The equation everyone uses
T = K × D × F
Torque T equals the nut factor K times the nominal bolt diameter D times the preload F. The equation is popular because two of its terms are easy: you know the diameter, and you know the load you want. All the uncertainty is in K.
K is not the coefficient of friction from a physics textbook. It is an experimental constant that bundles together:
- friction between the nut face and the washer or flange (usually the biggest piece),
- friction between the male and female threads,
- the thread geometry: helix angle and the 60° flank angle, which turn some torque into stretch.
Measure K on a given bolt, nut, washer and lubricant combination and it is fairly repeatable. Change any one of them and it moves.
Where the torque goes
The commonly cited split for a lubricated steel bolt is about 50% under the nut face, 40% in the threads and 10% into stretching the bolt. Only that last tenth does useful work. When friction changes a little, the useful tenth changes a lot. Suppose friction losses rise from 90% to 92% of the applied torque. The share left for stretch drops from 10% to 8%, which is 20% less preload at the same torque reading.
This is why torque control, on its own, commonly produces preload scatter of ±25% or more from bolt to bolt, even with a perfectly calibrated wrench. The wrench is accurate. Friction isn't.
Typical nut factor values
These are typical published ranges for steel bolts and nuts. Your lubricant manufacturer's steel-on-steel value is better than this table, and a value measured on your own hardware is better than both.
| Thread condition | Typical K | Notes |
|---|---|---|
| Clean, as-received steel, light oil | 0.18 – 0.22 | 0.20 is the customary default |
| Machine oil, well lubricated | 0.15 – 0.18 | |
| Nickel- or copper-based anti-seize | 0.13 – 0.19 | Wide spread between products; check the datasheet |
| Molybdenum disulfide paste | 0.10 – 0.14 | Common on large flange studs |
| PTFE / fluoropolymer-coated studs | 0.07 – 0.12 | Coating wear on reuse raises K |
| Hot-dip galvanized, dry | 0.25 – 0.35+ | Can gall; lubricate per the nut manufacturer |
| Rusty, dirty or damaged threads | Unknown | Clean, chase or replace. Don't torque |
What changes K on a real job
- Lubricant: wrong type, too little, or applied to only one face. Lubricate the threads and the nut bearing face. Skipping the face leaves the biggest friction term untouched.
- Coatings and plating. Zinc, cadmium, PTFE, galvanizing and phosphate all behave differently, and some change after the first tightening.
- Reuse. The first tightening burnishes surfaces, and later ones see a different K. Studs and nuts that have galled once will gall again.
- Washer hardness and condition. A soft or cupped washer, or a rough spot face, raises under-nut friction. Through-hardened washers keep it consistent, which is why PCC-1 calls for them.
- Thread fit and damage. Dings, paint, rust, sand and thread damage all add friction that doesn't stretch anything.
- Temperature. Lubricant viscosity and the behavior of anti-seize compounds change with temperature at assembly.
- Tightening speed. Impact and fast-rundown tools see a different effective friction than slow, steady hydraulic strokes.
How to measure K on your own bolts
A bolt tension calibrator, such as a Skidmore-Wilhelm unit, is a hydraulic load cell the bolt passes through. Tighten a sample bolt in the calibrator with your actual nut, washer, lubricant and tool, then read the tension directly. Divide the applied torque by D × F and you have your K.
Run several samples from the same lot and the spread tells you how much scatter to expect in the field. Steel erectors use the same device for pre-installation verification of structural bolts under RCSC rules. Plants use it to settle arguments about what a procedure actually delivers. We stock calibrators. Ask about one.
When K is the wrong thing to fight
You can tighten lubricant control, harden washers and calibrate everything, and still have ±15–25% scatter from torque alone. When a joint can't tolerate that, stop controlling torque and control or measure something closer to the load:
- Hydraulic tensioning stretches the stud directly, with no nut friction in the loop.
- Torque-and-angle, or turn-of-nut, uses rotation past snug, which depends less on friction.
- Ultrasonic elongation measurement checks the actual stretch after the fact.
- Load-monitoring fasteners read clamp load directly for the life of the joint.
The full comparison is in bolt tightening methods compared.
Frequently asked questions
What is the K factor in bolt torque?
K, the nut factor, is an experimentally determined constant in T = K × D × F that lumps together thread friction, friction under the nut face and thread geometry. It converts the torque you apply into the preload you get. It is not a pure coefficient of friction, though friction dominates it.
What K factor should I use for dry bolts?
0.20 is the customary assumption for clean, as-received steel bolts with only a light oil film. Truly dry, clean steel or plated parts can run anywhere from about 0.15 to 0.30, which is why measuring K matters on critical work.
Does lubrication increase bolt preload?
At the same torque, yes. A lower K means more of the torque becomes stretch. That's why a lubricated bolt tightened to a dry torque value can be overloaded, possibly past yield, and why the lubricant must be specified together with the torque.
How much of the torque actually stretches the bolt?
Roughly 10%. Commonly cited splits put about 50% into friction under the nut face and about 40% into thread friction, which leaves around 10% to produce preload. The exact split varies with lubrication and surface condition.