Calculate the rotational deformation of a shaft under torque.
Mechanical Parameters
Calculation Results
Enter parameters to calculate
About this calculator
Quick Reference
θAngle of Twist (rad)
TApplied Torque (N·m)
LShaft Length (m)
JPolar Moment of Inertia (m⁴)
GShear Modulus (Pa)
Overview
The angle of twist measures how much a shaft rotates about its longitudinal axis when a torsional load is applied. This is critical in mechanical engineering to ensure shafts don't deform excessively or fail.
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Pro Tips
The angle of twist is proportional to length and torque, and inversely proportional to the polar moment of inertia and shear modulus.
The formula θ = TL/JG is valid for shafts with circular cross-sections.
For hollow shafts, a larger diameter provides much more torsional stiffness than the same mass in a solid shaft.
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Fun Facts
"The driveshaft in your car twists slightly every time you accelerate!"
"Modern high-precision machinery uses feedback systems to compensate for the micro-twists in long spindles."
"Torsion springs, like those in a screen door or a mouse trap, are designed to maximize this twisting effect."
