Nut factor K explained: typical values and how to choose

By The CheckedCalc editor, mechanical design engineer. Published 28 September 2026. Last checked 28 September 2026.

The short-form bolt torque formula is $T = K\,F\,d$ : tightening torque equals the nut factor K times the preload F times the nominal diameter d. It is simple enough to do in your head, and that is its danger. K is not a material property or a friction coefficient. It is an experimental constant that lumps together everything between the wrench and the bolt tension. A guessed K is often the largest single source of error in a torque specification.

What K lumps together

When you turn a nut, the torque goes three ways. A small part stretches the bolt by driving the thread helix up its ramp. The rest is lost to friction: between the nut and bolt threads, and under the nut or head where it bears on the joint. VDI 2230 Part 1:2015 writes this for a 60° thread, in the form given by Motosh (1976), as

T = F\left(0.16\,P + 0.58\,d_{2}\,\mu_{\text{th}} + \dfrac{D_{\text{Km}}}{2}\,\mu_{\text{b}}\right)

where P is the pitch, d₂ the pitch diameter, μ_th the thread friction coefficient, D_Km the effective bearing diameter under the nut or head and μ_b the bearing friction coefficient. Divide by F d and you have K:

K = \dfrac{T}{F\,d} = \dfrac{0.16\,P}{d} + \dfrac{0.58\,d_{2}}{d}\,\mu_{\text{th}} + \dfrac{D_{\text{Km}}}{2d}\,\mu_{\text{b}}

Term	Physical meaning	M12 × 1.75	1/2-13 UNC
0.16 P / d	Thread lead: the useful work that stretches the bolt	0.023	0.025
0.58 d₂ / d	Multiplier on thread friction μ_th	0.525	0.522
D_Km / 2d	Multiplier on bearing friction μ_b	0.617	0.638

M12 geometry: d₂ = 10.863 mm, washer face d_w = 16.6 mm, clearance hole d_h = 13 mm, $D_{\text{Km}} = (d_{\text{w}} + d_{\text{h}})/2 = 14.80\ \text{mm}$ . For 1/2-13 UNC the calculator uses a hex head face of 0.95 × across flats and a 1/16 in clearance. With μ = 0.12 on an M12 class 8.8 bolt at 36.7 kN preload, the torque of 70.5 N·m splits into 15 % stretching the bolt, 39 % thread friction and 46 % bearing friction. About 85 % of the wrench effort is friction, which is why small changes in friction move the preload so much.

K from friction: computed values

These values come from the engine behind the bolt torque calculator, with the same friction under the head and in the thread. The two sizes agree closely because K is nearly dimensionless in geometry: the bearing and thread diameters scale with d.

μ_th = μ_b	K, M12 × 1.75	K, 1/2-13 UNC
0.06	0.092	0.094
0.08	0.115	0.117
0.10	0.138	0.141
0.12	0.160	0.164
0.14	0.183	0.187
0.16	0.206	0.210
0.18	0.229	0.233
0.20	0.252	0.257
0.24	0.297	0.303

Two useful reverse readings for M12: K = 0.20 corresponds to μ ≈ 0.155, and K = 0.15 to μ ≈ 0.111. NASA RP-1228 (Barrett, 1990) Table VI gives a cross-check from a similar friction model: 0.133 at μ = 0.10, 0.189 at μ = 0.15 and 0.250 at μ = 0.20. These are within about 0.01 of the values above. The small differences come from its slightly different geometry constants.

Typical K values by surface condition

Published K values differ by source because they come from different tests, fastener sizes and lubricant brands. Treat each row as the source's value, not a universal constant.

Condition	K	Source
Non-plated, black finish	0.30	Shigley 10th ed., Table 8-15
Zinc plated	0.20	Shigley 10th ed., Table 8-15
Lubricated	0.18	Shigley 10th ed., Table 8-15
Cadmium plated	0.16	Shigley 10th ed., Table 8-15
With Bowman anti-seize	0.12	Shigley 10th ed., Table 8-15
With Bowman-Grip nuts	0.09	Shigley 10th ed., Table 8-15
Condition not stated	0.20	Shigley 10th ed., text with Table 8-15 (default when the bolt condition is not stated)
Steel on steel, "typical"	0.15	NASA RP-1228 (1990), which warns against using 0.2 blindly
VDI 2230 friction class A, μ 0.04 to 0.10: solid lubricants such as MoS2 or graphite pastes, wax	0.07 to 0.14	VDI 2230 Part 1:2015 Table A5 friction class, converted to K for M12 by the equation above
VDI 2230 friction class B, μ 0.08 to 0.16: oiled parts, most zinc coatings with lubricant	0.11 to 0.21	VDI 2230 Part 1:2015 Table A5 friction class, converted to K for M12 by the equation above
VDI 2230 friction class C, μ 0.14 to 0.24: dry zinc coatings, stainless with solid lubricant	0.18 to 0.30	VDI 2230 Part 1:2015 Table A5 friction class, converted to K for M12 by the equation above

The VDI 2230 rows show the real width of each condition. A class C part can sit anywhere from K ≈ 0.18 to 0.30. Bickford (2008) makes the same point at length: K varies with finish, lubricant, hardness, thread fit, speed of tightening and reuse. Published tables are starting points for a test, not substitutes for one.

