The von Mises stress calculator above takes the six components of a stress tensor and reduces them to one number that can be compared directly against a uniaxial yield strength. That comparison is the whole point. A tensile test gives one number for a material; a real component is loaded in several directions at once, and the von Mises criterion is the standard way of asking whether that combined state is as severe as the tensile test that caused yielding.
Arb Digital builds free tools that are honest about their limits. This page publishes no table of allowable stresses and no library of material strengths, because yield strength depends on the exact alloy, heat treatment, product form, thickness and service temperature, and a generic figure attached to a metal's name would be misleading in exactly the cases where it matters. This is an educational and estimating tool. It is not structural design advice, and a qualified engineer must analyse, verify and sign off any real design against the applicable design code.
What the Von Mises Criterion Actually Says
The criterion rests on one physical idea: a ductile metal does not yield because it is squeezed uniformly, it yields because its shape is being distorted. Take an element deep in the ocean and it is under enormous pressure, equal in all directions, and it does not yield at all. Take the same element and shear it, and it yields at a modest stress. The difference is that pressure changes volume while shear changes shape.
The von Mises criterion formalises that by splitting the stress tensor into a hydrostatic part, which is the average of the three normal stresses and changes only volume, and a deviatoric part, which is everything left over and changes only shape. Yielding is then predicted to depend on the deviatoric part alone. Section 3.7 of A. F. Bower's Applied Mechanics of Solids, on rate-independent plasticity, presents it in exactly these terms as a criterion based on the deviatoric stress components, and notes that it fits experiment slightly better than the alternative Tresca criterion.
The practical consequence is worth stating plainly. Superimpose a uniform pressure on any stress state and the von Mises stress does not change at all. That is not an artefact of the algebra, it is the criterion's central claim, and it is why the hydrostatic stress appears nowhere in the answer.
How to Use It
- Pick the right stress state. Plane stress covers a thin sheet or a free surface, where nothing acts perpendicular to the surface. Use the three-dimensional mode for a point inside a thick body or wherever a third normal stress genuinely exists.
- Enter the components in one consistent unit. The unit menu is only a label, so MPa throughout or ksi throughout, including the yield strength.
- Sign the normal stresses. Tension positive, compression negative. Getting a sign wrong changes the answer substantially, because the criterion depends on the differences between the normal stresses.
- Enter a yield strength you can defend. From the certificate for the material actually in the part, at the temperature it will run at, not a textbook value for the alloy family.
- Read the factor of safety as an arithmetic ratio. It is yield strength divided by equivalent stress and nothing more. What margin is acceptable is a question for the governing design code, not for this page.
The Formula and a Worked Example
In three dimensions, σv = √(½[(σx−σy)² + (σy−σz)² + (σz−σx)²] + 3[τxy² + τyz² + τzx²]). Written in principal stresses it becomes σv = √(½[(σ1−σ2)² + (σ2−σ3)² + (σ3−σ1)²]), which makes the dependence on differences obvious.
Work the defaults through. With σx = 200, σy = 100, σz = 0 and τxy = 50 MPa, the bracket gives ½[100² + 100² + (−200)²] = ½ × 60,000 = 30,000, and the shear term gives 3 × 50² = 7,500. The sum is 37,500, whose square root is 193.65 MPa.
The principal stresses check the same answer a second way. In the x-y plane the mean is 150 and the radius is √(50² + 50²) = 70.71, so σ1 = 220.71, σ2 = 79.29 and σ3 = 0. Feeding those into the principal-stress form gives ½[141.42² + 79.29² + 220.71²] = 37,500 again. Against a 250 MPa yield strength the factor of safety is 250 ÷ 193.65 = 1.29. The Tresca criterion, which uses σ1 − σ3 = 220.71, would give 1.13 for the same state, and that gap is the subject of the next section.
Von Mises Against Tresca, and Why Both Are Reported
Tresca predicts yielding when the maximum shear stress reaches its value at yield in a tensile test, which reduces to the difference between the largest and smallest principal stresses. Von Mises predicts it from the distortion energy. They agree exactly in uniaxial tension, which is how both are calibrated, and they differ most in pure shear, where Tresca is about 15 per cent more conservative.
Neither is a law of nature. Both are empirical criteria fitted to test data on ductile metals, and von Mises generally matches that data more closely. Tresca is nonetheless written into several design codes precisely because it is the conservative one and because its algebra is simpler. When a code specifies a criterion, that criterion is the one that governs, regardless of which fits the physics better. The tool reports both so the difference is visible rather than assumed away.
Where This Criterion Does Not Apply
The von Mises criterion predicts the onset of plastic yielding in a ductile, isotropic material. Every word in that sentence is a restriction.
