque consists of a sum of two parts, the torque in the thread, Mt, and the torque caused by friction under the head, Mh,

Here, μh is the coefficient of friction under the bolt head (or nut, whichever is rotating), and re is an effective radius at which the circumferential force can be considered as acting. If the contact pressure under the bolt head is assumed to be constant, then the effective radius can be computed as

Here, r is the distance from the bolt axis, and the integrals are taken over the contact area under the bolt head.

where do is the outer diameter of the bolt head, and dh is the bolt hole diameter.

Here, H is the width (spanner size) of the bolt.

Here, dp is the mean diameter of the bolt thread.

where l is the lead (expressed in the same units as dp). This term, which is purely geometrical, gives the relation between torque and bolt force under ideal (frictionless) conditions.

The friction angle ε is defined as

Here, μt is the coefficient of friction in the thread, while α is half the thread angle.