Young's Modulus Calculator
Enter the axial force, cross-sectional area, original length and elongation of a specimen. The calculator returns stress σ, strain ε and Young's modulus E.
Young's modulus E (GPa)
200
- Stress σ (MPa)
- 100
- Strain ε (dimensionless)
- 0
- Young's modulus E (Pa)
- 200,000,000,000
Stress σ = F/A. Strain ε = ΔL/L₀. Young's modulus E = σ/ε = (F·L₀)/(A·ΔL). Valid only in the linear elastic region — below the proportional limit. Typical values: rubber ~0.01–0.1 GPa, wood 9–13 GPa, aluminium ~69 GPa, steel ~200 GPa, diamond ~1,200 GPa.
How to use this calculator
Fill in the four boxes using SI base units: force F in newtons, area A in square metres (1 cm² = 0.0001 m²), original length L₀ in metres, and change in length ΔL in metres (1 mm = 0.001 m). The defaults show a steel rod under 10 kN of tension — the result lands at ~200 GPa, which is the textbook value for structural steel.
How the calculation works
Stress is force per unit area: σ = F/A, measured in pascals (1 Pa = 1 N/m²). Strain is the fractional change in length: ε = ΔL/L₀, dimensionless. Young's modulus is the ratio of the two in the linear elastic region: E = σ/ε. Combining the three gives the working formula E = (F·L₀)/(A·ΔL). E is a material property — geometry cancels out, so a thick rod and a thin wire of the same material give the same E.
Worked example
A steel rod 2 m long with a 1 cm² (1 × 10⁻⁴ m²) cross-section carries a 10 kN tensile load and stretches by 1 mm. Stress σ = 10,000 / 0.0001 = 1 × 10⁸ Pa = 100 MPa. Strain ε = 0.001 / 2 = 5 × 10⁻⁴. Young's modulus E = σ/ε = 1 × 10⁸ / 5 × 10⁻⁴ = 2 × 10¹¹ Pa = 200 GPa, the standard value for structural steel.
Frequently asked questions
What is Young's modulus in plain English?
It's a number that says how stiff a material is. Stretch a steel bar and an aluminium bar of the same shape with the same force and the steel bar barely moves while the aluminium bar moves about three times as much — because steel's Young's modulus (~200 GPa) is about three times aluminium's (~69 GPa). It measures resistance to elastic deformation along the loading axis.
What units should I use?
Stick to SI base units in the inputs: newtons for force, square metres for area, metres for length and elongation. The result is presented in pascals, megapascals (MPa) and gigapascals (GPa) because real materials sit at very large numbers — steel at 2 × 10¹¹ Pa is more readable as 200 GPa.
What's the difference between Young's modulus, shear modulus and bulk modulus?
Young's modulus E covers stretching or compressing along one axis. Shear modulus G covers shape change at constant volume (twisting a rod). Bulk modulus K covers uniform compression on all sides (hydrostatic pressure). For isotropic materials they are linked by Poisson's ratio ν: E = 2G(1 + ν) = 3K(1 − 2ν).
Does this work past the yield point?
No. Young's modulus is the slope of the stress–strain curve only while that curve is straight — the linear elastic region. Once a metal yields, deformation becomes plastic and the relationship is no longer described by a single constant. For design work, keep the calculated stress σ well below the material's yield stress.
What are typical values?
Rubber 0.01–0.1 GPa, polyethylene ~0.8 GPa, wood (along the grain) 9–13 GPa, concrete 17–30 GPa, glass 50–90 GPa, aluminium ~69 GPa, brass ~110 GPa, copper ~117 GPa, structural steel ~200 GPa, tungsten ~400 GPa, diamond ~1,200 GPa. Anisotropic materials like wood or carbon fibre have a different E along and across the grain.
Why is strain dimensionless?
Strain divides a length change by a length, so the units cancel. It is sometimes given as a percentage (multiply by 100) or in microstrain (multiply by 10⁶). A strain of 0.001 is 0.1 % or 1,000 µε — three ways of saying the same thing.
Can the inputs be negative?
For uniaxial tension keep them positive and the calculator handles the magnitudes. Compression flips the sign of both stress and strain, so the modulus comes out the same. This calculator clamps to non-negative inputs; track signs separately if you are solving a mesh of internal forces.
How does temperature affect E?
Young's modulus drops slowly as temperature rises — for most metals around 2–5 % per 100 °C in the working range, and much faster as you approach the melting point. Design handbooks tabulate E at room temperature; for hot service, use the value at the operating temperature.