Bolt tightening torque and preload calculator

Where the tightening torque goes

Only a small part of the torque stretches the bolt and creates preload; the rest is lost as friction under the head and in the threads. A small change in friction from lubrication or plating therefore changes the preload a lot for the same torque. Unbrako gives the example of using a nut factor meant for zinc-plated bolts on cadmium-plated ones: the preload nearly doubles and the bolt can break.

Thread and bearing-face diameters

• Thread friction is taken to act at the pitch diameter d2 (from the thread size pages).
• For the bearing outer diameter Do, the minimum bearing-face diameter dw of the hex bolt or cap screw is used. With a washer, the contact outer diameter is the smaller of dw and the washer OD.
• The bearing inner diameter Di is the clearance hole. If the head turns on a washer that does not turn, use the washer’s inner diameter d1.
• For some sizes (hex bolt dw for M14, M18, M22, M27 etc., JIS B 1001 clearance holes for M1.6, M2.5, M27 and M30) no value is in the source tables, so the field stays empty — enter a value yourself.

How it is calculated

Preload from yield　F = ν × σy × As
Preload with torsion　F = ν × σy × As ÷ √(1 + 3 × [2 × (P/π + μs × d2 × 1.155) ÷ dA]²)　　dA = √(4As/π)
Simple formula　T = K × d × F
Split-friction formula　T = F/2 × (P/π + μs × d2 × sec30° + μw × Dw)　　sec30° ≒ 1.155
Equivalent bearing diameter　Dw = 2(Do³ − Di³) ÷ 3(Do² − Di²)
K from μ　K = (P/π + μs × d2 × 1.155 + μw × Dw) ÷ 2d
Tightening factor　Q = Fmax ÷ Fmin　　torque aiming at the mean T × (1 + 1/Q) ÷ 2
Stress area　As = π/4 × (d − 0.938194P)²

• The three terms are, in order, the part that creates preload (pitch), thread friction and bearing friction (the approach of JIS B 1083, as given in a JSPE journal tutorial and a Hard Lock Industry technical article). The VDI 2230 form MA = FM × (0.16P + 0.58 d2 μG + Dkm/2 × μK) is the same formula.
• For M16, class 8.8, μ = 0.12, a preload of 80.9 kN and Dw = (22.49 + 17.5)/2 give 205.2 N·m, within 0.4 % of the 206 N·m in the Bossard and Würth tables (choose “Mean” for the friction diameter to reproduce it).
• “Combined stress” gives the preload at which the combined tensile and torsional stress during tightening (distortion-energy criterion) reaches ν % of yield (formula from the JSPE tutorial). Lower friction allows a higher preload. The VDI 2230 tables (Bossard, Würth, ν = 90 %) use slightly different coefficients, so they do not match this formula exactly.
• Tightening a class 8.8 bolt of d ≤ 16 mm beyond its proof load risks stripping the nut threads (NBK note). The calculator warns when the preload exceeds the proof load or the yield load.

Typical nut factors K

The nut factor K is not a friction coefficient but a factor found by testing; plating and lubrication can change it by a factor of two or more. In the MISUMI rows the pairs are “clamped part material − internal thread material”: S10C = unhardened mild steel, SCM = hardened and tempered steel (35 HRC), FC = cast iron (FC200), AL = aluminum, SUS = stainless (SUS304).

Friction coefficient classes (VDI 2230)

Friction classes of VDI 2230 as given in Würth’s technical data. If μ is uncertain, calculate with the lowest plausible friction so the bolt is not overloaded; aim for class B, which has the least scatter. Stainless (A2/A4) on stainless has a total μ of 0.23–0.5 dry and 0.10–0.20 lubricated (Schäfer + Peters); it galls easily, so use a lubricant.

Typical tightening factors Q (αA)

Bossard uses αA = 1.6–2.0 for an ordinary torque wrench with estimated friction; its example takes M12 8.8, μ = 0.14, a maximum preload of 41.9 kN and αA = 1.8 to get a minimum preload of 23.3 kN.

Mechanical properties by property class

In N/mm². Two values such as “800 / 830” are for d ≤ 16 mm and d > 16 mm. In the class number, the part before the point × 100 is the nominal tensile strength and the part after × 10 is the yield ratio in % (10.9 → 1000 N/mm², yield 90 % of that). A2 (304-type) and A4 (316-type) have the same mechanical properties in the same class; they differ in corrosion resistance.

Related pages

Thread dimensions, tap drills and matching washers are on the thread size pages. Parallel pins are on the parallel pin page, and fits in the fits calculator.