Bolt Torque Calculator: Preload, Tightening Torque and Thread Stress (ISO 898-1, SAE J429, VDI 2230)
Choose a metric (ISO 261 and ISO 262) or unified inch (ASME B1.1) thread, a grade from ISO 898-1, SAE J429, ASTM F3125, ASTM A193, ISO 3506-1 stainless or a common aerospace alloy, and a target preload as a percentage of proof load. The calculator returns the tensile stress area, proof load and preload, and the tightening torque two ways: the short-form nut factor relation T = K F d and the thread-geometry relation of VDI 2230 with separate thread and bearing friction, split into the part that stretches the bolt and the parts lost to friction. It shows how far the preload can spread for the same torque when friction scatters, and checks the combined tension and torsion in the thread during tightening against yield. Values are SI by default (mm, kN, N·m, MPa) with an inch toggle for in, lbf, lbf·ft and ksi. The inputs are stored in the page URL so a case can be shared, exported as CSV or printed as a report.
Thread and grade
Preload
Method A, nut factor
Method B, thread geometry (VDI 2230)
Results
Tightening torque
for 36.66 kN preload, 75.0 % of the 48.87 kN proof load
Method A, nut factor
T = K F d, K 0.200
87.97 N·m
64.89 lbf·ft
Method B, thread geometry
VDI 2230, μ_th 0.120, μ_b 0.120
70.53 N·m
52.02 lbf·ft
Equivalent K 0.160
Thread
| Thread | M12 × 1.75 |
|---|---|
| Standard | ISO 261 coarse |
| Pitch P (mm) | 1.750 |
| Pitch diameter d2 (mm) | 10.863 |
| Minor diameter d3 (mm) | 9.853 |
| Tensile stress area As (mm²) | 84.27 |
Grade and preload
| Grade | Class 8.8 |
|---|---|
| Proof stress (MPa) | 580.0 |
| Yield strength (MPa) | 640.0 |
| Tensile strength (MPa) | 800.0 |
| Proof load (kN) | 48.87 |
| Target preload (kN) | 36.66 |
| Preload, % of proof load (%) | 75.0 |
Preload scatter
| Friction scatter (%) | ±20 |
|---|---|
| Thread friction range | 0.096 to 0.144 |
| Bearing friction range | 0.096 to 0.144 |
| Minimum preload (high friction) (kN) | 31.31 |
| Maximum preload (low friction) (kN) | 44.21 |
| Band, % of proof load (%) | 64.1 to 90.5 |
Preload for the method B torque when both friction coefficients vary by the scatter.
Thread stress during tightening
Pass| Tensile stress σ (MPa) | 435.0 |
|---|---|
| Torsional stress τ (MPa) | 174.0 |
| Von Mises σ_vm (MPa) | 529.2 |
| Utilisation against yield | 0.827 |
| Check | Pass |
Torque
| Method A, nut factor K 0.200 (N·m) | 87.97 |
|---|---|
| Method A, other unit (lbf·ft) | 64.89 |
| Method B, VDI 2230, μ_th 0.120, μ_b 0.120 (N·m) | 70.53 |
| Method B, other unit (lbf·ft) | 52.02 |
| Equivalent K of method B | 0.160 |
| Bearing friction diameter D_km (mm) | 14.800 |
| Pitch torque (14.6 %) (N·m) | 10.26 |
| Thread friction torque (39.3 %) (N·m) | 27.72 |
| Bearing friction torque (46.2 %) (N·m) | 32.55 |
Method B split: only the pitch part stretches the bolt. Torque values are estimates; check critical joints by test.
Every value below uses the inputs above and updates as you edit them. The lines work in mm, kN and MPa (1 MPa × 1 mm² = 1 N, 1 kN × 1 mm = 1 N·m), so each product closes without hidden factors.
1. Thread geometry and stress area
A 60° thread is fixed by its nominal diameter and pitch. The pitch diameter sits where the thread and the gap are equally wide; the minor diameter is the root. The tensile stress area uses a diameter between the two, which matches the strength of a threaded rod in tension tests.
