Hooke Law Calculator
Calculate stress, strain, or Young’s modulus using Hooke’s Law. Step-by-step formulas included for rods, beams, shafts, and elastic materials under axial load.
Poisson’s ratio calculator:
This Hookes Law Calculator is used to calculate stress, strain, deformation, or Young's modulus of elastic material. Specify axial load, area, length, or strain to calculate elastic behavior. Calculations are carried out step by step, so that there is no confusion.
Poisson’s ratio Tool Formula:
Hooke's Law:
\[ F = K \times x \]
(where F = force, k = spring constant, x = displacement)
The Hooke's Law Calculator is used to study the elastic behavior of materials subjected to axial load by engineers, students, and designers. According to Hooke's Law, stress in a material is equal to strain within its elastic limit, σ = E × ε, where σ is stress, ε is strain, and E is Young's modulus.
The user may type in the applied load or cross-sectional area, the original length, the Young's modulus of material, or the strain that is measured. The calculator can compute tensile or compressive stress, axial strain, deformation, and elastic modulus. The solutions are presented in a step-by-step format displaying formulas of stress, strain, and elongation, and it is simple to analyze a rod, beam, shaft, or any other mechanical element.
SI units are allowed: N, kN, mm, m, MPa, GPa. This is the perfect tool to be used by mechanical engineers, civil engineers, design engineers, and students in the field of elastic deformation, structural elements, rods, and shafts to design properly and securely by the behavior of elastic material.
⚡ Work & Installation Input to Output:
Input:
- Applied axial load (F)
- Cross-sectional area (A)
- Original length (L0)
- Material Young’s modulus (E)
- Measured strain (ε) if available
- Units: N, kN, mm, m, MPa, GPa
Processing:
- Compute axial stress: σ = F / A
- Compute axial strain: ε = σ / E or from measurement
- Compute elongation: δ = ε × L0
- Compute Young’s modulus if stress and strain are known: E = σ / ε
- Validate input values and unit consistency
Output:
- Axial stress (σ)
- Axial strain (ε)
- Deformation/elongation (δ)
- Young’s modulus (E)
- Step-by-step formulas and calculations
Testing and Final Adjustments
Test common scenarios:
- Rod under F = 50 kN, A = 200 mm², E = 200 GPa, L0 = 1 m → compute σ, ε, δ
- Beam with measured strain ε = 0.001 → compute σ and E
- Edge cases: small or large cross-sections, high loads, extreme Young’s modulus values
- Units validation: N ↔ kN, mm ↔ m, MPa ↔ GPa
- Step-by-step clarity for students and engineers
- Mobile/desktop UX: numeric keypad, labels, error messages
- Include material examples: steel, aluminum, polymers
- SEO metadata: "Hooke’s Law Calculator," "Stress-Strain Calculator," "Elastic Deformation," schema markup
Frequently Asked Questions - Hooke Law Calculator:
What is Hooke's Law?
Hooke's Law states that stress in an elastic material is proportional to strain within the elastic limit, σ = E × ε.
How do I calculate stress?
Axial stress σ = F / A, where F is applied load and A is cross-sectional area.
How do I calculate strain?
Axial strain ε = δ / L0, or ε = σ / E if Young's modulus is known.
How do I calculate elongation?
Elongation δ = ε × L0, where L0 is the original length of the member.
How do I calculate Young's modulus?
E = σ / ε, using known stress and strain values.
Which units are supported?
Force in N or kN, length in mm or m, stress in MPa or GPa.
Who should use this calculator?
Mechanical engineers, civil engineers, design engineers, and students analyzing elastic material behavior.
Why is Hooke's Law important?
It allows calculation of deformation and stress in materials within the elastic limit, ensuring safe design.
Can it be used for all elastic materials?
Yes, for metals, polymers, composites, and other materials within the elastic limit.
Does it show step-by-step calculations?
Yes, all formulas and intermediate steps are displayed for clarity and verification.
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