Calculate shear stress τ = F/A from a force applied parallel to a cross-sectional area — not perpendicular through it, like normal stress — solve for force or area instead, and read the result in Pa, kPa, MPa, or psi.
Enter the applied parallel force and the cross-sectional area it acts over. Shear stress comes from a force sliding one layer of material past another — parallel to the surface, unlike normal stress where the force pushes or pulls straight through it.
The load applied parallel to the cross-section, in newtons.
The area of the plane the force slides across, in square meters.
Use 1 for single shear or 2 for a typical double-shear joint.
The model uses τ = F/(nA), where n is the number of equally loaded shear planes.
Already know the shear stress? Solve for the force or the area instead of computing shear stress directly.
The applied parallel load, in newtons.
The area the force slides across, in square meters.
The known or allowable shear stress, in megapascals.
Default example: solving for area at τ = 50 MPa and F = 5,000 N gives A = 100 mm².
A standalone stress-unit converter. Edit any one field and the other three update instantly — useful for translating a datasheet's psi rating into MPa, or vice versa.
Result
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Enter the parallel force and area to compute shear stress.
Pa—
kPa—
MPa—
psi—
5 min read4 steps6 terms3 examples6 FAQsτ = F / A
Shear stress describes the internal force that develops when a load tries to slide one layer of a material past an adjacent layer, rather than pulling or pushing straight through it.
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Walk-through
How to Use This Calculator
4 steps▸
1
Enter the parallel force and cross-sectional area
On the Shear Stress tab, type in the force applied parallel to the surface in newtons (N) and the cross-sectional area it slides across in square meters (m²). The calculator updates the shear stress instantly as you type.
2
Read the result in your preferred unit
The result card shows τ in megapascals (MPa) as the headline number, with pascals (Pa), kilopascals (kPa), and psi shown alongside it — no separate conversion step needed.
3
Or solve for force or area
Switch to the Solve tab if you already know the shear stress and one other value. Pick what you're solving for — Shear Stress, Force, or Area — enter the other two, and the calculator rearranges τ = F/A for you.
4
Convert a standalone shear stress value
The Units tab is a free-standing converter: type a value into any of the Pa, kPa, MPa, or psi fields and the other three update automatically, independent of the Shear Stress and Solve tabs.
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Reference
Formula & Methodology
2 formulas▸
Shear stress
τ = F / A
Shear stress (τ, the Greek letter tau) is the internal force per unit area that develops when a force acts parallel to a cross-section, sliding one layer of material past another. F is the applied force in newtons (N), and A is the cross-sectional area it acts over in square meters (m²). Because a newton per square meter is defined as a pascal, τ = F/A comes out directly in pascals (Pa), exactly like normal stress — the only difference is the direction the force is applied.
Rearranged for force or area
F = τA A = F / τ
The same relationship rearranges to solve for either of the other two variables: multiply shear stress by area to get force, or divide force by shear stress to get the required area. This is exactly how a fastener is sized — given the load it must carry and the material's allowable shear stress, solving for A gives the minimum shear area needed.
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Glossary
Key Terms Explained
6 terms▸
Shear stress (τ) ↗The internal force per unit area that develops when a force acts parallel to a cross-section, causing one layer of material to slide relative to an adjacent layer. Measured in pascals (Pa), or pounds per square inch (psi) in US customary units.
Parallel force ↗The load that produces shear stress, applied parallel to (in the plane of) the cross-section being sheared — as opposed to a normal force, which acts perpendicular to the cross-section and produces tensile or compressive stress instead.
Cross-section ↗The plane along which the shearing action occurs — for a bolt, this is the plane where the two clamped pieces meet and try to slide past each other. Its area is what F is divided by to get τ.
Transverse force ↗Another name for a shear-producing force, emphasizing that it acts across (transverse to) the member's axis rather than along it.
Tau (τ) ↗The Greek letter conventionally used to denote shear stress, distinguishing it from sigma (σ), which denotes normal stress, in engineering formulas and textbooks.
Bolt shear ↗The most common real-world application of this formula: a bolt clamped through two plates carries the joint's load in shear across its cross-section, and engineers size the bolt diameter so that shear stress stays below the bolt material's allowable shear strength.
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Scenarios
Real-World Examples
3 worked examples▸
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Mechanical designer
A bolt carrying a joint load in single shear
Parallel force, F 5,000 NCross-sectional area, A 0.0001 m²
τ = 5,000 N ÷ 0.0001 m² = 50,000,000 Pa = 50 MPa. That's a moderate shear stress — many bolt-grade steels have an allowable shear strength well above 50 MPa, so this connection likely has margin, but the specific bolt's rating should still be checked.
