Physics
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Mohr's Circle Calculator.
Calculate the 2D plane-stress Mohr circle and principal stresses from explicit normal and shear stresses.
Set your values
Results update as you type.
Results update automatically as you type.
This is the 2D plane-stress convention with signed tensor components. It does not certify a material, failure criterion, or structural design.
Use Cases
Mechanical Design Stress Analysis
Engineers use Mohr's circle to evaluate stress states in machine components under biaxial loading, ensuring designs stay within material yield limits.
Example: Check a pressure vessel wall with σx=100 MPa, σy=50 MPa, τ=20 MPa.
Civil Engineering Soil Mechanics
Geotechnical engineers apply Mohr's circle to analyze soil strength and stability, determining failure planes and principal stresses in soil masses.
Example: Assess a soil element with σx=80 kPa, σy=40 kPa, τ=15 kPa.
Frequently Asked Questions
- What does the Mohr's Circle Calculator do?
- This calculator takes the normal stresses in the X and Y directions and the shear stress on the plane, then computes the Mohr's circle parameters: center, radius, principal stresses, and maximum shear stress for a 2D plane-stress state.
- What are principal stresses?
- Principal stresses are the maximum and minimum normal stresses at a point where shear stress is zero. They are calculated from the center and radius of Mohr's circle: σ1 = center + radius, σ2 = center - radius.
- Can I use this calculator for 3D stress states?
- No, this calculator is specifically for 2D plane-stress conditions. It uses only the X normal stress, Y normal stress, and shear stress components. For 3D stress analysis, you would need a different tool.
Tips & Common Mistakes
Tips
- Ensure all stress values are in the same unit (e.g., all in Pa or all in MPa) before entering them.
- Use consistent sign conventions: tensile normal stresses are positive, compressive are negative; shear stress sign depends on the plane orientation.
- The principal stresses are always the maximum and minimum normal stresses; they are independent of the coordinate system.
- For a quick check, the center of Mohr's circle is the average of the two normal stresses, and the radius is the square root of ((σx-σy)/2)^2 + τ^2.
Common Mistakes to Avoid
- Forgetting to convert units to a consistent system, leading to incorrect results.
- Misinterpreting the sign of shear stress; the calculator assumes a specific sign convention, so check the input description.
- Using the calculator for 3D stress states when it is only designed for 2D plane stress.
Last updated: August 13, 2026