Principal Stress Calculator
Enter signed σx, σy, and τxy values in one consistent stress unit. The tool calculates principal stresses and orientation for the stated plane-stress model.
A QUICK WALKTHROUGH
How to use this tool
- Enter σx, σy, and τxy using one consistent stress unit and sign convention.
- Calculate the principal stresses, principal-plane angle, and maximum in-plane shear.
- Review the plane-stress limitation and source before applying the result.
Equations and source
For plane stress: σavg=(σx+σy)/2; R=√[((σx−σy)/2)²+τxy²]; σ1=σavg+R; σ2=σavg−R; θ1=0.5·atan2(2τxy, σx−σy). The maximum in-plane shear magnitude is R. Angle is measured counterclockwise from the x-axis to the plane normal for σ1 under the displayed sign convention. Reference: University of Illinois Urbana-Champaign, TAM 251 Stress Transformation, https://mechref.engr.illinois.edu/sol/transformation.html.
Scope limits
This is a two-dimensional plane-stress calculation. It does not calculate the full three-dimensional principal stress state, assess material failure, yield, fatigue, design allowables, code compliance, or safety/suitability. Stress inputs must use the same units and sign convention.
GOOD TO KNOW
Common questions
Does this include all three-dimensional principal stresses?
No. It reports only the two in-plane principal stresses and maximum in-plane shear for the supplied plane-stress state.
What does the angle mean?
It is the counterclockwise angle from the x-axis to the plane normal associated with σ1, using the stated sign convention.
Are inputs uploaded?
No. The calculation runs in this browser.