Hooke's law stress-strain calculation tool was developed to calculate stress-strain relations for a homogeneous isotropic material under most general stress/strain conditions. If strains on a structure are measured in elastic range, stresses can be calculated from these results with the usage of Hooke's law strain - stress calculator.

The formulas used for the calculations are given in the "List of Equations" section.


Parameter Symbol Value Unit
Elastic modulus E
Poisson's ratio v ---
Known parameters           
Modulus of rigidity G --- ---
Parameter Symbol Value Unit
Normal stress σx
Normal stress σy
Normal stress σz
Shear stress τxy
Shear stress τyz
Shear stress τzx
Symbol Parameter Value Unit
Normal strain εx μm/m (μin/in)
Normal strain εy
Normal strain εz
Shear strain γxy
Shear strain γyz
Shear strain γzx


Note: Use dot "." as decimal separator.


Homogeneous Material: Material which has got same material properties at all of its points.

Hooke's Law: The relation in which the stress σ is directly proportional to the strain ε. (σ=E ε). Hooke’s law is also valid for shear stress and strain in the linear elastic range (τ=Gγ)

Isotropic Material: Material in which strength, elastic modulus and thermal conductivity properties are independent from the choice of coordinate system.

Modulus of elasticity (Young’s modulus): The rate of change of unit tensile or compressive stress with respect to unit tensile or compressive strain for the condition of uniaxial stress within the proportional limit. Typical values: Aluminum: 69 GPa, Steel: 200GPa.

Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

Poisson’s ratio: The ratio of lateral unit strain to longitudinal unit strain under the condition of uniform and uniaxial longitudinal stress within the proportional limit.

List of Equations:

Parameter Symbol Formula
Normal strain
εx x/E-vσy/E-vσz/E)
Normal strain εy y/E-vσz/E-vσx/E)
Normal strain εz z/E-vσx/E-vσy/E)
Shear strain γxy τxy/G
Shear strain γyz τyz/G
Shear strain γzx τzx/G
Modulus of rigidity G E/(2(1+v))