Shear Stress Calculator — Direct and Torsional
Calculate direct shear stress (F/A) or torsional shear stress in circular shafts (Tr/J).
Returns results in Pa, kPa, MPa, and psi for engineering.
Shear stress acts parallel to a cross-section, as opposed to normal (tensile/compressive) stress which acts perpendicular. Two cases come up constantly in mechanical design.
Direct shear: tau = F / A
A bolt in single shear, a fillet weld under transverse load, a pin through a clevis – the applied force acts parallel to the shear plane of area A. For an 8 mm diameter bolt (A = pi x 0.004^2 = 5.03 x 10^-5 m^2) carrying 20 kN, the shear stress is 398 MPa. Whether the bolt survives depends on its shear strength – for structural steel typically 57-65% of tensile strength.
Torsional shear in a solid circular shaft: tau = T * r / J
T is the applied torque in N m, r is the radial distance from the shaft center, and J is the polar moment of inertia. For a solid shaft of diameter d: J = pi * d^4 / 32. Maximum stress occurs at the outer surface where r = d/2. Substituting: tau_max = 16T / (pi * d^3).
Hollow shafts are more efficient – the material near the center contributes little to torque resistance (stress is proportional to r) while adding significant weight. This is why driveshafts are hollow.
Shear strength of common materials: structural steel A36 about 200 MPa, stainless steel 316 about 400 MPa, 6061-T6 aluminum about 207 MPa, yellow brass about 200 MPa.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.