What friction coefficient should I use for bolt torque calculations?

Use the coefficient that matches the actual surface and lubrication condition: roughly 0.14-0.20 for dry steel threads, 0.08-0.14 for lightly oiled threads, and 0.04-0.08 for MoS2-lubricated threads. Zinc-plated fasteners typically sit around 0.14. Because roughly 90% of the applied torque is consumed by friction, the friction coefficient is the single most influential input - when preload accuracy matters, use the value certified by the fastener or coating supplier.

Why can the equivalent stress exceed yield even when the tensile stress is below yield?

During tightening the bolt carries tensile stress from the preload and torsional shear stress from thread friction at the same time. The Von Mises equivalent stress combines both: sigma_e = sqrt(sigma_t^2 + 3*tau^2). For typical friction values, targeting 90% of yield in pure tension can push the combined equivalent stress 10-20% above the yield strength, which is why the calculator flags EXCEED YIELD. Reduce the stress fraction until the equivalent stress stays at or below R_p0.2.

Does the torsional stress remain in the bolt after tightening?

Mostly no. The torsional stress caused by thread friction relaxes shortly after the wrench is removed, through microscopic slip and embedding. In service, essentially only the tensile stress from the preload remains. That is why the equivalent-stress check applies to the tightening moment itself, while service calculations such as fatigue use the tensile stress only.

What is the difference between this calculator and the maximum tightening torque calculator?

This calculator works forward: you choose the initial tensile stress as a fraction of yield and it returns the torque and the resulting combined stress. The maximum tightening torque calculator works backward: you set an allowable equivalent (Von Mises) stress - typically 90-100% of yield - and it iterates to find the largest preload and torque that respect that limit, including the torsional contribution.

Why is the head friction torque calculated with 1.3 times d/2?

The friction force under the bolt head acts on an annular contact face, not at the hole edge. Its resultant acts at an effective friction radius of about 0.65 times the nominal diameter for standard hexagon heads and washer faces, which the formula expresses as mu_head x 1.3 x d/2. Flanged heads or oversized washers increase this radius and therefore the required torque.

Tightening Torque Calculator — ISO 724 / DIN 13

Thread geometry
Nominal diameter d	—
Pitch P	—
Pitch diameter d₂	—
Root diameter d₃	—
Mean stress dia. d_m	—
Tensile stress area A_t	—
A_t calc. check (π/4·d_m²)	—

Material properties & stress goals
Strength class	—
Ultimate tensile str. R_m	—
Yield strength R_p0.2	—
Applied stress fraction σ_t′	—
Tensile stress σ_t	—
Thread friction μ_thread	—
Head friction μ_head	—

Parameter	Value	Unit	Notes / formula
Thread friction torque M_G	—	N·m	Torque to overcome helical thread friction
Head/face friction torque M_WD	—	N·m	M_WD = F_i × μ_head × 1.3 × d/2
Total tightening torque M_A	—	N·m	M_A = M_G + M_WD
Torsional stress τ	—	MPa	τ = M_G / (π/16 × d₃³) — relaxes after tightening
Tensile stress σ_t	—	MPa	σ_t = σ_t′ × R_p0.2
Von Mises equiv. stress σ_e	—	MPa	σ_e = √(σ_t² + 3τ²)
Yield strength R_p0.2	—	MPa	σ_e must stay ≤ R_p0.2

(1) Torsional stress relaxes after tightening — only tensile stress remains in service.

(2) Equivalent stress must stay ≤ R_p0.2.

About this calculator

This tool answers the everyday assembly question: how much torque do I apply to reach a chosen bolt preload? You select a metric coarse thread (M6–M42), a strength class from EN ISO 898-1, the target initial tensile stress as a fraction of the yield strength R_p0.2, and the friction coefficients for the thread and the head bearing face. The calculator returns the tightening torque M_A, the preload F_i, and — crucially — the combined Von Mises stress during tightening, so you can see immediately whether your target preload is actually achievable without yielding the bolt.

If you want to work the other way around — start from an allowable equivalent stress and find the largest safe torque — use the companion Maximum Tightening Torque Calculator, which solves the same equations iteratively for the preload limit.

Theory: from preload to torque

The torque applied by the wrench is consumed by three effects: stretching the bolt (useful work, typically only ~10%), friction in the thread, and friction under the head or nut face. The calculator splits the total into the thread torque M_G and the head friction torque M_WD:

M_A = M_G + M_WD

The preload follows directly from the chosen tensile stress and the tensile stress area of the thread:

F_i = σ_t · A_t, A_t = (π/4)(d − 0.938194 P)²

The thread torque uses the inclined-plane model of the screw with the ISO metric flank angle of 60° (half-angle 30°), where λ is the thread lead angle at the pitch diameter d₂:

M_G = F_i · (d₂/2) · (tan λ + μ_thread/cos 30°) / (1 − μ_thread tan λ/cos 30°), tan λ = P/(π d₂)

The head friction torque assumes the friction resultant acts at an effective radius of 0.65 d, appropriate for standard hexagon heads and washer faces:

M_WD = F_i · μ_head · 1.3 · d/2

While the wrench is turning, the thread friction torque also twists the bolt shank. The torsional shear stress in the thread root section and the resulting Von Mises equivalent stress are:

τ = M_G / (π/16 · d₃³), σ_e = √(σ_t² + 3τ²) ≤ R_p0.2

The equivalent stress is the quantity that must stay at or below yield during tightening. The torsional part relaxes shortly after tightening, so in service only the tensile stress remains — this is why fatigue and clamping checks elsewhere on this site use σ_t alone.

