Shear Stress Calculator

Shear stress: Force spread over an area parallel to the surface. In this tool, it is reported as average shear stress in force-area and bolt/pin modes, and as maximum shear stress in torsion mode.

Calculation mode: The case you choose so the calculator uses the correct equation branch.

Shear force (N): The load acting parallel to the resisting area.

Shear area (mm^2): The area resisting sliding in average shear mode.

Shear planes: The number of places where the part can shear. Double shear means two resisting planes, so the effective area doubles.

Effective shear area: The total area actually used in the denominator of the stress calculation.

Torque (N mm): A twisting moment applied to a shaft.

Polar moment of area: A geometry value that shows how strongly a round section resists twisting. Bigger values lower torsional shear stress for the same torque [1].

Outer radius: Half of the outer shaft diameter. In a round shaft, the maximum torsional shear stress occurs at this outer surface [1].

Mistake: Leaving Calculation mode on average shear when the problem is really a bolt, pin, or twisting shaft case.
Fix: Pick the correct Calculation mode first, then verify the Formula used output before trusting the answer.

Mistake: Entering the area of one plane in Shear area (mm^2) for a double-shear bolt problem instead of using Shear planes .
Fix: In bolt or pin problems, enter only the bolt Diameter (mm) and set Shear planes to Single shear or Double shear so the calculator builds the correct Effective shear area .

Mistake: Typing diameter in inches or area in m^2 even though the labels say Diameter (mm) and Shear area (mm^2) .
Fix: Convert your numbers to the labeled units before calculating, then use Stress output unit only for the result display.

Mistake: Using 0 or a negative number in Shear force (N) , Shear area (mm^2) , Diameter (mm) , or Torque (N mm) .
Fix: Enter positive values for the active mode. If the problem gives a load direction, use the load magnitude here and interpret the result as stress magnitude.

Mistake: Entering a hollow-shaft Inner diameter (mm) that is equal to or larger than Diameter (mm) .
Fix: Keep Inner diameter (mm) at 0 for a solid shaft, or enter a positive value strictly smaller than the outer Diameter (mm) .

Mistake: Comparing torsion results directly to average shear values without noticing the meaning of Shear stress changed.
Fix: Read the Formula used output and remember that torsion mode gives the maximum outer-surface shear stress, not an average over the whole cross section.

• This calculator is for the specific solid-mechanics cases shown in Calculation mode. It does not cover fluid shear stress, shear modulus, beam shear-distribution formulas, or non-round torsion sections.
• Average and bolt/pin modes report average shear stress, using τ = V/A or τ = V/(nA). Real stress can be uneven across a section.
• Torsion mode reports the maximum shear stress at the outside surface of a round shaft, not an average value through the cross section [1].
• Inputs are assumed to use the exact labeled units: N, mm, mm^2, and N mm. Wrong unit entry is one of the biggest sources of bad results.
• For bolt or pin shear, the model assumes a circular cross section with area based on Diameter (mm) and either 1 or 2 shear planes. It does not account for threads, clearance, bending, bearing, or eccentric loading.
• For hollow-shaft torsion, Inner diameter (mm) must be 0 or smaller than the outer Diameter (mm). If the geometry is not a circular annulus, this torsion formula does not apply.
• The tool reports stress magnitude from positive load magnitudes. It does not track sign conventions, directions, failure criteria, or safety factors.
• Output unit changes only the displayed stress value. The internal geometry and load formulas stay based on the entered SI-style units.

Equations used

Each mode uses one standard solid-mechanics formula so you can match the equation to the physical situation.

τ = V / A

Average shear from force and area. Here, τ is shear stress, V is shear force, and A is resisting area.

τ = V / (nA)

A = πd^2 / 4

Bolt or pin shear. The calculator first finds the circular area from Diameter (mm), then multiplies by the number of shear planes n, which is 1 for single shear or 2 for double shear [2].

τ_max = Tc / J

c = d_o / 2

J = πd_o^4 / 32

J = π(d_o^4 - d_i^4) / 32

Round-shaft torsion. The calculator uses the outer radius c and polar moment of area J. For torsion mode, the reported value is the maximum shear stress at the outer surface of a solid or hollow circular shaft [1].

Unit handling

With force in N and area in mm^2, stress comes out naturally in N/mm^2, which is numerically equal to MPa.

1 N/mm^2 = 1 MPa

1 MPa = 1,000,000 Pa

1 psi = 6894.757293168 Pa

1 ksi = 1000 psi

If you choose Pa, psi, or ksi, the calculator converts the stress after solving in the base unit.

Worked mini-examples

Average shear example: If V = 12000 N and A = 300 mm^2, then

τ = 12000 / 300 = 40 N/mm^2 = 40 MPa

Double-shear bolt example: If V = 10000 N, d = 20 mm, and n = 2, then one-plane area is

A = π(20)^2 / 4 = 314.159 mm^2

The effective area is 2A = 628.319 mm^2, so

τ = 10000 / 628.319 = 15.915 MPa

Solid shaft torsion example: If T = 500000 N mm and d_o = 20 mm, then c = 10 mm and

J = π(20)^4 / 32 = 15707.963 mm^4

τ_max = 500000 x 10 / 15707.963 = 318.310 MPa

How to interpret outputs

Shear stress is the main result. Higher values mean stronger shearing action. Compare it only to a limit or allowable value that uses the same units and the same stress definition.

Effective shear area helps you catch denominator mistakes, especially in double shear.

Polar moment of area and Outer radius are shown in torsion mode so you can trace where the torsion result came from.

Formula used is a quick check that you selected the right mode before using the number in homework or design steps.

Assumptions behind the math

The formulas assume the selected load case is idealized and that the entered dimensions represent the resisting section directly. Average-shear formulas do not show local stress concentrations, and the torsion formula applies to circular shafts under torsion rather than combined loading [1].