How to choose K

Situation	What to do
Fastener supplier gives a K or friction class for the coating	Use it. Coating systems with integral lubricant (zinc flake, for example) are usually specified to a μ range; convert with the table above.
Known lubricant, no supplier data	Use μ from VDI 2230 Table A5 for the class and compute K with the calculator, or take a textbook K from the table above for the matching condition.
Condition unknown or uncontrolled	Assume K = 0.20 for the torque value. Then check the bolt for overload at the low end of friction (K ≈ 0.12 to 0.15), and for loss of clamp at the high end (K ≈ 0.25 to 0.30).
Critical joint, production volume	Measure it. ISO 16047 describes a torque and clamp force test on the actual parts; ten to twenty samples give a mean K and its spread.
Assembly changes lubricant or coating	Revise the torque. The same torque with a better lubricant can take the bolt past yield.

The last row is where most field failures start. On M12 class 8.8, take a torque of 88.0 N·m set for K = 0.20 (preload 36.7 kN). If the parts are actually lightly oiled at μ = 0.10, it produces 53.3 kN. That is a +45 % change on a preload that was already 75 % of proof load.

Scatter and preload uncertainty

Even with the right mean K, friction scatters from bolt to bolt. With the torque fixed at 70.5 N·m (M12 class 8.8, μ = 0.12, target 36.7 kN), the engine gives:

Friction scatter	Preload range (kN)	Relative to target
μ ± 20 %	31.3 to 44.2	-15 % / +21 %
μ ± 30 %	29.2 to 49.3	-20 % / +34 %

This is consistent with the rule of thumb that a torque wrench controls preload to about ± 25 % (NASA RP-1228). The band is not symmetric: low friction overshoots by more than high friction undershoots, so the upper end is the one that yields bolts. When the joint cannot tolerate that spread, control something closer to the bolt stretch.

Method	Preload accuracy	Notes
Torque wrench	± 25 %	K scatter dominates; calibrate the wrench anyway.
Turn of nut	± 15 %	Snug, then a specified rotation; needs a stiff, well-defined joint. RCSC practice for structural bolts.
Bolt stretch measurement (micrometer or ultrasonic)	± 1 % to ± 8 %	Measures elongation directly; needs access to both ends or an ultrasonic calibration per bolt batch.
Strain-gauged bolts	± 1 %	Laboratory and critical joints; each bolt is instrumented.
Direct tension indicator (DTI) washers	Not quantified in the sources here	Protrusions flatten at a set load (ASTM F959); independent of friction.

Accuracies from NASA RP-1228 (1990), which also quotes ± 15 % to ± 30 % for torque control in general.

Worked check

M12 × 1.75, class 8.8, 75 % of proof load = 36.7 kN. With K = 0.20, and with the friction model at μ = 0.12:

\begin{aligned} T_{K} &= K\,F\,d = 0.20 \times 36.7\ \text{kN} \times 12\ \text{mm} = 88.0\ \text{N}\cdot\text{m} \\[0.4em] T_{\mu} &= F\left(0.16\,P + 0.58\,d_{2}\,\mu_{\text{th}} + \dfrac{D_{\text{Km}}}{2}\,\mu_{\text{b}}\right) \\ &= 36.7\ \text{kN} \times (0.16 \times 1.75 + 0.58 \times 10.863 \times 0.12 + 7.40 \times 0.12)\ \text{mm} \\ &= 70.5\ \text{N}\cdot\text{m}, \quad \text{which is } K = 0.160 \end{aligned}

The calculator shows both, side by side. Open this case in the bolt torque calculator, or read the full tables in the metric bolt torque chart, the SAE J429 chart and the ASTM F3125 structural bolt chart.

References

Source	Used for
VDI 2230 Part 1:2015, Systematic calculation of highly stressed bolted joints	Torque equation, friction classes (Table A5).
Motosh, N. (1976), "Development of design charts for bolts preloaded up to the plastic range", Journal of Engineering for Industry, 98(3), ASME	The 0.16 P + 0.58 d₂ μ form of the thread torque.
Budynas, R. G. and Nisbett, J. K., Shigley's Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015	T = K F d, Table 8-15 torque factors.
Bickford, J. H., Introduction to the Design and Behavior of Bolted Joints, 4th ed., CRC Press, 2008	Nature of the nut factor and its variability.
Barrett, R. T., Fastener Design Manual, NASA Reference Publication 1228, 1990	K versus friction (Table VI), typical K, preload accuracy by method.
ISO 16047:2005, Fasteners, torque/clamp force testing	Test method for K and friction coefficients.