Standards used

ISO 724 / DIN 13 T1 — basic dimensions of ISO metric coarse threads: pitch diameter d₂ = d − 0.649519 P and root diameter d₃ = d − 1.226869 P.
ISO 262 / DIN 13 — first-choice nominal diameter and pitch combinations (M6 to M42, coarse pitch).
EN ISO 898-1 — nominal tensile strength R_m and 0.2% proof strength R_p0.2 for strength classes 3.6 through 12.9, and the tensile stress area formula A_t.

Worked example: M12, class 8.8, 70% preload

Take an M12 coarse bolt (P = 1.75 mm), strength class 8.8 (R_p0.2 = 640 MPa), lightly oiled so μ_thread = μ_head = 0.12, tightened to an initial tensile stress of 70% of yield.

Thread geometry: d₂ = 12 − 0.649519 × 1.75 = 10.863 mm; d₃ = 12 − 1.226869 × 1.75 = 9.853 mm; A_t = (π/4)(12 − 0.938194 × 1.75)² = 84.27 mm². Lead angle λ ≈ 2.94°.
Target stress and preload: σ_t = 0.70 × 640 = 448 MPa; F_i = 448 × 84.27 = 37.75 kN.
Thread torque: M_G = 39.21 N·m; head friction torque: M_WD = 37 753 × 0.12 × 1.3 × 0.006 = 35.34 N·m.
Total tightening torque: M_A = 39.21 + 35.34 = 74.5 N·m.
Stress check: τ = 208.7 MPa, so σ_e = √(448² + 3 × 208.7²) = 575.7 MPa — a utilisation of 90.0% of R_p0.2. OK.

Note what happens if you push the slider to 90% instead: the preload rises, but the combined equivalent stress reaches about 740 MPa — 116% of yield — and the calculator flags exceed yield. With μ = 0.12, roughly 70% tensile utilisation is the practical ceiling for torque-controlled tightening of this joint; this illustrates why the torsion term cannot be ignored when specifying assembly torques.

Assumptions and limitations

Coarse-pitch ISO metric threads only; fine pitches have smaller lead angles and slightly different stress areas.
Friction coefficients are assumed constant during tightening. Real scatter of ±20–30% on μ translates almost directly into preload scatter — this is inherent to torque-controlled tightening.
The head friction radius 0.65 d applies to standard hexagon heads and plain washers; flanged bolts need a larger effective radius.
Nominal EN ISO 898-1 properties are used; for sizes above M16 some classes have slightly different guaranteed values (e.g. 8.8 rises to R_p0.2 = 660 MPa).
Results are for reference; verify safety-critical joints against VDI 2230 or test data.

Frequently asked questions

What friction coefficient should I use?

Match the actual surface and lubrication state: dry steel 0.14–0.20, lightly oiled 0.08–0.14, MoS₂ paste 0.04–0.08, zinc-plated around 0.14. Since ~90% of the torque goes into friction, this input dominates the result — for critical joints use the value certified by the fastener or coating supplier.

Why can the equivalent stress exceed yield when the tensile stress is below yield?

During tightening the bolt sees tension and torsion simultaneously, combined as σ_e = √(σ_t² + 3τ²). With typical friction, targeting 90% of yield in pure tension pushes the combined stress 10–20% above R_p0.2. Reduce the stress fraction until the utilisation bar stays at or below 100%.

Does the torsional stress stay in the bolt after tightening?

Mostly no — it relaxes shortly after the wrench is removed through micro-slip and embedding. In service essentially only the tensile preload stress remains, which is why fatigue checks use σ_t alone.

How is this different from the maximum tightening torque calculator?

Here you choose the tensile stress and get the torque plus a yield check. The maximum tightening torque calculator inverts the problem: you set the allowable equivalent stress (e.g. 100% of R_p0.2 for tightening to yield) and it solves for the largest admissible preload and torque.

Why is the head friction torque based on 1.3 × d/2?

The friction force under the head acts on an annular face whose resultant sits at an effective radius of about 0.65 d for standard hexagon heads and washer faces — written in the formula as μ_head × 1.3 × d/2. Flange heads or large washers increase this radius and the required torque.

Tightening Torque Calculator

User inputs

Thread & material parameters (ISO 724)

Key results

Stress & torque breakdown