It does not predict brittle failure. Cast iron, ceramics, glass and hardened tool steels fail by fracture rather than by yielding, and their strength in compression is far higher than in tension. A criterion that ignores hydrostatic stress cannot possibly capture that asymmetry, and applying it to a brittle material can be dangerously unconservative. Brittle materials are assessed with maximum-normal-stress or Mohr-Coulomb type criteria instead.
It does not predict fatigue. A component cycled well below its yield strength can still crack and fail after enough cycles, and the equivalent stress here says nothing about that. Nor does it predict buckling, which is a stability problem in which a slender member fails at a stress far below yield; the column buckling calculator covers that separate failure mode.
It also assumes isotropy. Rolled plate, extrusions, composites and additively manufactured parts have direction-dependent strength, and comparing a single equivalent stress against a single yield number quietly ignores that. Finally, it says nothing about creep at elevated temperature, about stress concentrations at notches and fillets, or about residual stresses left by manufacturing, all of which have to be assessed separately.
How This Differs From the Adjacent Arb Digital Tools
The boundary in one sentence: the Mohr's circle calculator transforms a plane stress state to find principal stresses and the planes they act on, while this page reduces a full three-dimensional state to one equivalent stress and compares it to a yield strength you supply. Use Mohr's circle when you want the orientation; use this when you want the yield margin, and particularly when the third normal stress is not zero.
The stress strain calculator and the Young's modulus calculator handle the elastic relationship between a single stress and the strain it produces. The shear stress calculator computes the shear component this page consumes as an input, and the hoop stress calculator generates the biaxial state found in a pressure vessel wall, which is a natural input to this criterion. For member sizing, see the section modulus calculator and the beam deflection calculator. The underlying definitions of stress and strain are set out in OpenStax University Physics Volume 1, section 12.3 on stress, strain and elastic modulus.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Applying it to a brittle material — cast iron and ceramics fracture rather than yield, and their compressive strength greatly exceeds their tensile strength. This criterion cannot represent that.
- Getting a compression sign wrong — the criterion depends on differences between normal stresses, so flipping one sign can change the answer by a large factor.
- Treating plane stress as plane strain — a thick section restrained out of plane develops a third normal stress that a two-dimensional model omits entirely.
- Reading a factor of safety above one as adequate — the acceptable margin is set by the governing design code and by the confidence in the loads, not by the ratio being greater than unity.
- Using it where fatigue governs — repeated loading fails components at stresses far below yield, and that is a separate calculation with separate data.
Related Free Tools From Arb Digital
For stress transformation and the planes involved, use the Mohr's circle calculator. The stress strain calculator, Young's modulus calculator and shear modulus calculator cover elastic behaviour, while the shear stress calculator and hoop stress calculator generate the components this page combines. For member checks see the section modulus calculator, the beam deflection calculator and the column buckling calculator, and browse the full free online tools hub for the rest.
Frequently Asked Questions
It is a single number that represents how severely a combined stress state is distorting a material, scaled so that it can be compared directly against the yield strength measured in an ordinary tensile test. It is a calculated equivalent, not a stress you could measure on any plane.
No. It is the square root of a sum of squares, so it is always zero or positive. A state of pure uniform compression gives a von Mises stress of zero, because nothing is being distorted.
No. It predicts yielding in ductile materials. Brittle materials such as cast iron, ceramics and glass fail by fracture, and they are far stronger in compression than in tension, which this criterion cannot represent. Use a maximum-normal-stress or Mohr-Coulomb criterion for those.
Because the criterion assumes yielding depends only on distortion, not on volume change. Adding the same normal stress to all three directions leaves the equivalent stress unchanged, which matches the observation that materials under uniform pressure do not yield.
Tresca uses the maximum shear stress, which is the difference between the largest and smallest principal stresses. Von Mises uses the distortion energy. They agree in uniaxial tension and differ most in pure shear, where Tresca is about 15 per cent more conservative.
That is not something a calculator can tell you. The required margin is set by the design code that governs the component, by how well the loads are known and by the consequences of failure, and it is the responsibility of the engineer signing off the design.
Because yield strength depends on the specific alloy, heat treatment, product form, thickness and temperature. A single figure attached to a metal's name would be wrong for many real materials, and wrong in the unconservative direction often enough to be unsafe.
Not necessarily. It means local plastic deformation begins, which many designs prohibit but some deliberately allow. Whether that constitutes failure depends entirely on the design code and the function of the part.
This tool is provided for educational and estimating use only. It is not structural or mechanical design advice. It addresses one failure mode, yielding in a ductile isotropic material, and does not address brittle fracture, fatigue, creep, buckling, stress concentration, residual stress or any code compliance requirement. Any real design must be analysed, verified and approved by a qualified engineer under the applicable design code.