Pitch diameter: d2 = d − 0.649519 P = 12.000 − 0.649519 × 1.750 = 10.863 mm
Minor diameter: d3 = d − 1.226869 P = 12.000 − 1.226869 × 1.750 = 9.853 mm
Stress area (ISO 898-1): As = π/4 × ((d2 + d3)/2)² = π/4 × ((10.863 + 9.853)/2)² = π/4 × 10.358² = 84.27 mm²
2. Proof load and target preload
The proof load is the force the bolt must carry without permanent set. The target preload is a share of it: high enough to keep the joint closed, with a margin for the torsion added while tightening.
Proof load: F_p = S_p × As = 580.0 MPa × 84.27 mm² = 48.87 kN
Target preload: F = 75.0 % × 48.87 = 36.66 kN
3. Torque, method A and method B
Method A folds all the friction into one nut factor K. Method B keeps the three parts apart: the pitch term that stretches the bolt, friction in the thread, and friction under the head or nut at the mean bearing diameter.
Method A: T = K F d = 0.200 × 36.66 kN × 12.000 mm = 87.97 N·m
Bearing diameter: D_km = (d_w + d_h) / 2 = (16.600 + 13.000) / 2 = 14.800 mm
Method B: T = F (0.16 P + 0.58 d2 μ_th + D_km/2 μ_b) = 36.66 kN × (0.16 × 1.750 + 0.58 × 10.863 × 0.120 + 14.800 / 2 × 0.120) mm = 36.66 × 1.9241 = 70.53 N·m
Split: pitch 10.26 N·m (14.6 %), thread friction 27.72 N·m (39.3 %), bearing friction 32.55 N·m (46.2 %)
Equivalent K: K = T / (F d) = 70.53 N·m / (36.66 kN × 12.000 mm) = 0.160
4. Friction scatter
A torque wrench controls torque, not preload. With the torque fixed, lower friction than expected gives more preload and higher friction less. Scaling both friction coefficients by the scatter gives the range to expect.
Friction range: ±20 %: μ_th 0.096 to 0.144, μ_b 0.096 to 0.144
Maximum preload: F = 70.53 N·m / (0.16 × 1.750 + 0.58 × 10.863 × 0.096 + 14.800 / 2 × 0.096) = 44.21 kN
Minimum preload: F = 70.53 N·m / (0.16 × 1.750 + 0.58 × 10.863 × 0.144 + 14.800 / 2 × 0.144) = 31.31 kN
Band: 31.31 to 44.21 kN, −14.6 % to +20.6 % around the target
5. Thread stress during tightening
While the nut turns, the thread carries the preload in tension and the thread torque in torsion. Von Mises combines the two; compared with the yield strength it shows how close tightening comes to yielding the bolt.
Tension: σ = F / As = 36.66 kN × 1000 / 84.27 mm² = 435.0 MPa
Thread torque: T_th = F (0.16 P + 0.58 d2 μ_th) = 37.98 N·m (method B without the bearing friction)
Torsion: τ = T_th / (π d0³ / 16), d0 = (d2 + d3) / 2 = 10.358 mm: τ = 174.0 MPa
Von Mises: σ_vm = √(σ² + 3τ²) = √(435.0² + 3 × 174.0²) = 529.2 MPa
Utilisation: σ_vm / R_p0.2 = 529.2 / 640.0 = 0.827, below the 0.9 warning line
Method
Thread geometry. For a 60° thread of nominal diameter d and pitch P the basic pitch diameter is d2 = d − 0.649519 P and the minor diameter of the external thread is d3 = d − 1.226869 P (ISO 724, ASME B1.1). The tensile stress area is As = π/4 × ((d2 + d3)/2)² for metric threads (ISO 898-1:2013) and As = 0.7854 (d − 0.9743/n)² for inch threads with n threads per inch (ASME B1.1-2019). For the ISO coarse series the formula reproduces the ISO 898-1 tabulated As within 0.5 %.
Proof load and preload. The proof load is the proof stress times the stress area, F_p = S_p × As, with S_p from ISO 898-1:2013 (class 8.8: 580 MPa up to M16 and 600 MPa above), SAE J429 or ASTM F3125. For ASTM A193 B7, ISO 3506-1 stainless and the aerospace alloys, which have no proof stress in the same sense, S_p is taken as 0.9 × yield. The target preload is a percentage of the proof load, 75 % by default, or a force entered directly.
