Tightening torque and preload calculator — allowable torque, set torque, preload range
Enter size, property class, head type, friction range and torque scatter to get the maximum allowable torque, the set torque with its scatter band, and the preload range. Simplified VDI 2230.
"How many N·m should I tighten to?" is the question we hear most from design and assembly. Enter size, property class, head type, friction range and torque scatter, and this calculator returns the maximum allowable torque, the set torque with its scatter band and the preload range. The calculation follows a simplified form of the German bolted-joint guideline VDI 2230.
Scope: metric coarse-thread hexagon bolts, socket head cap screws and pan head machine screws with a defined property class (4.8–12.9, A2-50–A2-80), sizes M2–M8 (including M2.3 and M2.6). It does not cover all machine screws.
By size — same conditions
How to read the results
- Maximum allowable torque — the allowable assembly torque for the friction range and dimensional assumptions entered. It is taken at the most unfavourable independent combination of thread friction (μG) and under-head friction (μK), and the bolt is checked at 41 × 41 evaluation points to stay within the permissible assembly preload (combined tension and torsion during tightening, 90% of yield). Low friction raises preload and high thread friction raises torsion, so the worst combination depends on the case; in high-friction ranges such as dry stainless, "maximum thread friction + minimum under-head friction" can be the worst.
- Set torque — the maximum allowable torque reduced by the torque scatter, so that even a high-side torque stays within the maximum. A ±6% torque scatter is scatter of torque, not of preload (the friction range adds to it). Before writing it into a work standard, confirm it with the actual parts together with the scatter band shown.
- Preload range — the same set torque gives scattered preload because of friction and torque scatter. Minimum preload is at maximum friction on both surfaces and low-side torque; maximum preload is at minimum friction on both and maximum torque. Use minimum preload to check clamping, and maximum preload to check bolt and part strength.
Our stainless products are acid cleaned and shipped without rust-preventive oil, wax or lubricant film. This condition (unlubricated austenitic) is VDI 2230 friction class E, which sets friction only as 0.30 or more with no upper limit; the acid-cleaned condition alone does not guarantee a consistent friction coefficient. The calculator takes the maximum allowable torque at the most unfavourable independent combination of thread and under-head friction within 0.30–0.50, and minimum preload at the upper limit on both. The upper limit of 0.50 is an assumption, not a measurement. Because preload scatters widely at the same torque, confirm important joints by tightening tests on the actual parts. Watch for thread galling too (more on galling).
Why most of the torque goes into friction, and how much preload changes at the same torque, are shown with a graph in Most tightening torque goes into friction.
What this calculator does not cover
- Flat and raised countersunk heads — the higher seat friction of a conical seat can be calculated: with ideal conical contact and the same preload, seat friction coefficient and effective friction diameter, the seat friction term of a 90° countersink is about 1.41 times that of a flat seat (not 1.41 times the total torque). But the head geometry does not guarantee that the head carries the property class. KS B 0233 (mechanical properties of steel bolts and screws) states in its scope that screws such as countersunk, raised countersunk and cheese heads may not meet the tensile and torsional requirements because the head shape reduces the shear area. The allowable torque here comes from the property class, so for a countersunk head it could be a value at which the head fails first. That is why they are excluded; we will review the scope again once we have breaking-load, torsion and torque–preload test data for our countersunk products.
- Other heads and screws — truss, binding and round heads, precision screws, SEMS (the washer changes the under-head contact), tapping and trilobular thread-forming screws, fine threads and products without a property class are not calculated.
- Number of bolts and external loads — how many bolts a load needs depends strongly on joint stiffness and embedding loss (preload lost as contact surfaces settle just after tightening). This will be added once the basis for both is confirmed.
- Under-head surface pressure — to be added once the basis for the under-head contact dimensions is confirmed.
- Vibration, cyclic load, fatigue and loosening — not covered.
- Plastic and thin-sheet joints, tapping screws — plastics lose preload over time by creep, so this formula does not apply. We plan to publish our own tightening and failure torque data by pilot-hole diameter separately.
- Thread stripping — check engagement length separately using engagement length and tap depth.
Show basis and assumptions
Permissible assembly preload FMzul(μG) = 0.9 · Rp0.2 · As / √(1 + 3k²), k = 1.5 · d2/d0 · (P/(π·d2) + 1.155·μG)
Torque–preload MA = F · X(μG, μK), X = 0.16·P + 0.58·d2·μG + μK·Dkm/2, Dkm = (dw + dh)/2
Maximum allowable torque MAmax = min FMzul(μG) · X(μG, μK) (μG and μK independent within the range)
Set torque MAset = MAmax / (1 + ε), scatter band MAset·(1 − ε) to MAset·(1 + ε)
Preload range FMmax = MAmax / X(μmin, μmin), FMmin = MAset · (1 − ε) / X(μmax, μmax)
- Thread assembly stress: the permissible assembly preload combines tension and torsion during tightening at 90% utilisation of yield. Only the threaded section (stress area) is checked — not the head, drive recess or mating thread. Class 4.8 has no minimum 0.2% proof stress in ISO 898-1, so the value the standard gives for calculation, 340 N/mm² (Rpf, not a test value), is used in place of Rp0.2. Results for 4.8 are therefore weaker reference values than for 8.8 and above; confirm important joints by tightening tests. At the maximum allowable torque, the 41 × 41 grid (corners included) over the μG and μK ranges is checked against this limit and the maximum utilisation and its location are shown. This does not mathematically guarantee every point between grid points.
