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Bolt Torque Calculator

Tightening torque and preload for ISO metric bolts, with a VDI 2230 stress check.

Find the tightening torque for a target preload on M6 to M36 coarse-thread bolts in property classes 8.8, 10.9 and 12.9. The calculator uses ISO 898-1 proof stresses and the thread and head friction torque equation, not a single rule-of-thumb nut factor.

  • Live results
  • Full step-by-step working
  • PASS / FAIL checks
  • Free PDF report

Inputs

75% reusable joints, 90% permanent joints

Results

Tightening torque
83.01 N·m
Preload Fi
36.66 kN
Nut factor K
0.189
Yield utilisation ν
86.1 %
PASS
Step-by-step calculation (8 steps)
  1. 1Thread geometry
    Formulad₂ = d − 0.6495·P, d₃ = d − 1.2269·P
    Solutiond₂ = 12 − 0.6495 × 1.75, d₃ = 12 − 1.2269 × 1.75
    Resultd₂ = 10.86 mm, d₃ = 9.853 mm
  2. 2Tensile stress area (ISO 898-1)
    FormulaAs = (π/4)·((d₂ + d₃)/2)²
    SolutionAs = 0.7854 × ((10.86 + 9.853)/2)²
    ResultAs = 84.27 mm²
  3. 3Proof load
    FormulaFp = Sp·As
    SolutionFp = 580 × 84.27
    ResultFp = 48.87 kN
  4. 4Target preload (clamp force)
    FormulaFi = k·Fp
    SolutionFi = 0.75 × 48875
    ResultFi = 36.66 kN
  5. 5Tightening torque
    FormulaT = Fi·(0.16·P + 0.58·μ·d₂ + μ·Dkm/2)
    SolutionT = 36656 × (0.16 × 1.75 + 0.58 × 0.14 × 10.86 + 0.14 × 15.75/2) = 36656 × (0.28 + 0.882 + 1.1)
    ResultT = 83.01 N·m
  6. 6Torque split
    Formulapitch : thread friction : head friction
    Solution0.28 : 0.882 : 1.1 mm
    Result12.4% : 39% : 48.7%
  7. 7Equivalent nut factor
    FormulaK = T / (Fi·d)
    SolutionK = 83011 / (36656 × 12)
    ResultK = 0.189
  8. 8Combined stress during tightening (VDI 2230)
    Formulaσred = √(σ² + 3τ²), σ = Fi/As, τ = Fi·(0.16P + 0.58μd₂) / (π·ds³/16)
    Solutionσ = 435 MPa, τ = 42598 / 218.2 = 195.2 MPa, σred = √(435² + 3 × 195.2²)
    Resultσred = 551 MPa, ν = σred / Rp0.2 = 0.861 ≤ 0.90PASS

Engineering takeaways

  • About 87.6% of the torque is lost to friction. A change in lubrication changes the clamp force far more than a change in torque setting.
  • Torque wrench tightening scatters preload by roughly ±25%. Use angle-controlled or tension-controlled tightening for critical joints.
  • Use the same friction value as your actual condition. Torque tables assume a specific lubrication state.

The PDF report contains every input, formula, substitution and check shown above, in LTM calculation-sheet format.

Worked Example

The calculator also checks the combined tension and torsion stress during tightening against 90% of yield, the VDI 2230 limit, and shows how the torque splits between thread pitch, thread friction and head friction.

The calculator above opens with this example. Change any input to run your own case.

Inputs

Thread size (ISO metric coarse)M12 × 1.75
Property class (ISO 898-1)8.8
Friction coefficient μ (thread and head)0.14 zinc plated, lightly oiled
Target preload75 % of proof load

Results

Tightening torque83.01 N·m
Preload Fi36.66 kN
Nut factor K0.189
Yield utilisation ν86.1 % PASS

Bolt Torque Formulas Used

Tensile stress area

As=π4(d2+d32)2,d2=d−0.6495P, d3=d−1.2269PA_s = \frac{\pi}{4}\left(\frac{d_2 + d_3}{2}\right)^2,\quad d_2 = d - 0.6495P,\ d_3 = d - 1.2269P
  • dnominal diameter
  • Pthread pitch

Preload

Fi=k⋅Sp⋅AsF_i = k \cdot S_p \cdot A_s
  • Spproof stress (ISO 898-1)
  • ktarget fraction, 0.75 for reusable joints

Tightening torque

T=Fi(0.16 P+0.58 μ d2+μ Dkm2)T = F_i\left(0.16\,P + 0.58\,\mu\,d_2 + \mu\,\frac{D_{km}}{2}\right)
  • μfriction coefficient (thread and head)
  • Dkmmean head bearing diameter

Nut factor

K=TFi dK = \frac{T}{F_i\,d}

Tightening stress check

σred=σ2+3τ2≤0.9 Rp0.2\sigma_{red} = \sqrt{\sigma^2 + 3\tau^2} \le 0.9\,R_{p0.2}

Basis: ISO 898-1 property classes; VDI 2230 tightening torque. Results are for preliminary design and should be confirmed against supplier data and the governing standard.

Bolt Torque Calculator FAQ

What torque should I use for an M12 8.8 bolt?

With lightly oiled zinc-plated bolts (μ ≈ 0.14) and a preload of 75% of proof load, the torque is about 83 N·m. Dry plain bolts need more torque for the same clamp force; lubricated bolts need less. Always use the friction value that matches your condition.

What is the difference between proof load and yield?

Proof load is the force a bolt must carry without permanent set (580 MPa × stress area for 8.8 up to M16). Yield (Rp0.2) is higher, 640 MPa for 8.8. Preload is usually set as a percentage of proof load.

Why does friction change the torque so much?

Typically 85 to 90% of tightening torque is consumed by friction in the threads and under the head. Only 10 to 15% actually stretches the bolt. A small change in lubrication therefore changes the clamp force much more than the torque reading suggests.

What is the nut factor K?

K combines all friction and geometry effects into T = K·F·d. Dry steel gives K ≈ 0.20, lubricated about 0.15. The calculator computes K from the full equation so you can compare with tables.

Should I use 75% or 90% preload?

Use about 75% of proof load for joints that will be reopened, and up to 90% for permanent structural joints. Higher preload improves fatigue and slip resistance but leaves less margin for tightening scatter.

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