KEVOS® MAKEOS · Fasteners
Bolt Tightening Torque with Separate Thread and Bearing Friction
What tightening torque gives my bolt preload when the thread friction and the nut or head bearing friction differ, how much of the torque goes into stretching the bolt, and how do the handbook’s simplified forms compare?
Tightening torque by the handbook’s Equations (21) to (24): T = PB [l ÷ 2π + d2 μ1 ÷ (2 cos α) + (d + b) μ2 ÷ 4] with the lead l, pitch diameter d2, thread half angle α, bearing face diameter b and the thread and bearing friction coefficients μ1 and μ2 you enter, the 60° thread forms T = PB [0.159 l + d (0.531 μ1 + 0.625 μ2)] and T = PB (0.159 l + 1.156 μ d), and the preload PB from a share of the tensile strength on the stress area of Equation (9) or entered directly.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal (major) diameter d | mm | Nominal diameter of the bolt. |
| Thread pitch | mm | Pitch of the thread; for inch threads 25.4 ÷ TPI. |
| Number of thread starts | starts | Number of starts; the lead is starts × pitch. |
| Thread half angle α | ° | Half the included thread angle; 30° for 60° threads. |
| Preload from | choice | Whether the preload comes from the bolt strength or is entered directly. |
| Minimum tensile strength of the bolt | MPa | Minimum tensile strength of the bolt grade. |
| Preload as a share of the tensile strength | % | Share of the tensile strength the preload is to reach. |
| Preload PB (when entered directly) | kN | Axial preload in the bolt, when entered directly. |
| Thread friction coefficient μ1 | Friction coefficient between the bolt and nut threads. | |
| Nut or head bearing friction coefficient μ2 | Friction coefficient under the turned nut or bolt head. | |
| Bearing face diameter b (0 = 1.5 d, no loose washer) | mm | Outer diameter of the pressure face under the turned nut or head. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Nominal (major) diameter d
- What it is
- Nominal outside diameter of the bolt thread.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the stress area and the friction radii.
- Get it right
- For inch bolts multiply the size by 25.4, e.g. 1/2 in is 12.7 mm.
What this means: Thread pitch
- What it is
- Axial distance between neighbouring threads of the bolt.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.953846 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the lead, the stress area and the pitch diameter.
- Get it right
- For inch threads divide 25.4 by the threads per inch, e.g. 13 TPI is 1.9538 mm.
What this means: Number of thread starts
- What it is
- How many separate threads run side by side along the bolt.
- Units and format
- Enter a number in starts: a number of thread starts. The form accepts 1 starts to 8 starts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 starts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The lead and the stretching torque rise in proportion.
- Get it right
- Almost all bolts are single start.
What this means: Thread half angle α
- What it is
- Half the included angle between the thread flanks.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger angle raises the thread friction torque.
- Get it right
- Use 30° for unified and metric 60° threads.
What this means: Preload from
- What it is
- Whether the preload is worked out from the bolt strength or entered.
- Units and format
- Choose one of 2 options from the list: A share of the tensile strength on the stress area; A preload you enter.
- Example
- The form opens with “A share of the tensile strength on the stress area” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Chooses how PB is found.
- Get it right
- Choose the direct preload when a joint calculation already gives it.
What this means: Minimum tensile strength of the bolt
- What it is
- Lowest tensile strength the bolt grade is guaranteed to reach.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1034.21 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preload and torque rise in proportion.
- Get it right
- Take it from the bolt grade standard, e.g. 1034 MPa (150,000 psi) for SAE grade 8.
What this means: Preload as a share of the tensile strength
- What it is
- Share of the minimum tensile strength the preload is to reach.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.000001% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 55% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preload and torque rise in proportion.
- Get it right
- Use the share your joint design or company standard calls for.
What this means: Preload PB (when entered directly)
- What it is
- Axial clamping force the bolt is to carry after tightening.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The torque rises in proportion.
- Get it right
- Only used when the preload is entered directly.
What this means: Thread friction coefficient μ1
- What it is
- Coefficient of friction between the bolt and nut thread flanks.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the thread friction part of the torque.
- Get it right
- Measure it or take it for your plating and lubricant; dry steel is about 0.15.
What this means: Nut or head bearing friction coefficient μ2
- What it is
- Coefficient of friction under the face of the turned nut or bolt head.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the bearing friction part of the torque.
- Get it right
- Measure it or take it for your surfaces; it may differ from the thread value.
What this means: Bearing face diameter b (0 = 1.5 d, no loose wa…
- What it is
- Outer diameter of the pressure face under the turned nut or bolt head.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 400 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger face raises the bearing friction torque.
- Get it right
- Enter 0 to use 1.5 d, the handbook value with no loose washer.
Method and formulas
- Stress area As = π ÷ 4 × ((dp + dm) ÷ 2)² with dp = d − 0.6495P and dm = d − 1.2990P (Equation 9); PB = share × tensile strength × As.
- T1 = PB l ÷ 2π (stretching the bolt), T2 = PB d2 μ1 ÷ (2 cos α) (thread friction) with d2 = d − 0.6495P, T3 = PB (d + b) μ2 ÷ 4 (bearing friction); T = T1 + T2 + T3 (Equation 22).
- For 60° threads with d2 ≈ 0.92d and b ≈ 1.5d: T = PB [0.159 l + d (0.531 μ1 + 0.625 μ2)] (Equation 23); with μ1 = μ2 = μ: T = PB (0.159 l + 1.156 μ d) (Equation 24).
- Example: the preload of 52.074 kN needs 129.75 N·m by Equation (22).
Limitations
- Friction coefficients vary widely with finish, plating and lubrication; measure or take them for your parts.
- The stress area of Equation (9) is for unified inch threads; metric stress areas differ slightly.
- Most of the torque is lost in friction, so small changes in friction change the preload a lot.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set a tightening torque when the thread and bearing friction differ
- See how much of the torque is lost in friction
- Check a torque figure against the simplified handbook forms
Who it is for
- Mechanical designers
- Maintenance fitters
- Assembly engineers
What you get
- Stress area and preload
- Torque by Equation (22) and its three parts
- Torque by the simplified Equations (23) and (24)
- Share of the torque that stretches the bolt
Interpreting the result
- When the two coefficients are equal, Equation (24) gives the same torque as Equation (23).
- A loose washer under the nut changes the bearing diameter b and the bearing friction.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1529–1534. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Tightening by torque: the nut factor and its scatter
In Bolted Joints by the Numbers
What it covers: How tightening torque becomes preload through the nut factor, why friction makes that uncertain, how lubricants change it, and how to correct a torque wrench for an adapter.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Bolt Tightening Torque with Separate Thread and Bearing Friction calculator