The shear stress calculator above is a preliminary sizing and teaching tool, not a structural design. It computes the stress produced when a force acts across a section rather than along it — the load on a bolt holding two plates together, the punch pressing a hole through sheet, the internal shear carried by a beam near its supports. It gives you both the average stress and, where the distribution is not uniform, the peak value that actually governs.
Arb Digital builds free physics calculators that show the working. Most shear stress pages stop at force divided by area. That answer is correct for a pin or a bolt and materially wrong for a beam, where the shear stress varies parabolically through the depth and the maximum can be twice the average. This page tells you which case you are in and prints the factor between the two.
What This Shear Stress Calculator Does
In the direct shear case it divides the shear force by the area being sheared, optionally split across two planes for a bolt in double shear. That is the standard treatment for fasteners, pins, keys, welds and punching operations, where the shear surface is small, well defined, and the assumption of uniform stress across it is close enough to be the accepted method.
In the transverse cases it computes the peak shear stress in a beam section carrying a shear force. The distribution there is not uniform: it is zero at the top and bottom faces, where there is no material above or below to transfer the flow, and maximum at the neutral axis. For a rectangle the peak is 1.5 times the average. For a solid circle it is 4/3 times. For a thin-walled tube it is close to twice.
The grid reports the average stress, the peak-to-average factor for the case you chose, the area that is actually resisting the shear, and the peak stress converted to psi. That conversion earns its place because material data in North America is still published in psi and ksi while the calculation runs in SI.
How to Use It
- Choose the case that matches your geometry. A fastener, pin or punched hole is direct shear. A beam carrying a transverse load is one of the three section cases.
- Enter the shear force. For a beam this is the internal shear at the section you are checking, which is largest at the supports, not the total applied load.
- For direct shear, enter the sheared area and the number of planes. For a bolt this is the shank or thread root area, whichever the joint actually presents to the shear plane.
- For the section cases, enter the dimensions. Only the boxes the case uses are read; the field hint says which is which for each geometry.
- Read the peak, not the average. The headline figure is the one that governs. The average is shown so you can see how much a uniform-stress assumption would have understated it.
The Formula: How Shear Stress Is Calculated
Average shear stress is τ = V ÷ A, where V is the force parallel to the surface and A is the area it acts across. With n shear planes it becomes τ = V ÷ (nA). OpenStax University Physics Volume 1, section 12.3 on stress, strain and elastic modulus, defines shear stress in exactly this form and contrasts it with normal stress.
Transverse shear in a beam follows τ = VQ ÷ (It), where Q is the first moment of the area above the level being checked, I is the second moment of area of the whole section, and t is the width at that level. Evaluating that expression at the neutral axis for common shapes collapses it to a simple multiple of the average stress, and those multiples are what the tool applies: 3/2 for a rectangle, 4/3 for a solid circle and 2 for a thin-walled tube.
Work the default numbers. A 50 kN shear force on a rectangular section 50 mm wide by 200 mm deep gives an area of 10,000 mm², which is 0.01 m². The average stress is 50,000 ÷ 0.01 = 5 MPa. The peak at the neutral axis is 1.5 × 5 = 7.5 MPa. Checking against the average alone would have understated the governing stress by a third of its true value.
Assumptions and Where They Stop Holding
Every result here rests on a specific set of assumptions, and most wrong answers come from a correct formula applied outside its range. The transverse shear formula assumes a prismatic beam of homogeneous, linearly elastic material, loaded in a plane of symmetry, with the section far enough from a support or a point load that local effects have died out. The linear elastic requirement is the strictest of those: as OpenStax University Physics Volume 1, section 12.4 on elasticity and plasticity sets out, once the material yields the stress no longer distributes the way the elastic formula predicts. It assumes the section does not warp appreciably and that no torsion is present.
It stops holding for thin-walled open sections such as channels and angles, where the shear centre does not coincide with the centroid and a load through the centroid also twists the member. It stops holding for built-up and composite sections, where the shear flow across the joint between components is the governing check rather than the peak stress in either one. It stops holding within roughly one section depth of a support or a concentrated load, where the elementary theory does not describe the real stress field.
The direct shear formula has an even blunter assumption: that the stress is uniform. It is not, and never is. The value it returns is a nominal design stress that only means anything when it is compared against an allowable derived the same nominal way. That is why mixing a nominal stress from one method with an allowable from another is a genuine error rather than a rounding difference.
