Mohr's Circle Calculator

Interactive 2D & 3D analysis for principal stresses, max shear, and strain transformation — trusted by engineers, students, and geotechnicians.

Master stress & strain visualization with our free mohr's circle calculator. Whether you need a 2d mohr's circle calculator, strain mohr's circle calculator, or insights into 3d mohr's circle calculator, this tool provides instant results with graphical circle representation. Calculate principal stresses, maximum shear stress, orientation angles, and even transform strain states — all in one place.

Stress Mohr's Circle (2D)

Compute σ₁, σ₂, τ_max, and rotation angle. Ideal for mohr's stress circle calculator.

σ_x (Normal stress, MPa / psi)

σ_y (Normal stress)

τ_xy (Shear stress, positive direction)

Principal stresses σ₁, σ₂: —

Max in-plane shear τ_max: —

Angle θ_p (to principal plane): —

Updates live – drag values or type.

Strain Mohr's Circle (2D)

strain mohr's circle calculator – principal strains & maximum shear strain. Use for mohr's circle strain rosette analysis.

ε_x (Normal strain, µε or in/in)

ε_y (Normal strain)

γ_xy (Engineering shear strain)

Principal strains ε₁, ε₂: —

Max shear strain (γ_max/2): —

Angle θ_ε: —

3D Mohr's Circle & Advanced Analysis

For triaxial loads and complete 3d principal stress evaluation (2026 engineering standards)

For a full 3D stress state with principal stresses σ₁ ≥ σ₂ ≥ σ₃, the 3d mohr's circle calculator plots three circles representing the stress combinations (σ₁,σ₂), (σ₂,σ₃), and (σ₁,σ₃). The absolute maximum shear stress is τ_max,3D = (σ₁ - σ₃)/2. Our 3d mohr's circle calculator with steps follows this approach: given σ₁, σ₂, σ₃, you can instantly compute extreme shear. Use for mohr's circle method for calculation of stresses in soil mechanics, structural engineering, and material design.

Quick 3D insight formula: Maximum shear (3D) = (σ_max - σ_min)/2. For plane stress, σ₃ = 0.

Try our manual 3D input: → τ_max,3D = 50 MPa

Essential Mohr's Circle Formulas (2026 Quick Reference)

Parameter	Formula	Use case
Center (σ_avg)	σ_avg = (σ_x + σ_y)/2	Mohr's circle radius base
Radius R	R = √[((σ_x-σ_y)/2)² + τ_xy²]	Maximum shear stress τ_max = R
Principal stresses	σ_1,2 = σ_avg ± R	Max & min normal stress
Principal angle θ_p	tan(2θ_p) = τ_xy / ((σ_x-σ_y)/2)	Orientation of principal plane
Strain center ε_avg	ε_avg = (ε_x+ε_y)/2	Strain circle center
Strain radius R_ε	R_ε = √[((ε_x-ε_y)/2)² + (γ_xy/2)²]	Max shear strain/2

How to Calculate Mohr's Circle: Step-by-Step (2026 Edition)

✍️ 5‑Step method for stress transformation

Identify knowns: σ_x, σ_y, τ_xy (positive if shear tends to rotate element counterclockwise).
Compute center C = (σ_x+σ_y)/2.
Calculate radius R = √[((σ_x-σ_y)/2)² + τ_xy²].
Principal stresses = C ± R; τ_max = R.
Angle 2θ_p = arctan(τ_xy / ((σ_x-σ_y)/2)). Then θ_p gives orientation.

Exclusive 2026 insight: Use mohr's circle calculator angle to verify failure criteria (Mohr-Coulomb for soil). Our interactive canvas plots the exact circle – no manual drafting required. For strain rosettes (45° or 60°), our strain calculator directly uses γ_xy to derive principal strains.

Pro Tip (2026): Many FE exams now require digital Mohr's circle. Use our mohr's circle calculator with steps to double-check solutions.

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Frequently asked questions: Mohr's Circle

1. How do I calculate principal stresses using Mohr's circle?
Simply enter σx, σy, τxy in our mohr's circle calculator; it automatically computes center and radius, giving σ₁ and σ₂. The formula: σ₁,₂ = (σx+σy)/2 ± √[((σx-σy)/2)² + τxy²].

2. Can this tool handle 3D stress states?
Yes — we provide a 3d mohr's circle calculator explanation and a live 3D τmax evaluator. For full three-circle representation, the absolute max shear is (σ₁-σ₃)/2. The page supports 3d mohr's circle calculator draw plane/element concepts.

3. What's the difference between stress and strain Mohr's circle?
Stress circle uses σ and τ; strain circle uses ε and γ/2. The mathematics are analogous: replace σ with ε, and τ with γ/2. Our strain mohr's circle calculator does exactly that for rosette data.

4. How accurate is the free mohr's circle calculator for engineering exams?
We use double-precision arithmetic, matching standard textbooks. Always cross-check but proven reliable for homework and preliminary design.

5. Does the calculator show the orientation angle of principal planes?
Absolutely — angle θp is calculated using tan(2θp) = 2τxy/(σx-σy). Both stress and strain sections output the rotation angle. Perfect for mohr's circle calculator with rotation demands.

6. Can I use this for 45-degree strain rosette calculations?
Yes. Given εx, εy, and γxy (from rosette equations), our strain calculator instantly outputs principal strains and direction, acting as a 45 degree strain rosette calculating principal mohr's circle tool.

7. Is there a downloadable excel or offline version?
Our online mohr's circle calculator excel alternative runs directly in browser — no download required, works on all devices.

Important notice

TotalCalcHub's Mohr's Circle Calculator is for educational & estimation purposes. Results may vary with real-world conditions. For professional structural/geotechnical decisions, validate with licensed engineers. All data is processed locally (no server storage).