Principal Stress Calculator (2D)
σ1, σ2, max shear and principal angle — Mohr's circle without the drawing.
Cracks in brittle materials open perpendicular to σ₁ — read the principal angle and you can predict the crack path on a shaft (the classic 45° torsion spiral).
Formula
Principal Stress Calculator (2D) is a free principal stress for design engineers, metallurgists and QA inspectors — instant, accurate and 100% client-side, with the governing formula and reference shown next to the result so the number can be defended, not just quoted.
About Principal Stress Calculator (2D)
σ1, σ2, max shear and principal angle — Mohr's circle without the drawing. The calculation implements σ₁,₂ = (σx+σy)/2 ± √(((σx−σy)/2)² + τ²) (Mohr (1882); stress transformation). Cracks in brittle materials open perpendicular to σ₁ — read the principal angle and you can predict the crack path on a shaft (the classic 45° torsion spiral).
How to use Principal Stress Calculator (2D)
- 1Enter σ_x in MPa.
- 2Enter σ_y in MPa.
- 3Enter τ_xy in MPa.
- 4Read σ₁ (max principal), σ₂ (min principal), Max in-plane shear instantly — no submit button needed.
- 5Need US units? Flip the SI/Imperial toggle and every field converts.
Why use Principal Stress Calculator (2D)?
- ✓Implements the standard formula — σ₁,₂ = (σx+σy)/2 ± √(((σx−σy)/2)² + τ²)
- ✓Reference cited on-page: Mohr (1882); stress transformation
- ✓One-click SI ⇄ Imperial toggle — values convert in place, physics stays in SI
- ✓Runs entirely in your browser — nothing uploaded, free forever
Frequently asked questions
What formula does the Principal Stress Calculator (2D) use?+
It computes σ₁,₂ = (σx+σy)/2 ± √(((σx−σy)/2)² + τ²), per Mohr (1882); stress transformation. The formula is displayed under the result.
What should I keep in mind when using this calculator?+
Cracks in brittle materials open perpendicular to σ₁ — read the principal angle and you can predict the crack path on a shaft (the classic 45° torsion spiral).
Where do the material property defaults come from?+
Defaults are standard handbook values (ASM, manufacturer datasheets, the cited standard). Always substitute certified values from your material's test certificate for critical work.
Is the Principal Stress Calculator (2D) free to use?+
Yes — completely free, no sign-up, no limits. It runs client-side in your browser, so inputs stay private and results are instant even on slow connections.
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