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Structural engineer
Sizing a shear pin for an allowable stress
Solve for AreaParallel force, F 5,000 NAllowable shear stress, τ 50 MPa
A = F/τ = 5,000 N ÷ 50,000,000 Pa = 0.0001 m² = 100 mm². The pin's cross-section needs to be at least 100 mm² to keep the shear stress at or below the 50 MPa allowable — roughly an 11 mm diameter round pin.
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Materials researcher reading a datasheet
Converting a psi rating to MPa
Given rating 7,252 psiTab used Units converter
7,252 psi converts to roughly 50 MPa (50,000,000 Pa) — the same shear stress as the first example, just expressed in US customary units. The Units tab handles this conversion directly without needing the force and area that produced it.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Shear stress describes the internal force that develops when a load tries to slide one layer of a material past an adjacent layer, rather than pulling or pushing straight through it. It's the governing calculation for bolts, rivets, pins, welds, and any other fastener or joint that carries load by resisting sliding rather than tension or compression.
Shear versus normal stress: direction is everything
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The formula τ = F/A looks identical to normal stress, σ = F/A, and the arithmetic really is the same — but the physical setup is different. Normal stress comes from a force acting perpendicular to a cross-section, pulling it apart (tension) or pushing it together (compression). Shear stress comes from a force acting parallel to the cross-section, trying to slide one face past the other, the way scissor blades cut paper by sliding past each other rather than crushing it. A single component can experience both kinds of stress simultaneously depending on how the load is applied — see the companion Stress Calculator for the normal-stress case.
Why bolts and pins are sized by shear
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Most bolted and pinned connections transfer load primarily through shear, not tension. A bolt clamping two plates together resists the plates sliding relative to each other along the bolt's cross-section — that's a shear load. Engineers size the bolt diameter (and therefore its cross-sectional area) so the resulting shear stress stays comfortably below the bolt material's allowable shear strength, which is itself typically a fraction of the material's tensile strength.
Single shear versus double shear
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A joint is in single shear when the fastener has one shear plane — one place where the two connected pieces can slide relative to each other, as in a simple lap joint. A joint is in double shear when the fastener passes through three overlapping pieces (or a clevis-and-pin arrangement), creating two shear planes that share the load. Because two planes resist the same total force, the shear stress on each plane in a double-shear joint is about half what it would be in an equivalent single-shear joint — divide this calculator's single-shear result by 2, or halve the force before entering it, to model the double-shear case.
Limits of this simple model
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This calculator assumes the parallel force is distributed uniformly across the shear plane — a reasonable first approximation for a bolt, pin, or rivet in direct shear. Real fasteners can see uneven stress distribution near edges and holes, combined loading (shear plus bending), or fatigue effects from repeated loading that a single static τ = F/A calculation doesn't capture. For safety-critical joints, cross-check this result against the fastener manufacturer's rated shear strength and apply an appropriate safety factor before finalizing a design.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for shear stress?+
τ = F/A — shear stress equals the applied force divided by the cross-sectional area it acts over, where the force is applied parallel to the surface. Force is in newtons (N) and area is in square meters (m²), giving shear stress directly in pascals (Pa).
How is shear stress different from normal stress?+
Both use the same F/A arithmetic, but the direction of the force differs. Normal stress (σ = F/A) comes from a force acting perpendicular to the cross-section, pulling or pushing straight through it. Shear stress (τ = F/A) comes from a force acting parallel to the cross-section, sliding one layer past another — like scissors cutting rather than a hydraulic press crushing.
Why are bolts sized using shear stress?+
Most bolted and pinned connections transfer their load primarily by resisting the connected pieces sliding past each other along the fastener's cross-section — that's a shear load, not a tensile one. Engineers pick a bolt diameter large enough that the resulting shear stress stays below the material's allowable shear strength.
What units does this calculator use?+
Force is entered in newtons (N) and area in square meters (m²) on the Shear Stress and Solve tabs. The result is shown in pascals (Pa), kilopascals (kPa), megapascals (MPa), and psi simultaneously. The Units tab lets you convert freely between all four without entering a force or area.
Can I solve for force or area instead of shear stress?+
Yes — use the Solve tab and choose what you're solving for. Pick Force to compute F = τA from a known shear stress and area, or pick Area to compute A = F/τ from a known force and allowable shear stress. This is the common workflow for sizing a bolt or pin to a target shear stress limit.
What's the difference between single shear and double shear?+
A single-shear joint has one shear plane resisting the load, which is what this calculator computes directly. A double-shear joint (like a pin through a clevis) has two shear planes sharing the same total force, so the stress on each plane is roughly half the single-shear value — divide this calculator's result by 2, or halve the input force, to model a double-shear connection.
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