Why This Page Publishes No Allowable Stress Table
There is no table of allowable shear stresses on this page, and that is deliberate. It follows the same rule as the breaker size calculator, which publishes no ampacity table for the same reason: a design value that is wrong by a grade, a bolt class, a duration of load or a service condition is worse than no value at all, because it carries an air of authority it has not earned.
Allowable shear stresses come from the governing standard for your material and jurisdiction — AISC for structural steel in the United States, the NDS for wood, Eurocode 3 in Europe, and the relevant fastener standard for bolts — and local code amendments differ by state, province and country. Whichever applies, the margin between the calculated stress and the permitted one is set through a safety factor or a set of load and resistance factors. The factor of safety calculator covers that ratio; this page stops at the calculated stress.
Where This Sits Next to the Other Stress Tools
The stress and strain calculator handles normal stress: an axial force acting perpendicular to the section, producing stretching rather than sliding. This page handles the parallel case. The shear modulus calculator takes a shear stress and the strain it produced and returns the material's rigidity modulus, which is the stiffness side of the same physics rather than the strength side.
When normal and shear stresses act together, neither one on its own describes how close the material is to yielding, and the von Mises stress calculator combines them into a single equivalent stress. For pressure vessels and pipes, the hoop stress calculator covers the circumferential case. On the geometry side, the section modulus calculator gives the second moment of area this page uses internally, and the beam load calculator works out the shear force to feed in here in the first place.
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
- Using the average stress on a beam — the transverse distribution peaks at the neutral axis, and for a rectangle that peak is 50 per cent above the average.
- Forgetting double shear — a bolt through three plates carries the load on two planes, so the stress is half what a single-shear calculation gives. Getting this backwards is unconservative.
- Using the total load instead of the internal shear — for a beam the shear force varies along the span and is largest at the supports. Take it from a shear diagram, not from the applied load.
- Applying the beam formula to a channel or angle — open thin-walled sections twist unless the load passes through the shear centre, and the elementary formula does not capture that.
- Comparing a nominal stress against an allowable from a different method — nominal shear stresses only mean something against allowables derived on the same nominal basis.
Related Free Tools From Arb Digital
Get the shear force to enter here from the beam load calculator, and the section properties from the section modulus calculator. For the stiffness rather than the stress, use the shear modulus calculator, and for the axial case the stress and strain calculator. Fastener work usually also needs the bolt torque calculator, and results in pascals move to psi or bar through the pressure converter. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
Normal stress acts perpendicular to a surface and pulls it apart or pushes it together. Shear stress acts along the surface and makes one part slide relative to another. They are computed from the same force divided by area, but the direction of the force relative to the surface is what distinguishes them.
Because the shear stress is not uniform through the depth. It is zero at the top and bottom faces, where there is no material beyond them to carry the flow, and maximum at the neutral axis. For a rectangular section the peak is exactly 1.5 times the average, and for a solid circle it is 4/3 times.
A bolt or pin loaded so that the load crosses two of its cross-sections rather than one, as when a central plate is sandwiched between two outer plates. The same force is resisted by twice the area, so the shear stress is half what it would be in single shear.
Whichever one the shear plane actually passes through. If the joint is designed so that the shear plane falls on the unthreaded shank, use the shank area. If threads are in the shear plane, the smaller stress area governs, and the relevant fastener standard specifies which figure to use.
No. It reports a calculated stress. Whether that stress is acceptable depends on the material, the governing standard, the load combination and the safety or resistance factors that apply, and that judgement belongs to a qualified engineer working to the code in force where the work is built.
Evaluating the transverse shear formula at the neutral axis of a thin-walled circular tube gives a peak of almost exactly twice the average stress, in the limit where the wall is thin compared with the diameter. For thick-walled tubes the true factor sits between the 4/3 of a solid circle and this value.
As a rule of thumb, within about one section depth of a support or a concentrated load. In that region the stress field is governed by local bearing and disturbance effects rather than by elementary beam theory, and a more detailed analysis is needed.
This tool is provided for educational and preliminary sizing use. It is not a structural design, it is not stamped, and it publishes no allowable stress values of its own. Local codes and standards govern, and any load-bearing application must be checked by a licensed engineer.
