Bolt Torque Calculator (T = K·D·F, Preload & Stress)
By Santaji GadepatilinUpdated November 3, 2026
Tightening torque is the practical way to set a bolt's clamping force, but only a small part of the torque stretches the bolt — most is lost to friction in the threads and under the nut. This bolt torque calculator uses the short-form equation T = K × D × F, with the nut factor K capturing that friction, and checks the resulting tensile stress in the bolt.
How to use the bolt torque calculator
Enter the nut factor K, the nominal bolt diameter, the target preload and the bolt’s tensile stress area. The calculator returns the tightening torque and the tensile stress the preload creates. To find the preload a given torque produces, enter the torque and clear the preload.
Bolt torque formula
T = K × D × F · σ = F ÷ At
For ISO metric threads the tensile stress area is At = π/4 × (d − 0.9382 p)², where p is the thread pitch.
Example
An M12 × 1.75 bolt (At = 84.3 mm²) tightened dry (K = 0.2) to a 30 kN preload:
- T = 0.2 × 0.012 m × 30,000 N = 72 N·m
- Bolt stress σ = 30,000 ÷ 84.3 = 356 MPa — about 61% of the 580 MPa proof stress of class 8.8
Indicative torque for ISO metric coarse bolts (K = 0.2, 75% of proof load)
| Thread | Stress area | Preload 8.8 | Torque 8.8 | Preload 10.9 | Torque 10.9 |
|---|---|---|---|---|---|
| M6 × 1 | 20.1 mm² | 8.8 kN | 11 N·m | 12.5 kN | 15 N·m |
| M8 × 1.25 | 36.6 mm² | 15.9 kN | 25 N·m | 22.8 kN | 36 N·m |
| M10 × 1.5 | 58.0 mm² | 25.2 kN | 50 N·m | 36.1 kN | 72 N·m |
| M12 × 1.75 | 84.3 mm² | 36.7 kN | 88 N·m | 52.5 kN | 126 N·m |
| M16 × 2 | 156.7 mm² | 68.2 kN | 218 N·m | 97.5 kN | 312 N·m |
| M20 × 2.5 | 244.8 mm² | 110.2 kN | 441 N·m | 152.4 kN | 610 N·m |
| M24 × 3 | 352.5 mm² | 158.6 kN | 761 N·m | 219.4 kN | 1053 N·m |
| M30 × 3.5 | 560.6 mm² | 252.3 kN | 1514 N·m | 349.0 kN | 2094 N·m |
Proof stresses from ISO 898-1: class 8.8 — 580 MPa (≤ M16), 600 MPa (> M16); class 10.9 — 830 MPa. Use the fastener supplier’s data for critical joints.
Notes
- Check the clamped joint as well as the bolt: soft gaskets and painted surfaces relax and lose preload.
- Use the factor of safety calculator to compare the bolt stress with the material’s proof or yield strength.
Frequently asked questions
What is the formula for bolt torque?
T = K × D × F, where K is the nut factor (about 0.2 for dry steel), D the nominal diameter and F the desired preload. Use metres and newtons to get N·m.
What preload should a bolt have?
A common target is 70–75% of the bolt's proof load for reusable joints. For an ISO 8.8 bolt up to M16 the proof stress is 580 MPa, so 75% is about 435 MPa on the tensile stress area.
How much does lubrication change the torque?
A lot. Oiled or MoS₂-coated threads have a lower K, so the same torque produces 30–60% more preload. Always use the K value matching the actual thread condition, or the bolt may be over-stressed.
Why is torque tightening imprecise?
Friction varies from bolt to bolt, so the same torque can give ±25% scatter in preload. Critical joints use torque-angle tightening, hydraulic tensioners or ultrasonic bolt-elongation measurement.