Mohr Circle Plane Stress Calculator
Calculate principal stresses, in-plane shear radius and a rotated normal stress from a planar stress state.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the symmetric two-dimensional stress tensor eigenvalues and the standard double-angle normal-stress transformation.
Center=(σx+σy)/2; radius=√(((σx−σy)/2)²+τxy²); principal=center±radius
Worked example
σx=100 MPa, σy=20 MPa and τxy=30 MPa give circle center 60 MPa, radius 50 MPa and principal stresses 110 and 10 MPa.
Assumptions and input details
Plane stress and tensile-positive normals; positive τxy uses the symmetric tensor convention. The reported maximum shear is in-plane only, not necessarily the 3D absolute maximum with σz=0. No material failure criterion, allowable stress or component design.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Calculate elastic surface shear stress, twist and strain energy for a solid or hollow circular shaft.
Calculate ideal membrane stresses in a closed thin cylindrical or spherical shell from differential pressure, internal diameter and wall thickness.
Enter two three-component vectors to calculate their sum, difference, dot product, cross product, magnitudes and angle, with an XY-projection diagram.
Reserved advertising space.