Mechanical & Civil Engineering
Mohr's Circle Principal Stresses Calculator
Compute principal stresses and maximum shear stress using Mohr's circle from a 2D stress state.
Your inputs
Change any value to update the result instantly.
Max principal stress σ1
112.426 MPa
Min principal stress σ2
27.574 MPa
Max shear stress
42.426 MPa
Average stress
70 MPa
What this calculator does
Mohr's Circle Principal Stresses Calculator: Applies the standard mechanics-of-materials relationship for this load case so a student can see how the stress, strain or deflection follows from the geometry and the load.
What your result means
The headline figure tells you how hard the material is being worked, or how much it moves, under the load you entered. Compare it with the allowable value for your material and required factor of safety.
Formula and working
σ1,2 = (σx+σy)/2 ± √(((σx-σy)/2)² + τxy²)
- 1
Collect the inputs
Normal stress σx = 100 MPa; Normal stress σy = 40 MPa; Shear stress τxy = 30 MPa
- 2
Apply the formula
σ1,2 = (σx+σy)/2 ± √(((σx-σy)/2)² + τxy²)
- 3
Result
Max principal stress σ1 = 112.426 MPa
Frequently asked questions
Symbols and assumptions
- sx
- Normal stress σx (MPa)
- sy
- Normal stress σy (MPa)
- txy
- Shear stress τxy (MPa)
- • The material is homogeneous, isotropic and loaded within its linear-elastic range.
- • Inputs are entered in a consistent unit system, as labelled on each field.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
Report a mistake or request an improvement
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