Inputs
Nominal thread diameter d, pitch P, bearing friction diameter Db, and measured preload F and tightening torque T; optionally separately measured thread and bearing torque.
Bolted joints · torque-tension test
ISO 16047 Friction Coefficient Calculator for Torque-Tension Tests
Unlike the tightening-torque and preload calculators, which start from assumed friction values, this calculator evaluates an actual torque-tension test: from preload F and tightening torque T measured on the test stand, it determines the total friction coefficient μtot per ISO 16047 clause 10.2. If thread and bearing torque were measured separately, it also returns μth and μb individually.
Use the resulting friction values for design: Tightening Torque and Preload.
ISO16047
02
Friction coefficients to ISO 16047
Enter the measured values.
Inputs and method
Friction coefficient from a torque-tension test to ISO 16047
Determine the total, thread and bearing friction coefficient and the K-factor from torque and preload measured on a test stand.
Calculation
The total friction coefficient follows the approximation mu_tot = (T/F - P/2pi) / (0.577*d2 + 0.5*Db) per ISO 16047 clause 10.2. When measured separately, clauses 10.3 and 10.4 give mu_th and mu_b individually.
Example
M10, P = 1.5 mm, F = 30,000 N, T = 52.447 N·m, Db = 14.63 mm: mu_tot = 0.1205. With separately measured Tth = 26.113 N·m and Tb = 26.334 N·m, mu_th = 0.1213 and mu_b = 0.1200 -- back-calculated from a case with an assumed mu = 0.12 on both sides, to check approximation accuracy.
Sources and limits: ISO 16047:2005 + A1:2012 (DIN EN ISO 16047:2025-08), clauses 10.2 to 10.4.
Friction coefficient from a torque-tension test to ISO 16047 in detail
Determine the total, thread and bearing friction coefficient and the K-factor from torque and preload measured on a test stand.
Why is this the inverse of the tightening-torque calculation?
The tightening-torque and preload calculators start from assumed or datasheet friction values to predict torque or preload -- that is design. This calculator solves the inverse problem: an actual torque-tension test with an instrumented bolt or load washer supplies F and T as measurements, and from those the actual friction coefficient is determined. That is the test that produces the assumptions the design calculation relies on in the first place.
Formula and variables
mu_tot = (T/F - P/2*pi) / (0.577*d2 + 0.5*Db)
mu_th = (Tth/F - P/2*pi) / (0.577*d2)mu_b = Tb / (0.5*Db*F)K = T / (F*d)
| Symbol / input | Meaning |
|---|---|
| T | Measured total tightening torque, in N*mm. |
| F | Preload (clamp force) measured in the test, in N, usually at 75% of the proof load Fp. |
| P | Thread pitch, in mm. |
| d2 | Pitch diameter of the bolt thread, d2 = d - 0.6495*P per ISO 724. |
| Db | Friction diameter of the head or nut bearing area, Db = (Do+dh)/2. |
| Tth | Thread torque, either measured separately or from Tth = T - Tb. |
| Tb | Bearing torque (head or nut contact area), either measured separately or from Tb = T - Tth. |
| mu_tot | Total friction coefficient -- assumes equal friction in thread and bearing area. |
| mu_th | Thread friction coefficient, determinable only with an additionally measured Tth. |
| mu_b | Bearing-area friction coefficient, determinable only with an additionally measured Tb. |
| K | K-factor, a normalized tightening characteristic without a split into thread and bearing shares. |
Choose the inputs correctly
Nominal thread diameter d, pitch P, bearing friction diameter Db, and measured preload F and tightening torque T; optionally separately measured thread and bearing torque.
How to use the calculator
Enter geometry (d, P, Db) and the preload F measured in the test together with the corresponding tightening torque T. If thread and bearing torque were also measured separately, the option additionally returns mu_th and mu_b.
Worked example
M10, P = 1.5 mm, F = 30,000 N, T = 52.447 N·m, Db = 14.63 mm: mu_tot = 0.1205. With separately measured Tth = 26.113 N·m and Tb = 26.334 N·m, mu_th = 0.1213 and mu_b = 0.1200 -- back-calculated from a case with an assumed mu = 0.12 on both sides, to check approximation accuracy.
Why does the total friction coefficient only give a comparison value?
mu_tot explicitly assumes thread and bearing friction coefficients are equal (ISO 16047, 10.2) -- in practice that's almost never exactly true, because the thread flank and the head bearing area have different contact pressures, sliding speeds and often different coatings. mu_tot is therefore suited to comparing batches, coatings or lubricants against each other, not as an exact input to a torque-preload calculation when thread and bearing friction genuinely differ. For that, use the separately measured mu_th and mu_b.
Friction coefficients and the K-factor are dimensionless, forces in newtons, torques in newton-metres, lengths in millimetres.
Typical applications
Quality assurance of bolt batches, comparing coatings or lubricants, obtaining realistic friction values for the tightening-torque and preload calculators when surfaces differ from the assumed defaults.
Assumptions, limits and common mistakes
ISO 16047:2005 + A1:2012 (DIN EN ISO 16047:2025-08), clauses 10.2 to 10.4.
Common mistake: Don't confuse Db with the washer's hole diameter -- Db is the mean friction diameter of the bearing area, (Do+dh)/2, not its inner or outer dimension alone. The standard specifies measuring at 75% of the proof load Fp; at a markedly different preload level, transferability to other tightening cases is limited.
Frequently asked questions
How is the friction coefficient of a bolted joint determined per ISO 16047?
From preload F and tightening torque T measured in a torque-tension test, via the approximation mu_tot = (T/F - P/2*pi)/(0.577*d2 + 0.5*Db) per clause 10.2 of the standard.
What is the difference between thread friction and head friction?
Thread friction mu_th acts in the thread flanks while converting torque into axial force; head or bearing friction mu_b acts in the contact area between the bolt head or nut and the component. Together they approximately make up the total tightening torque.
Why can the same tightening torque produce different preloads?
Because most of the torque -- often 80 to 90% -- is consumed as friction in the thread and bearing area rather than becoming preload. Varying lubrication, surface or coating change that friction share and therefore the preload achieved at the same torque.
Which measurements does an ISO 16047 test require?
At minimum preload F and tightening torque T for the total friction coefficient. For separate thread and bearing friction coefficients, thread torque Tth and/or bearing torque Tb are additionally needed, usually measured with an instrumented test mandrel.
Is the determined friction coefficient transferable to any bolt size?
Only if surface, coating, lubrication and material pairing stay the same -- the friction coefficient is a property of the contact conditions, not a fixed material constant. It can then be reused in the tightening-torque and preload calculators for other thread sizes under the same friction conditions.
What role do lubrication and coating play?
They directly set the friction coefficient: a lubricated or coated thread can lower mu by a factor of 2 or more compared with bare, dry steel. That is why the ISO 16047 test must be run separately for each surface/lubricant combination, not taken from a generic table.