Tools › Mechanical Design

3D Principal Stress Calculator

Enter the six independent components of a 3D stress tensor to get the principal stresses, maximum shear (Tresca), von Mises stress, tensor invariants, and principal directions.

3D PRINCIPAL STRESS CALCULATOR
Stress tensor σij — enter the six independent components

Grayed cells fill automatically from symmetry (τij = τji). Units: any consistent stress unit (MPa shown); results carry the same unit.

Principal solution
σⅠ
Principal stress I (max)
–
σⅡ
Principal stress II (mid)
–
σⅢ
Principal stress III (min)
–
τMAX
Max shear (Tresca / Guest)
–
σVM
von Mises (Huber–Hencky)
–
Invariants
I1
First invariant (trace)
–
I2
Second invariant
–
I3
Third invariant (det)
–
Principal Directions
vⅠ
Direction of σⅠ
–
vⅡ
Direction of σⅡ
–
vⅢ
Direction of σⅢ
–