Von Mises Stress Calculator

The von Mises equivalent stress for a general three-dimensional stress state is:

For plane stress mode, the out-of-plane terms are set to zero (σz = τyz = τzx = 0) before evaluation.

1. Select the stress state: 3D for full tensors, or plane stress.
2. Choose a unit, then enter normal and shear stresses.
3. Optional: enable yield strength to compute a safety factor.
4. Press Calculate to show results above the form.
5. Use the CSV and PDF buttons to export your report.

Why von Mises stress is used

Von Mises stress converts a multiaxial stress state into one comparable value, letting you check yielding in ductile metals. It is based on distortion energy, so it reacts strongly to shear. Engineers use it for shafts, brackets, pressure parts, and welded frames where stresses act together. For brittle materials, other criteria may be preferable.

Stress components and sign convention

Enter normal stresses σx, σy, σz and shear stresses τxy, τyz, τzx in a consistent sign convention. Tension is typically positive and compression negative. Shear sign follows your axis orientation, but von Mises uses squared terms, so the magnitude is what matters most for yielding checks.

Equivalent stress calculation and units

The calculator evaluates the standard 3D equation and outputs σvm in your chosen unit (Pa, kPa, MPa, GPa, psi, or ksi). For reference, 1 ksi ≈ 6.895 MPa and 1 MPa = 10^6 Pa. Keep your inputs within realistic ranges for your material and load case.

Plane stress versus three-dimensional loading

Thin plates and sheet parts often use plane stress, where σz, τyz, and τzx are near zero. Thick components, bolted joints, and constrained regions can develop significant out‑of‑plane terms. Switching modes helps you match the assumption to the physics of your part.

Material yield data for context

To interpret σvm, compare it with an appropriate yield strength Sy. Typical room‑temperature values are about 250 MPa for mild steel, 275 MPa for 6061‑T6 aluminum, and 355 MPa for structural S355 steel. Heat treatment, thickness, and temperature can change Sy substantially.

Using factor of safety effectively

When you enable yield strength, the calculator reports FoS = Sy/σvm. Many static designs target FoS between 1.5 and 3.0, while fatigue, impact, or uncertainty may require higher margins. Use the governing code, specification, or test data for your project.

Common input and modeling pitfalls

A frequent mistake is mixing units, such as entering MPa numbers while selecting psi. Another is double‑counting loads: if stresses already come from FEA, do not recompute them from forces again. Check that stress components refer to the same point and coordinate system.

Reporting and traceability

Record the stress state, unit, mode, and yield value used, then export CSV or PDF for review. For audits, include the load case ID, measurement source (hand calc or simulation), and assumptions (plane stress, temperature, or material grade). Consistent documentation speeds verification.

Is von Mises stress valid for brittle materials?

It is mainly used for ductile metals where yielding governs. Brittle materials may fail by maximum normal stress or fracture mechanics before yielding, so choose a criterion that matches your material behavior and available test data.

What is the difference between plane stress and 3D mode?

Plane stress assumes σz, τyz, and τzx are negligible, common for thin plates. 3D mode includes all normal and shear components, which is important near constraints, thick sections, and complex load paths.

Can I enter compressive stresses as negative values?

Yes. Use negative values for compression and positive for tension, consistent with your sign convention. The von Mises result is an equivalent magnitude, but keeping correct signs improves traceability and interpretation of the stress state.

How do I compute factor of safety in this tool?

Check the yield comparison option and enter your material yield strength in the same unit as the stresses. The tool reports FoS = Sy/σvm. If σvm is zero, FoS is not meaningful.

Which unit should I select for engineering work?

Use the unit that matches your source data. FEA outputs are often in MPa, while some standards use psi or ksi. Avoid mixing units across inputs; convert first, then calculate in one consistent system.

Why is my von Mises stress larger than my largest normal stress?

Shear stress and differences between principal stresses contribute strongly to σvm. A moderate shear value can raise the equivalent stress even if individual normal stresses look small, especially under combined loading.

Do these results replace a full structural code check?

No. The calculator provides an equivalent stress and optional safety factor. Final acceptance should consider geometry, buckling, fatigue, temperature, weld details, and the requirements of relevant design codes and specifications.