Torsion Calculator

• •Use the Torsion Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Torsion Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Calculate shear stress and angle of twist for solid and hollow circular shafts under torsion All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

Torsion refers to twisting of a shaft about its longitudinal axis under applied torque. For circular cross-sections (solid or hollow), the shear stress varies linearly from zero at the axis to a maximum at the outer surface: τ = T·r/J, where T is the applied torque, r is the radial distance from the axis, and J is the polar moment of inertia. For a solid circle of radius R, J = πR⁴/2; for a hollow circle, J = π(R_out⁴ − R_in⁴)/2. The maximum shear stress occurs at the outer surface: τ_max = TR/J. The angle of twist (relative rotation of one end of the shaft relative to the other) is φ = TL/(GJ), where L is the shaft length and G is the shear modulus. These formulas are exact for circular cross-sections because the cross-section remains plane and circular during twisting — an important symmetry property. For non-circular cross-sections (rectangles, I-sections, open thin-walled sections), the analysis is much more complex: cross-sections warp out of plane during twisting, and the stress distribution involves both shear stress and a stress concentration at corners. Non-circular torsion is treated using specialized formulas and the St. Venant theory. In practice, power transmission shafts are nearly always circular because circular sections are both the most efficient carriers of torque and the easiest to manufacture on a lathe. Hollow shafts give 90-95% of the torsional strength of solid shafts of the same outer diameter but with only 50-60% of the material, making them significantly more efficient and lighter. The design approach for shafts is to compute the maximum shear stress under the expected torque, compare with allowable shear stress (typically yield in shear, which is about 0.577 × tensile yield for ductile metals), and verify the angle of twist is within deflection limits (often 1° per meter for precision machinery).

• •Drive shaft design: power transmission shafts in cars, trucks, and industrial machinery carry torque from an engine or motor to a driven component. Size the shaft diameter so maximum shear stress stays below allowable.
• •Helical spring analysis: wound helical springs experience torsion in the wire cross-section, with maximum stress at the inner surface. The torsion formula combined with the Wahl correction factor gives the peak stress in spring design.
• •Fastener torquing analysis: when a bolt is torqued, the shank experiences torsion that combines with axial tension to produce a combined stress state. Torsion analysis is needed for high-strength bolts and for dynamic applications.
• •Automotive steering shaft: steering shafts connect the steering wheel to the steering gear through multiple intermediate couplings and shafts. Torsion analysis sizes the shaft diameter and checks stiffness for steering feel.
• •Wind turbine shaft: the main shaft of a wind turbine carries the torque generated by the rotor blades to the gearbox and generator. Large wind turbines have shaft torques in the range of 1-10 MN·m, requiring careful torsional design.