Bolt Torque Formula & Friction Coefficients Explained | T = F x (0.16P + 0.58d2mu + 0.775dmu)
The full method behind our online torque calculator: tightening torque by T = F x (0.16P + 0.58d2mu + 0.775dmu), preload F = 0.7 x yield x stress area, for M5-M42 coarse threads; including pitch / pitch-diameter / stress-area formulas, the three friction-condition steps and the grade-to-yield lookup table.
Formula and Variables
The simplified formula applies to M5-M42 coarse metric threads; results are assembly references only - critical joints must follow design-specified torques.
Main formula: T = F x (0.16P + 0.58·d2·mu + 0.775·d·mu) - first compute the target preload from yield strength and stress area, then convert to recommended torque.
Preload utilisation: 70% of yield (the calculator default); field shortcuts take 60-75% of the proof load.
Standard coarse pitches (mm): M5=0.8, M6=1.0, M8=1.25, M10=1.5, M12=1.75, M14=2.0, M16=2.0, M20=2.5, M24=3.0, M30=3.5, M36=4.0, M42=4.5.
| Symbol | Meaning |
|---|---|
| T | Tightening torque (N·m) |
| F | Preload = 0.7 x yield x As (N) |
| P | Thread pitch (mm) |
| d2 | Pitch diameter = d - 0.6495P (mm) |
| d3 | = d - 1.2269P (mm) |
| As | Tensile stress area = pi/4 x ((d2+d3)/2)^2 (mm2) |
| mu | Overall friction coefficient (the 0.775d·mu term approximates bearing-face friction) |
Three Friction-Condition Steps (mu)
About 90% of tightening torque is eaten by friction (thread pair + bearing face); only roughly 10% becomes clamping preload. On the same M10 8.8 bolt, dropping mu from 0.20 to 0.10 nearly doubles the preload produced by a given torque - so "tighten by feel" is unreliable; use torque wrenches and keep the lubrication condition consistent in production.
The effect is large: between mu 0.10 (well lubricated) and 0.20 (dry) on the same M10 8.8 bolt, the torque needed for the same preload differs by 30-50%. Confirm the thread lubrication state and standardize the friction condition before assembly.
| Step | Friction Condition | mu |
|---|---|---|
| 1 | Well lubricated (oil, phosphated + soaped) | about 0.10 |
| 2 | Lightly oiled (normal as-shipped) | about 0.14 |
| 3 | Dry assembly (plain dry-tightened / zinc-plated unlubricated) | about 0.20 |
Grade to Yield Lookup
| Grade | Tensile (MPa) | Yield (MPa) | Typical Use |
|---|---|---|---|
| 8.8 | 800 | 640 | General machinery, steel structures |
| 10.9 | 1000 | 940 | High load, vibration service |
| 12.9 | 1200 | 1100 | Tooling, hydraulics |
| A2-70 | 700 | 450 | Corrosion-resistant, general environment |
| A4-80 | 800 | 600 | Marine / chemical, strong corrosion |
Frequently Asked Questions
The common simplified form is T = F x (0.16P + 0.58d2mu + 0.775dmu): T is tightening torque, F the preload, P the pitch, d2 the pitch diameter, mu the overall friction coefficient, and the 0.775d term approximates bearing-face friction. Preload F is typically 70% of yield strength times the tensile stress area As.
A lot: between mu 0.10 (well lubricated) and 0.20 (dry) on the same M10 8.8 bolt, the torque required for identical preload differs by 30-50%. Confirm the lubrication condition and standardize friction before assembly.
As an assembly reference, yes - but critical joints (flanges, pressure vessels, safety parts) must follow design-specified torques. For important batches, calibrate on hardware with torque-angle or ultrasonic preload measurement.
Need specific data from Bolt Torque Formula & Friction Coefficients Explained | T = F x (0.16P + 0.58d2mu + 0.775dmu)?
Submit your duty parameters (temperature, pressure, media, speed) — engineers reply with grade selection and quotation within 24 hours.