AIEngineeringTool

Shear Modulus Calculator

Calculate shear modulus from shear stress and shear strain.

LIVE INPUTS

Enter engineering parameters

Results update immediately. Select the unit used for each input before reviewing the result.

CALCULATION INPUTS

LIVE 2D EXPLANATION

80 GPaShear stress: 80 MPaarea A
G = τ / γThe geometry, arrow and label respond to the current calculation state.

PRIMARY RESULT

Shear modulus80GPa
Calculation basisMaterial Mechanics
Input unit basisMPa
✓
Live calculation ready for review

This is an educational or preliminary result. Apply relevant standards and engineering judgement before use.

ENGINEERING PRINCIPLE

Within the elastic range, shear stress is proportional to shear strain.

Calculate shear modulus from shear stress and shear strain.

FORMULA & VARIABLES

G = τ / γ

  • G = shear modulus (Pa)
  • τ = shear stress (Pa)
  • γ = shear strain (dimensionless)

CALCULATION STEPS

How this result is assembled

  1. Convert the entered values to the SI basis required by the formula.
  2. Apply G = τ / γ using the current inputs.
  3. Present the result as 80 GPa and review the stated assumptions.

FORMULA VERIFICATION

Units, scope and reference

Reference: NIST SP 811 for unit relationships; standard classical mechanics and strength-of-materials derivations for the stated scalar relation.

Internal basis: All inputs are converted to the calculator’s SI base before the formula is evaluated.

Valid conditions: Positive finite scalar input values in the current calculator model.

Limitations: The material is in its linear elastic range. This is a simple shear state.

ASSUMPTIONS

Use this result in context

  • The material is in its linear elastic range.
  • This is a simple shear state.

Results must be verified by a qualified engineer and checked against applicable engineering standards, material properties, loading conditions and design requirements.

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