The short-form torque equation
When you tighten a bolt, the torque you apply stretches it slightly, and that stretch creates the clamping force, or preload, that holds the joint together. The classic estimate is:
T = K × D × F
- T is the tightening torque.
- K is the nut factor, which lumps together thread and under-head friction. About 90% of the torque is lost to friction; only about 10% stretches the bolt.
- D is the nominal diameter.
- F is the target preload.
Choosing the preload
A common target is 75% of the proof load for joints that may be taken apart, and up to 90% for permanent joints. The proof load is the proof stress of the grade times the tensile stress area of the thread:
As = 0.7854 × (D − 0.9743 ÷ n)², with n threads per inch.
| SAE grade | Proof stress (up to 1 in) | Head marking |
|---|---|---|
| Grade 2 | 55 ksi (up to 3/4 in) | none |
| Grade 5 | 85 ksi | 3 radial lines |
| Grade 8 | 120 ksi | 6 radial lines |
Example
A dry 1/2-13 grade 5 bolt: As = 0.7854 × (0.5 − 0.9743 ÷ 13)² ≈ 0.1419 in². Proof load ≈ 85,000 × 0.1419 ≈ 12,060 lbf, so the 75% preload is about 9,050 lbf. With K = 0.20, T = 0.20 × 0.5 × 9,050 ≈ 905 lbf·in, or about 75 ft·lb.
Lubrication changes everything
| Thread condition | Typical K |
|---|---|
| Dry or black oxide | about 0.20 |
| Zinc plated | about 0.18 |
| Lightly oiled | about 0.15 |
| Anti-seize or moly paste | about 0.12 |
If you apply a “dry” torque value to a lubricated bolt, you can overload it by 30% or more and stretch or break it. If a specification gives a torque, check whether it assumes dry or lubricated threads.
Limits
- K varies widely from batch to batch, so torque alone controls preload only to about ±25%. Critical joints use torque-angle tightening, load-indicating washers or bolt stretch measurement.
- Soft materials such as aluminum threads or gaskets need lower torques.
- Always follow the torque given by the vehicle, machine or equipment manufacturer; this calculator is for general estimates.