Torque, method A (short form). T = K F d, where K is the nut factor. K lumps together thread and bearing friction and the thread geometry; typical values are 0.20 for dry or zinc-plated steel, 0.15 oiled, 0.16 cadmium, 0.12 with molybdenum disulphide paste and 0.10 with PTFE or wax (Bickford; Shigley).
Torque, method B (thread geometry). VDI 2230 Part 1:2015 gives the tightening torque as the sum of the pitch torque, the thread friction torque and the bearing friction torque. For a 60° thread this simplifies to the Motosh form T = F (0.16 P + 0.58 d2 μ_th + (D_km / 2) μ_b), where μ_th and μ_b are the thread and bearing friction coefficients and D_km = (d_w + d_h)/2 is the effective bearing diameter from the head bearing diameter d_w and the clearance hole d_h. Only the pitch term, typically 10 to 15 % of the total, stretches the bolt. The equivalent nut factor is T / (F d).
Scatter and thread stress. With the torque fixed at the method B value, the preload is recalculated with both friction coefficients multiplied by 1 ± the scatter (±20 % by default), giving the preload band a torque wrench actually produces. During tightening the thread carries the preload and the thread torque T_th = F (0.16 P + 0.58 d2 μ_th): σ = F / As, τ = T_th / (π d0³ / 16) with d0 = (d2 + d3)/2, and the von Mises stress σ_vm = √(σ² + 3τ²) is compared with the yield strength (VDI 2230-1, section 5.5.1). The calculator warns above 90 % utilisation.
Assumptions
- Torque-tension relations are estimates. Real preload scatter with a torque wrench is typically ±25 %, more with unknown lubrication or reused parts.
- Friction values are typical. They depend on surface finish, plating, lubrication and the number of times the fastener has been tightened.
- The thread-geometry method assumes 60° threads and a uniform bearing pressure between d_h and d_w.
- Preload percentage is of the proof load. For grades without a tabulated proof stress the proof stress is taken as 0.9 × yield.
- No joint stiffness, embedding or external load analysis. That is a separate joint calculation (VDI 2230 in full).
- Aerospace material strengths (A286, Ti-6Al-4V, Inconel 718) are typical minimums for the strength class; the procurement specification governs.
- Default bearing and hole diameters: ISO 4017 hex head washer face and ISO 273 fine series holes for metric sizes, approximate hex cap screw bearing faces and normal clearance holes for inch sizes. Enter your own values where they differ.
Standards and references
| Standard | Note |
|---|---|
| ISO 898-1:2013, Mechanical properties of fasteners made of carbon steel and alloy steel, Part 1: Bolts, screws and studs | Property classes 4.6 to 12.9: proof stress, yield and tensile strength; tensile stress area formula and tabulated As and proof loads. |
| ISO 3506-1:2020, Fasteners, Mechanical properties of corrosion-resistant stainless steel fasteners, Part 1 | A2-70 and A4-80 yield and tensile strength. |
| ISO 261:1998 and ISO 262:1998, ISO general purpose metric screw threads | Coarse and selected fine pitches, M3 to M64. |
| ISO 273:1979, Clearance holes for bolts and screws | Fine series hole diameters used as the default d_h. |
| ISO 4017:2022, Hexagon head screws | Minimum washer-face diameter d_w used as the default bearing diameter. |
| ASME B1.1-2019, Unified inch screw threads (UN, UNR and UNJ thread form) | UNC and UNF series and the tensile stress area As = 0.7854 (d − 0.9743/n)². |
| ASME B18.2.1-2012, Square, hex, heavy hex and askew head bolts and hex, heavy hex, hex flange, lobed head and lag screws | Hex head across-flats for the inch bearing diameter. |
| SAE J429, Mechanical and material requirements for externally threaded fasteners | Grades 2, 5 and 8 proof, yield and tensile strength by size. |
| ASTM F3125/F3125M-19, High strength structural bolts and assemblies | Grades A325 and A490. |
| ASTM A193/A193M, Alloy-steel and stainless steel bolting for high temperature or high pressure service | Grade B7 yield and tensile strength. |
| RCSC, Specification for Structural Joints Using High-Strength Bolts, 2020 | Table 8.1 minimum bolt pretension. |
| VDI 2230 Part 1:2015, Systematic calculation of highly stressed bolted joints | Tightening torque with separate thread and bearing friction, friction classes, stress during tightening. |
| Motosh, N., Development of design charts for bolts preloaded up to the plastic range, J. Eng. Ind., 1976 | The 0.16 P + 0.58 d2 μ_th + (D_km/2) μ_b torque-tension relation. |
| Bickford, J. H., An Introduction to the Design and Behavior of Bolted Joints, 4th ed., CRC Press, 2008 | Nut factors, preload scatter and torque control. |
Worked example: M12 × 1.75 class 8.8 at 75 % of proof load
An M12 × 1.75 coarse class 8.8 hex head screw (ISO 898-1 proof stress 580 MPa, yield 640 MPa) is tightened to 75 % of its proof load. Nut factor K = 0.20 for method A; thread and bearing friction μ = 0.12 for method B; head bearing diameter 16.6 mm (ISO 4017) and clearance hole 13.0 mm (ISO 273 fine). This is the default case loaded in the calculator.
