Enter the torque, nominal diameter, and axial force into the calculator to determine the bolt nut factor (also called the torque coefficient, K).

Bolt Nut Factor (Torque Coefficient) Calculator

Enter any 3 values to calculate the missing variable

Bolt Nut Factor (Torque Coefficient) Formula

The following formula is used to calculate the bolt nut factor (torque coefficient), K.

K = T / (F * d)

Variables:

  • K is the nut factor / torque coefficient (unitless)
  • T is the tightening torque (N·m)
  • F is the axial force (bolt preload) (N)
  • d is the bolt nominal diameter (m)

This equation is the common empirical torque–tension relation rearranged (T = K·F·d). The nut factor K is not a true coefficient of friction; it is an overall factor that lumps together thread friction, bearing (under-head/nut) friction, and geometry effects.

If you need an actual coefficient of friction (thread or bearing), you must also know additional details such as thread pitch/lead angle, effective friction diameters, and the split between thread and bearing friction.

What is a Bolt Nut Factor (Torque Coefficient)?

The bolt nut factor (also called the torque coefficient, K) is a dimensionless value used to estimate how much tightening torque is needed to achieve a desired bolt preload using the relation T = K·F·d. It is strongly influenced by lubrication, surface finish, coatings, and whether torque is consumed in thread friction and under-head (bearing) friction. Typical values are often in the range of about 0.10 to 0.30 depending on conditions, with ~0.20 commonly used as a rough assumption for steel fasteners under “as-received” conditions.

How to Calculate Bolt Nut Factor (Torque Coefficient)?

The following steps outline how to calculate the bolt nut factor (K).

  1. First, determine the tightening torque (T) in Newton-meters (N·m).
  2. Next, determine the nominal diameter of the bolt (d) in meters (m).
  3. Next, determine the axial force (preload) in the bolt (F) in Newtons (N).
  4. Next, gather the formula from above: K = T / (F * d).
  5. Finally, calculate the nut factor (K) using the formula.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Tightening torque (T) = 4 N·m

Nominal diameter of the bolt (d) = 0.02 m

Axial force (preload) (F) = 1000 N

Nut factor (K) = T / (F * d) = 4 / (1000 * 0.02) = 0.20