Calculate angle of twist, shear stress, and torsional stiffness for solid or hollow shafts under torque. Compare materials instantly.
The **Angle of Twist Calculator** computes how much a circular shaft rotates under an applied torque. This is one of the most fundamental calculations in mechanical and structural engineering — used every time a drive shaft, axle, or structural tube is designed.
Given the torque, shaft geometry (solid or hollow circular cross-section), length, and material shear modulus, the calculator finds the total twist angle in degrees and radians, plus the maximum shear stress at the outer surface. It also reports the torsional stiffness and the power the shaft can transmit at any given speed.
Choosing between a solid and hollow shaft is a critical design trade-off: hollow shafts are lighter but may buckle or have larger deflections. The built-in material presets — steel, aluminum, copper, brass, titanium, and cast iron — let you compare twist angles instantly. Use the reference tables to explore how twist varies with length and across materials.
Knowing the twist angle and shear stress prevents shaft failures, excessive vibration, and misalignment in power-transmission systems. This calculator replaces tedious manual calculations with instant results and material comparisons.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Angle of Twist: θ = T L / (G J) Polar Moment (solid): J = π D⁴ / 32 Polar Moment (hollow): J = π (D⁴ − d⁴) / 32 Max Shear Stress: τ = T r / J where T = torque, L = length, G = shear modulus, D = outer diameter, d = inner diameter, r = outer radius.
Result: 0.586° twist, 40.7 MPa max shear stress
A 50 mm solid steel shaft (G = 79.3 GPa) carrying 500 N·m over 2 m twists about 0.586° with a peak shear stress of 40.7 MPa — well within typical steel yield limits.
Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.
Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.
Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.
It is the angular deformation of one end of a shaft relative to the other when a torque is applied along its axis. Use this as a practical reminder before finalizing the result.
The formula yields radians; multiply by 180/π to convert to degrees. Keep this note short and outcome-focused for reuse.
J quantifies the cross-section's resistance to torsion. Larger J means less twist and lower shear stress for the same torque.
Hollow shafts save weight with only a modest increase in twist. They are preferred in aerospace, automotive, and bicycle frame design.
Typical allowable shear stress for structural steel is 0.4 × yield strength, roughly 100–150 MPa for common steels.
Yes. The shear modulus decreases at elevated temperatures, increasing the angle of twist.