Bolt Stress and Tightening Torque Calculator
The tensile stress area, the stress in the bolt and the torque to reach a given preload for a metric bolt.
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How this calculator works
A bolt's strength is based on its tensile stress area, which is a little smaller than the shank area because of the thread. For a metric thread it is At = (π / 4)(d - 0.9382 p)². The stress is the load divided by this area.
The tightening torque needed for a preload is estimated with the short-form equation T = K d F, where K is the nut factor. K is about 0.2 for dry steel and lower when lubricated, and it varies a lot, so the preload from a given torque is only an estimate.
Formulas used
- A_t = \frac{\pi}{4}(d - 0.9382\,p)^2
- \sigma = F / A_t
- T = K d F
Worked example
With the default numbers in the calculator above:
- Pitch and minor diameters: 10.9 and 9.85 mm
- Tensile stress area: 84.3 mm²
- Tensile stress in the bolt: 237 MPa
- Tightening torque for that load: 48 N m
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What nut factor should I use?
About 0.2 for plain dry steel. Lubrication can lower it to 0.1 to 0.15. Use the bolt supplier's figure when you have it.
Is the torque method accurate?
Only roughly. Friction varies by 25 percent or more, so the preload can be well above or below the target. Critical joints use tension indicators or turn-of-nut methods.
Does this check a joint?
No. It checks the bolt stress only. A joint also needs the bearing, shear, fatigue and clamp checks.
Related calculators
Further reading: Shigley, Mechanical Engineering Design (threaded fasteners and bolted joints); Bickford, An Introduction to the Design and Behavior of Bolted Joints.
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