How Is Bolt Tightening Torque Calculated? Preload and the K Factor

Tightening a bolt is really stretching a spring: during tightening the bolt elongates and creates a clamping force on the joined parts, known as preload. Torque is the practical way to control this preload indirectly.

The basic formula

T = K × F × d

• T: Tightening torque (N·mm; divide by 1,000 for Nm)
• K: Nut factor (depends on friction condition)
• F: Desired preload force (N)
• d: Nominal bolt diameter (mm)

How is preload found?

As a general rule, preload is chosen as 60-80% of the bolt's yield load. Yield load = Rp0.2 × As. As is the tensile stress area and for coarse-thread metric bolts it is calculated as As = 0.7854 × (d − 0.9382 × P)² (P: thread pitch).

Example: M10 8.8 bolt

• P = 1.5 mm → As = 0.7854 × (10 − 1.407)² = 58 mm²
• Rp0.2 = 640 MPa → yield load = 640 × 58 = 37,120 N
• 70% preload → F = 25,984 N ≈ 26 kN
• K = 0.20 for a galvanized dry surface
• T = 0.20 × 25,984 × 10 / 1000 ≈ 52 Nm

Why does the K factor matter?

Two bolts tightened with the same torque can give very different preload under different friction conditions. About 90% of the torque energy overcomes friction and only 10% stretches the bolt. An oiled bolt with K = 0.15 gives 25-30% more preload than a dry bolt. This is why torque values must be given together with coating and lubrication conditions.

Common mistakes

• Applying catalog torque values unchanged to a different coating and lubrication
• Not calibrating the torque wrench (at least once a year)
• Tightening in a single pass; multi-bolt flanges need cross-pattern, staged tightening
• Forgetting that preload changes in reused bolts

In safety-critical connections

In vehicles, pressure vessels and structural connections, torque-angle or yield-controlled tightening is preferred over the torque method; these methods reduce the dependence of preload on friction. The torque calculator on our site is a quick pre-design tool; for exact values you can use our application engineering support.