Torsional Stiffness Calculator

Your details

Outer diameter of the shaft (or the only diameter for a solid shaft).
mm
Effective length over which the torque is applied.
mm
Material shear modulus. Steel ~80 GPa (11,600 ksi), aluminium ~26 GPa (3,770 ksi), titanium ~42 GPa (6,090 ksi).
GPa
Torque (twisting moment) applied to the shaft.
N·m
Shaft speed in revolutions per minute. Used to calculate transmitted power.
RPM
Torsional stiffness (k)Low shear stress
12,723.4502

Torque required per radian of angular deflection (k = GJ / L)

Stiffness unitN·m/rad
Polar moment of inertia (J)79,521.564
J unitmm⁴
Angle of twist0.9006deg
Angle of twist (rad)0.015719rad
Max shear stress (tau)37.726
Shear stress unitMPa
Transmitted power30.369
Power unitkW
37.726 MPa
Low<60Moderate60-120High120+

Torsional stiffness: 12723.4502 N·m/rad

  • Torsional stiffness is 12723.4502 N·m/rad: the shaft requires this torque per radian of angular deflection.
  • Under the applied torque the shaft twists 0.901 degrees, which is moderate.
  • Maximum shear stress at the outer surface is 37.73 MPa, well within the typical yield range for steel (120-150 MPa).
  • At 1450 RPM, the shaft transmits 30.369 kW of mechanical power.

Next stepCompare the maximum shear stress to your material yield stress in shear (roughly 0.577 x tensile yield for ductile metals via von Mises). Add a safety factor of 2-4 for rotating machinery.

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