Bolt, one of the most widely used fasteners in the industry, is usually tightened by applying torque to the head and/or nut. As the bolt is tightened, it is stretched (preloaded). Preload tension is necessary to keep the bolt tight, increase join strength, create friction between parts, and improve fatigue resistance. The recommended preload force F_{i} is
For reusable connections:
For permanent connections:
where A_{t} is the tensile area of the bolt and S_{p} is the proof strength of the bolt. Although the above formulae look rather straightforward, the preload tension F_{i} is not easy to measure or control.
A common practice is to relate the preload tension F_{i} to a quantity that is easier to measure, the applied torque T. This torque, usually achieved by a torque wrench, the turnofnut, or an indicating washer, is
where d is the nominal outside diameter of the bolt and K is the correction factor that depends on the material, size, surface friction, and threading of the bolt. For most small to mid size bolts, K is between 0.15 and 0.3.
As a rough approximation:
dry (unlubricated) midsize steel bolts:  K = 0.2 
nonplated black finish:  K = 0.3 
zincplated:  K = 0.2 
cadmiumplated:  K = 0.16 
lubricated:  K = 0.15 ~ 0.18 
A more complicated torque formula is given as
where P is the lead (pitch) of the thread, D_{b} is the average mean diameter of the bolt, D_{n} is the average mean diameter of the nut, _{k} is the coefficient of friction, and is one half of the thread angle (usually 30°). This formula, although more complete, is seldom used, for the large errors (sometimes as much as 25%) involved in torque wrench readout usually renders using a more accurate formula pointless.