| Result | Value |
|---|---|
| Pitch diameter d2 / minor diameter d3 | 10.863 / 9.853 mm |
| Tensile stress area As | 84.27 mm² (ISO 898-1 tabulates 84.3) |
| Proof load (580 MPa) | 48.87 kN (ISO table 48.9 kN) |
| Target preload | 36.66 kN |
| Torque, method A (K 0.20) | 87.97 N·m |
| Torque, method B (μ 0.12) | 70.53 N·m |
| Equivalent K of method B | 0.160 |
| Method B split: pitch / thread / bearing | 10.26 / 27.72 / 32.55 N·m |
| Preload band at 70.53 N·m, friction ±20 % | 31.31 to 44.21 kN |
| Thread stress σ / τ / von Mises | 435.0 / 174.0 / 529.2 MPa |
| Utilisation against yield (640 MPa) | 0.827 |
Frequently asked questions
What torque should I use for an M12 8.8 bolt?
For 75 % of proof load (36.66 kN) the calculator gives 87.97 N·m with a dry nut factor of 0.20 and 70.53 N·m with the VDI 2230 thread-geometry method at μ 0.12. The difference is the friction assumption, not an error: K 0.20 corresponds to μ of about 0.16. Use the value that matches your lubrication, and check it with a torque-tension test if the preload matters.
Why do method A and method B give different torques?
Method A uses one nut factor K that hides the friction. Method B uses the thread pitch, the pitch diameter, the bearing diameter and separate friction coefficients for the thread and under the head. For the same friction they agree; K 0.20 is roughly μ 0.16 on a coarse thread, while μ 0.12 gives K of about 0.16. The equivalent K shown under method B lets you compare them directly.
What preload percentage should I use?
About 75 % of proof load is common for reusable joints and is the default here. Up to 90 % is used for permanent joints and where the assembly process is well controlled. Structural bolts to RCSC use a minimum pretension of 70 % of the minimum tensile strength, which is close to 100 % of proof load for A325.
How much does friction scatter change the preload?
A lot. With the default ±20 % friction scatter the M12 example tightened to 70.53 N·m ends up between 31.31 and 44.21 kN, about −15 % to +21 % around the 36.66 kN target. That is why torque control alone gives a preload scatter of about ±25 % in practice, and why critical joints use angle control, direct tension indicators or bolt elongation.
What is the thread stress utilisation?
While the bolt is being tightened the thread is in tension from the preload and in torsion from the thread friction torque. The calculator combines them with von Mises and compares the result with the yield strength. Above 90 % it warns, because friction lower than expected or a small overshoot can yield the bolt. The torsion relaxes after tightening, so the service stress is lower.
Can I use a metric bolt with inch units?
Yes. The thread standard follows the unit toggle until you set it yourself; after that you can show an M12 in inches, lbf and lbf·ft, or a 1/2-13 in mm and N·m. The engine always works in mm and N and converts only for display.
Are the aerospace grade strengths exact?
No. A286, Ti-6Al-4V and Inconel 718 are listed at typical minimums for the 160 and 180 ksi strength classes, and marked as typical. Aerospace fasteners are bought to a procurement specification (NAS, AS or a company standard) whose values govern. Enter the specification values as a custom preload if they differ.