- Friction: thread (μG) and under-head (μK) friction are treated as independent within the same range. Ranges are the VDI 2230 friction classes (Würth technical data, section 6.3 table, p.1790), not measurements of our products. Class E is defined only as 0.30 or more, so the upper limit of 0.50 is an assumption. The steel default "electro-zinc + chromate (trivalent or hexavalent), unlubricated" is our steel products' shipped condition; the VDI table lists unlubricated zinc coatings under both C (0.14–0.24) and D (0.20–0.35), so the combined 0.14–0.35 is used (the table does not distinguish chromate types). Top-coated (with lubricant) or oiled parts may be closer to class B; nickel over zinc has a nickel contact surface not listed in the table, so use direct input. Examples by class follow the material of the property class — steel (4.8–12.9) shows plain, black, phosphate and zinc coatings; stainless (A2) shows austenitic examples, and class A, which has no stainless example in the table, cannot be chosen for stainless.
- Torque scatter ε: the default ±6% is an assumption for preliminary calculation. Tool accuracy and the torque scatter in real assembly differ, so enter values matching your tool's specification, calibration and assembly conditions. It is not changed automatically with torque size.
- Contact dimensions: coarse thread, clearance holes ISO 273 medium. M2.3 and M2.6 are KS B 1023 annex sizes (pitch 0.4, 0.45); ISO 273 has no hole for them, so nominal diameter + 0.4 mm is assumed, as for neighbouring sizes. Hexagon bolts use dw min from KS B 1002:2016 Tables 10 and 14 (product grade A, M3 and above); socket head cap screws use KS B 1003:2015 Table 1 (no M2.3 or M2.6). Pan heads use dk and da from the KS B 1023 annex (Table A.1) followed by domestic production, and the under-head contact diameter is assumed to be dk (dk minimum for maximum allowable torque, dk basic for minimum preload). The outer edge of the pan head underside is not defined in the standard, so pan head results are preliminary values under this assumption.
- Formula check: permissible preload and tightening torque were checked against the VDI 2230-based reference table in Würth technical data (DINO technical part, ch. 6 "Dimensioning metric screw assemblies", Tab. 5): sizes M4–M8 within the calculator range, classes 8.8, 10.9 and 12.9, seven friction values from 0.08 to 0.24 — 84 conditions in all, calculated with hexagon bolt heads (KS B 1002 dimensions) and μG = μK (the table's condition). The largest absolute differences recorded were 1.32% for preload and 5.31% for torque; excluding one torque outlier whose source needs checking, the largest torque difference over the remaining 83 is 2.06%. This checks the preload and torque formulas, not real joint performance. Stainless (A2), pan heads, friction of 0.30 or more and μG ≠ μK are outside this check.
Results are preliminary values for early design review, not guaranteed values. Confirm important joints by tightening tests with the actual parts and tools. Tell us your conditions and we will review size, property class and finish with you. Specification enquiry
FAQ
Can I put the calculator's torque straight onto a drawing?
The maximum allowable torque is the allowable assembly torque for the friction range and dimensional assumptions entered, checked at 41 × 41 points against the permissible assembly preload. The set torque is that value reduced by the torque scatter. Both are calculated for assumed friction and scatter, so confirm them with the actual parts and tools before writing them into a work standard.
Why does the same torque give different preload?
Most of the torque is consumed by thread and under-head friction. Friction scatters within its range and the applied torque scatters too, so the same set torque gives a range of preload. Check clamping with the minimum preload and strength with the maximum.
What friction coefficient applies to stainless bolts?
Unlubricated stainless is VDI 2230 friction class E, defined only as 0.30 or more with no upper limit. The calculator takes the maximum allowable torque at the most unfavourable independent combination of thread and under-head friction, and minimum preload at the upper limit on both (an assumed 0.50). The acid-cleaned condition alone does not guarantee a consistent friction coefficient.
How do I convert N·m to kgf·cm?
1 N·m is about 10.2 kgf·cm; for example, 2.0 N·m is about 20.4 kgf·cm.
References
- VDI 2230 Blatt 1:2015 Systematic calculation of highly stressed bolted joints — Joints with one cylindrical bolt — permissible assembly preload (tension and torsion, 90% yield), tightening torque, friction classes A–E
- Würth Industrie, DINO technical part, ch. 6 "Dimensioning metric screw assemblies" — 6.3 friction class table (p.1790), Tab. 5 assembly preload and tightening torque per VDI 2230 (p.1791, used to check the formulas)
- ISO 898-1:2013 Fasteners — Mechanical properties of fasteners made of carbon steel and alloy steel — Part 1: Bolts, screws and studs with specified property classes — minimum yield and tensile strength of 4.8, 8.8, 10.9, 12.9
- ISO 3506-1:2020 Fasteners — Mechanical properties of corrosion-resistant stainless steel fasteners — Part 1: Bolts, screws and studs with specified grades and property classes — minimum proof and tensile strength of A2-50, A2-70, A2-80
- ISO 273:1979 Fasteners — Clearance holes for bolts and screws — clearance hole diameter (medium series)
- KS B 0233:2000 Mechanical properties of steel bolts and screws (ISO 898-1:1999) — scope: countersunk and similar heads may not meet the tensile and torsional requirements because of head geometry
- KS B 1002:2016 Hexagon head bolts, Tables 10 and 14 (product grade A) — bearing face diameter dw
- KS B 1003:2015 Hexagon socket head cap screws, Table 1 — bearing face diameter dw
- KS B 1023:2016 Cross-recessed machine screws, Annex Table A.1 — pan head diameter dk and tolerance, under-head fillet r and da
Last revised 2026-10-12