Formula for shear stress in torsion?

τ = T × r / J (max at outer radius)

Torsion Calculator

Calculate maximum shear stress, angle of twist, polar moment of inertia and power transmission capacity for solid and hollow circular shafts.

Max Shear Stress

85 MPa

Solid shaft d=50mm, T=5 kNm

Featured: Shear Stress, Angle of Twist, Power, Polar Moment J

Shaft Type

Outer Diameter D (mm)

Inner Diameter d (mm)

Shaft Length L (m)

Applied Torque T (kNm)

Shear Modulus G (GPa)

Allowable Shear τ_allow (MPa)

Power P (kW) - optional

Speed N (RPM) - if power given

Linear variation from centre to surface

τ_max = T × R / J
θ = T × L / (G × J) (radians)
J_solid = πD⁴/32
J_hollow = π(D⁴ - d⁴)/32

Enter shaft parameters to see results

Steel: G ≈ 80 GPa, τ_allow ≈ 50–150 MPa

Aluminum: G ≈ 26 GPa

Stainless: G ≈ 77 GPa

Hollow shafts: Better stiffness/weight

Max stress: Always at outer surface

Power: T = P × 2πN / 60