Mohr's Circle Online Calculator
Calculate and visualise 2D plane stress transformation, principal stresses, maximum shear stress, rotated element stresses, principal-plane angle, and stress-element diagrams in real time.
Mohr's Circle Visualisation
Input Parameters
| Result parameter | Symbol | Value | Angle θ | Mohr angle 2θ |
|---|
Unrotated Stress Element
Rotated Stress Element
Element at Principal Stress Direction
Element at Maximum Shear Direction
How to Use This Calculator
- Enter the known stress state: σx, σy, and τxy.
- Select the unit label used for your project, such as MPa or psi.
- Move the rotation slider or type an exact θ angle to calculate the transformed stresses.
- Check the Mohr circle, the table, and the stress-element figures together.
- Use the quick buttons to automatically rotate the element to the principal-stress or maximum-shear direction.
Engineering Interpretation
Mohr's circle is useful for checking the critical stress state in beams, plates, connections, concrete members, steel elements, soil mechanics problems, and general mechanics of materials. The rightmost and leftmost points on the circle show the principal stresses. The top and bottom points show the extreme shear stresses. A larger circle radius means a larger difference between the principal stresses and a higher maximum shear demand.
Mohr’s Circle Calculator for Principal Stress and Shear Stress Analysis
Mohr’s Circle is one of the most important graphical methods used in mechanics of materials, structural engineering, civil engineering, mechanical engineering, and geotechnical engineering to understand the state of stress at a point in a material. A Mohr’s Circle calculator helps engineers, students, and researchers quickly determine principal stresses, maximum shear stress, normal stress, shear stress, and stress transformation on an inclined plane. Instead of solving stress transformation equations manually, this online Mohr’s Circle calculator provides a fast and visual way to analyse two-dimensional plane stress conditions.
In many engineering problems, a material element is subjected to normal stress in the x-direction, normal stress in the y-direction, and shear stress on the x-y plane. These stresses are commonly written as σx, σy, and τxy. When the element is rotated, the normal and shear stresses acting on the new plane change. Mohr’s Circle represents this stress transformation graphically, allowing users to see how stress values vary with rotation angle. This makes it easier to identify the most critical stress conditions in beams, columns, plates, slabs, connections, pressure vessels, machine components, and structural members.
The centre of Mohr’s Circle is calculated from the average normal stress, while the radius of the circle represents the maximum difference between the stress states. The rightmost point of the circle gives the maximum principal stress, usually shown as σ₁, and the leftmost point gives the minimum principal stress, usually shown as σ₂. Principal stresses are very important because they occur on planes where the shear stress is zero. These values are commonly used in failure analysis, material design, structural safety checks, and strength assessment.
Another important result from Mohr’s Circle is the maximum shear stress. The maximum shear stress is equal to the radius of the circle and occurs at an angle 45 degrees away from the principal stress direction in the physical element. This value is especially important for checking shear failure, yielding, cracking, and material performance under combined loading. In structural and mechanical design, knowing the maximum shear stress helps engineers evaluate whether a material or component can safely resist the applied loads.
This online Mohr’s Circle calculator allows users to enter σx, σy, τxy, and the rotation angle. The calculator then displays the transformed normal stress, transformed shear stress, principal stresses, maximum shear stress, Mohr’s Circle diagram, and stress element diagrams. The live angle adjustment makes it easier to understand the relationship between the physical element rotation and the corresponding movement on Mohr’s Circle. It is important to remember that an angle θ in the physical stress element corresponds to an angle 2θ on Mohr’s Circle.
Mohr’s Circle is widely used in engineering education and professional design because it provides both numerical results and visual understanding. For students, it is a powerful learning tool for stress transformation and principal stress analysis. For engineers, it is a practical method for checking critical stress values in real design problems. By using this Mohr’s Circle calculator, users can save time, reduce calculation errors, and gain a clearer understanding of how normal stress and shear stress change with rotation.