Stress, strain and Young's modulus calculator
Stress, strain and Young's modulus for a specimen in tension.
Fill in the fields and the result will appear here automatically.
Calculate engineering axial stress F/A, measured modulus E=FL/(AΔL), or length change ΔL=FL/(AE). Positive force and ΔL denote tension, negative values compression. In stress mode, length and measured change may be omitted or zero; then only F/A is reported. Modulus is estimated only from a nonzero force and length change with matching signs.
How it works
Formula and logic
σ=F/A in MPa, ε=ΔL/L, E=FL/(AΔL), and ΔL=FL/(AE). A measured modulus refers to the linear part of an axial test, not automatically the whole range up to yield.
Example
10 kN on 100 mm² gives 100 MPa, and 0.5 mm of stretch over a metre gives a modulus of 200 GPa — steel.
Fields and units
- What to find — list option
- Axial force — N
- Cross-section area — mm²
- Original length — mm
- Elongation — mm
- Young's modulus — MPa
How to use
- — Choose what to solve for: stress, modulus or elongation.
- — Enter the force in newtons and the cross-section in square millimetres.
- — Calculate engineering axial stress F/A, measured modulus E=FL/(AΔL), or length change ΔL=FL/(AE). Positive force and ΔL denote tension, negative values compression. In stress mode, length and measured change may be omitted or zero; then only F/A is reported. Modulus is estimated only from a nonzero force and length change with matching signs.
- — Small uniaxial deformation and the linear relation σ=Eε with positive E. Original area, temperature and material properties are constant. The linear limit need not coincide with yield; neither limit nor component strength is determined here.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: linear axial stress and strain
- Limitation
- Small uniaxial deformation and the linear relation σ=Eε with positive E. Original area, temperature and material properties are constant. The linear limit need not coincide with yield; neither limit nor component strength is determined here.
FAQ
How does Young's modulus differ from spring stiffness?
Component stiffness depends on geometry: for a uniform rod k=EA/L. E characterises material under stated conditions, but may depend on temperature, direction, composition and test procedure. It is not automatically identical for every specimen.
Why do newtons per mm² come out as megapascals directly?
Because a pascal is a newton per square metre, and a square millimetre is a million times smaller. The units coincide exactly, so nothing needs converting.
Up to what load is this valid?
Small uniaxial deformation and the linear relation σ=Eε with positive E. Original area, temperature and material properties are constant. The linear limit need not coincide with yield; neither limit nor component strength is determined here.
Does it apply to compression?
For many metals the modulus in compression is practically the same and the formulas coincide. Concrete, cast iron and composites behave differently in tension and compression, so the result cannot be carried across.