Torsional Stress Calculator

Formula Used

How to Use This Calculator

1. Choose solid or hollow shaft and enter the torque.
2. Enter diameters, then set the diameter unit once.
3. Provide shaft length and shear modulus to compute twist.
4. If needed, set a stress factor to cover keyways or fillets.
5. Optionally add allowable stress for utilization and safety factor.

Torque and load path in shafts

Torque creates a linear shear stress distribution from the center to the outer radius. For a 300 N·m load on a 30 mm solid shaft, the peak stress is about 56.6 MPa. Because stress scales with torque, doubling torque doubles stress and twist. If you start from power and speed, use T = P/ω; for 15 kW at 1500 rpm, torque is about 95.5 N·m.

Diameter sensitivity and polar moment

The polar moment J depends on the fourth power of diameter, so small diameter changes dominate results. Increasing a solid shaft from 30 mm to 33 mm raises J by roughly (33/30)⁴ ≈ 1.46, cutting stress and twist by about 31%. This is why diameter control is critical in driveline design. Undersize machining raises τ by reducing J.

Solid versus hollow sections

Hollow shafts save mass while keeping stiffness by moving material away from the center. At the same outer diameter, removing a modest core can reduce weight significantly while keeping J high. The calculator uses J = π(D⁴ − d⁴)/32, so verify inner diameter tolerances and corrosion allowance. As a guide, a d/D ratio of 0.60 retains about 87% of the solid J, while removing 36% of the area.

Twist, rigidity, and serviceability limits

Angle of twist θ = TL/(JG) links strength to rigidity. A high-strength shaft can still fail a deflection limit if L is long or G is low. Typical G values are near 79 GPa for steel and about 26 GPa for aluminum, so aluminum shafts often twist about three times more at similar geometry. Many gear drives target twist limits near 0.25–1.0 deg per meter to protect alignment and backlash.

Design checks, factors, and allowable stress

Real shafts include keyways, steps, and fillets that raise local stress. Apply Kt as an engineering stress factor when detail stresses are unavailable, then compare τmax to an allowable shear stress from your code or material basis. With an allowable entered, the tool reports utilization and factor of safety for rapid screening. For fatigue-prone parts, treat Kt as a starting point and confirm notch sensitivity and alternating torque separately.

FAQs

What does this calculator output?

It returns nominal and factored maximum torsional shear stress, polar moment of inertia, angle of twist in degrees and radians, and an estimated maximum shear strain. Optional allowable stress adds utilization and factor of safety.

When should I use the stress factor Kt?

Use Kt when geometry features such as keyways, shoulders, or fillets increase local stress above the nominal value. If you have detailed finite element results or published concentration factors, enter the best estimate and document the basis.

Why is diameter so influential?

For circular shafts, J varies with diameter to the fourth power. A small diameter reduction sharply lowers J, increasing both stress and twist. Always verify machining tolerances, wear limits, and whether the diameter entered is outer diameter for hollow shafts.

How do I choose shear modulus G?

Use a material datasheet value at your operating temperature. Typical room-temperature values are about 79 GPa for steels and about 26 GPa for aluminum alloys. If you only know Young’s modulus and Poisson’s ratio, compute G = E/[2(1+ν)].

Can I use this for non-circular shafts?

No. The formulas here assume Saint-Venant torsion for circular shafts. Non-circular sections require torsional constants, warping considerations, and different stress distributions. Use a specialized method or FEA for rectangular, thin-walled, or open sections.

What if my twist is acceptable but stress is high?

Increase diameter, reduce torque, shorten the shaft, or switch to a material with higher allowable shear stress. Hollowing reduces mass but may not reduce stress. Also recheck Kt and confirm that the allowable stress reflects your governing design standard.