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
Friction Coefficients from a Torque-Tension Test to ISO 16047
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
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.
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
Why do mu_tot and mu_th differ slightly in my example?
Because mu_tot is an approximation with a simplified thread term (ISO 16047 itself states an error of about 1 to 2%), while mu_th uses the thread-specific approximation. Both are standard-compliant but differ slightly by design.
What if I can only measure F and T, not Tth and Tb?
Then the calculator returns only mu_tot -- sufficient to compare test pieces under identical conditions, but not for separately assessing thread versus head bearing friction.