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Estimate torsional shear stress, angle of twist, torque, power, and circular shaft size using SI-normalized elastic torsion formulas.
Maximum torsional shear stress
40.7437 MPa
Unit-normalization summary: 1,000 N*m; 6.13592e-7 m^4; 8.00000e+10 Pa
tau = T c / J; theta = T L / (J G); P = T omega
J = pi d^4 / 32 for solid shafts; tau = T c / J; theta = T L / (J G); P = T omega.
tau = 1,000 N*m x 0.025 m / 6.13592e-7 m^4
theta = 1,000 N*m x 0.001 m / (6.13592e-7 m^4 x 8.00000e+10 Pa)
Use the stress and twist values as preliminary elastic checks. Transfer combined bending and torsion cases to the shaft design calculator.
Torsion is twisting caused by torque about a member's longitudinal axis. For circular shafts, torque, polar moment of area, radius, length, and shear modulus govern shear stress and angle of twist within the elastic Saint-Venant model.
Torsion Calculator applies this concept to its defined inputs and workflow. This torsion workflow can feed preliminary shaft design, factor-of-safety checks, stress conversion, and power-torque-speed review. Its governing relationship or workflow is stated as follows: Torsional shear stress, angle of twist, and power relationship for elastic circular shafts.
The calculator evaluates Calculation mode, Material preset, and Display precision and returns Torsion, base-unit normalization, formula substitution, and calculation steps using the stated method. The selected units and sign or reference conventions must describe one consistent physical case. Users should interpret the output within the assumptions shown on the page and repeat the check with trusted reference values when the result affects engineering or research decisions. Circular elastic shafts only.
| Symbol | Meaning | Unit |
|---|---|---|
| T | Applied torque | N*m |
| J | Polar second moment of area | m^4 |
| tau | Maximum torsional shear stress | Pa |
| theta | Angle of twist | rad |
| GJ | Torsional rigidity | N*m^2 |
The torsion workflow can feed preliminary shaft design, factor-of-safety checks, stress conversion, and power-torque-speed review.
Professional FEA, simulation setup, solid-mechanics calculations, mechanical-design review, technical documentation, and research support are available through the connected services website. These calculators remain free to use without purchasing services.
Visit ScholarEaseThis tool is intended for educational, estimation, and preliminary engineering use. It does not certify designs or replace applicable codes, standards, validated software, physical testing, or qualified professional engineering judgment.
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