Bolt Preload & Tightening Torque Calculator — Recommended Bolt Clamp Force and Torque
Calculate preload force and tightening torque using nominal bolt diameter, nut factor, thread geometry, and bolt strength.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Bolt geometry
Thread parameters
Tightening torque
Required preload force
Bolt class
Nut factor
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Preload force formula:
F = T / (K · d)
Tightening torque formula:
T = K · F · d
Recommended preload force formula:
F = 0.7 · Re · As
Recommended tightening torque formula:
T = K · F · d
Metric tensile stress area:
As = π / 4 · (d − 0.9382 · p)2
Unified tensile stress area:
As = π / 4 · (d − 0.9743 · 1 / n)2
Bolt stress:
σ = F / As
Yield utilization:
σ/Re = (σ / Re) · 100%
Proof load:
Fproof = As · Sp
Proof utilization:
F/Fproof = (F / Fproof) · 100%
Preload sensitivity:
∂F/∂T = 1 / (K · d)
where:
- F — preload force (N)
- T — tightening torque (N·m)
- K — nut factor (–)
- d — nominal bolt diameter (m)
- Re — yield strength (Pa)
- Sp — proof strength (Pa)
- As — tensile stress area (m²)
- p — thread pitch (m)
- n — threads per inch, TPI (1/in)
- σ — bolt stress (Pa)
- Fproof — proof load (N)
When to use this calculator
When to use this calculator:
- To calculate preload force from an applied tightening torque, nut factor, and nominal bolt diameter.
- To calculate tightening torque required to reach a specified preload force.
- To calculate recommended preload force from bolt yield strength and tensile stress area.
- To evaluate bolt stress against yield strength when thread geometry and material strength are provided.
- To evaluate proof load utilization when proof strength is available.
- To check whether the selected nut factor is outside the friction condition range used by the calculator.
How to interpret the result
Preload force is defined as the axial clamp force generated or targeted in the bolt. Tightening torque is defined as the torque required to generate that preload force through the selected nut factor and nominal bolt diameter.
Preload force depends on tightening torque, nut factor, and nominal bolt diameter. Increasing tightening torque increases preload force. Increasing nut factor or nominal bolt diameter decreases preload force for the same tightening torque.
Tightening torque depends on preload force, nut factor, and nominal bolt diameter. Increasing preload force, nut factor, or nominal bolt diameter increases the required tightening torque.
- Safe — yield utilization is less than or equal to 75% when yield strength is provided.
- Warning — yield utilization is greater than 75% and less than or equal to 100%, or proof utilization is greater than 90% and less than or equal to 100%.
- Unsafe — yield utilization is greater than 100%, or proof utilization is greater than 100%.
- Info — preload force and tightening torque are calculated without an active yield or proof utilization classification.
- Invalid — required inputs are missing, non-finite, outside allowed limits, or inconsistent with the selected calculation mode.
A nut factor lower than 0.08 or higher than 0.3 produces a warning. In recommended preload mode, bolt stress lower than 10% of yield strength also produces a warning.
Calculation example
Example:
A user wants to calculate the tightening torque needed to reach a required preload force for a bolted joint.
- Calculation mode: Preload → Torque
- Required preload force F = 12000 N
- Nominal bolt diameter d = 0.01 m
- Nut factor K = 0.2
T = K · F · d = 0.2 · 12000 · 0.01 = 24 N·m
Assumptions and limitations
- Preload force and tightening torque are linked by T = K · F · d.
- Recommended preload force is calculated as 70% of yield strength multiplied by tensile stress area.
- Metric tensile stress area is calculated from nominal bolt diameter and thread pitch using As = π / 4 · (d − 0.9382 · p)2.
- Unified tensile stress area is calculated from nominal bolt diameter and threads per inch using As = π / 4 · (d − 0.9743 · 1 / n)2.
- Yield utilization is evaluated only when yield strength is provided.
- Proof utilization is evaluated only when proof strength is provided.