Hooke's Law Material Calculator
Calculate axial stress or engineering strain from Young’s modulus, including signed extension or shortening of a uniform member.
Apply the material form of Hooke’s law to a uniform member under axial loading. Enter Young’s modulus and either stress or engineering strain to find the other, together with extension or shortening of the original length.
How to use this tool
- Choose stress or strain as the unknown quantity.
- Enter a positive Young’s modulus and select its pressure unit.
- Supply signed stress or strain, taking tension as positive and compression as negative.
- Enter the original length and review the predicted change using that same length unit.
Formula
σ = Eε; ε = ΔL / L₀; ΔL = εL₀
σ is normal stress, E is Young’s modulus, and ε is engineering strain measured relative to original length L₀. The stress and modulus units are reconciled internally. This form assumes a linear uniaxial response and a uniform strain along the member; it is different from specifying a complete three-dimensional constitutive law.
Example
For E = 200 GPa and strain = 0.001, stress is 200 MPa. A member originally 2 m long extends by 0.001 × 2 = 0.002 m, giving a modeled final length of 2.002 m.
Frequently asked questions
How is this different from a spring constant?
Young’s modulus describes a material response. For an ideal uniform axial bar, the corresponding structural spring stiffness is EA/L, which also depends on cross-sectional area and length.
Can I use this after yielding?
No. A constant elastic modulus does not represent permanent plastic deformation. The tool cannot determine the proportional limit from the entered modulus alone.
Does a compression result include buckling?
No. It calculates uniform axial shortening. A slender member can become unstable before its material reaches a simple stress limit; geometry and restraint need separate analysis.
Sources
Last updated: 2026-10-30