Bolt tightening torque
Tightening torque for a required preload — as a share of the bolt's yield strength — through the nut factor K, which covers the friction in the thread and under the nut.
A_s = π/4 · (d − 0.9382 · P)² (UN: d − 0.9743 · P)F = k_y · σ_y · A_sT = K · F · dT = K · F · d is an approximate relation: the scatter of K scatters the preload by up to ±30 %, so critical joints are tightened with elongation control or a hydraulic tensioner. The exact method with separate thread and head friction coefficients is VDI 2230. The preload for a known torque is in the "Bolt preload from torque" calculator.
Source: Shigley's Mechanical Engineering Design — tightening torque and nut factor; ISO 898-1 and ASME B1.1 — tensile stress area
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Coarse pitch: M12 1.75; M16 2; M20 2.5; M24 3; M30 3.5; M36 4 mm. Inch threads: pitch = 25.4 / threads per inch (8UN: 3.175 mm).
ISO 898-1: class 5.6 300 MPa; 8.8 640 (d ≤ 16 mm) and 660 MPa (d > 16 mm); 10.9 940; 12.9 1 100. ASTM A193 B7 studs (d ≤ 64 mm): 725 MPa.
Reusable joints: about 70 % (Shigley: 75 % of the proof load); flanges: from the flange design, usually 40–70 %.
Per Shigley: plain black steel 0.30; zinc-plated 0.20; lubricated 0.18; cadmium-plated 0.16; with anti-seize compound 0.12. Condition not known: 0.20.
Unit converter for this formulaLength · Pressure · Torque · Force and load · Area · Fraction and percent
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- F — Preload–
- A_s — Tensile stress area–
More in Strength and bolting
Hoop and longitudinal stresses in the cylindrical shell of a vessel or pipe under internal pressure, the required wall thickness and the allowable pressure per GOST 34233.2 with the weld joint efficiency and allowances.
Preload and stress in a bolt or stud for a known wrench torque, and their share of the yield strength.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.