Young's Modulus Calculator — Stress, Strain & Stiffness
Young's modulus E quantifies how stiff a material is: how much stress it takes to produce a given strain. Enter the applied force, cross-sectional area, original length and extension to calculate E — or rearrange to find force or extension for a known material.
Solve for
N
m²
m
m
Stiffness of the material — GPa (= 10⁹ Pa)
20 GPa
E- 1
Stress σ = F ÷ A
1,000 ÷ 0.0001 = 10 MPa - 2
Strain ε = ΔL ÷ L₀
0.5 mm ÷ (1 × 1000) = 0.0005 - 3
Young's Modulus E = σ ÷ ε
10 MPa ÷ 0.0005 ÷ 1000 = 20MPa ÷ dimensionless strain = MPa; ÷ 1000 converts MPa to GPa.
How does this calculator work?
E = (F/A) / (ΔL/L₀): Young's modulus equals stress divided by strain. Enter force, cross-sectional area, original length and extension to get E in GPa, or rearrange to solve for force or extension. Steel ≈ 200 GPa, aluminium ≈ 70 GPa, rubber ≈ 0.01–0.1 GPa.
Formula
How this is calculated
Young's modulus (also called the elastic or longitudinal modulus) is defined as the ratio of axial stress to axial strain within the linear elastic (Hookean) region: E = σ/ε = (F/A)/(ΔL/L₀). Stress σ is the force per unit area acting along the specimen axis; strain ε is the fractional change in length. Both stress and E have units of Pascals (Pa), while strain is dimensionless. In practice E is reported in GPa: steel ≈ 200 GPa, aluminium alloys ≈ 69–72 GPa, titanium ≈ 116 GPa, concrete ≈ 25–35 GPa, wood (along grain) ≈ 10–15 GPa, and rubber ≈ 0.01–0.1 GPa.
The formula can be rearranged to solve for force (F = E × A × ΔL / L₀) or extension (ΔL = F × L₀ / (E × A)), which is Hooke's law in structural form. This calculator supports all three rearrangements via the 'Solve for' selector.
Limitations: the calculation assumes the material is isotropic, homogeneous, and loaded within its linear elastic range (well below the yield strength). Beyond the yield point, permanent plastic deformation occurs and E no longer applies. For anisotropic materials (composites, timber, bone) E varies with direction and you need the full stiffness tensor.
Frequently asked questions
Young's modulus E is an intrinsic material property, independent of specimen size. Stiffness k (N/m, used in Hooke's spring law F = kx) depends on both material and geometry: k = E × A / L₀. A short, thick steel rod is stiffer than a long, thin one, even though both have the same E.
The calculator uses SI base units internally: force in Newtons (N), area in m², lengths in metres (m). One centimetre² = 0.0001 m², one millimetre² = 1 × 10⁻⁶ m². The result is shown in GPa for convenience, since most engineering moduli are in that range.
The most direct method is a tensile test: clamp a standard dog-bone specimen, apply a known increasing force (recorded by a load cell), and measure elongation (via an extensometer). Plot stress vs strain; the slope of the initial linear region is E. Ultrasonic resonance and nanoindentation methods give E without destructive loading.
Also known as
TG we-Calculate Editorial Team. (2026). Young's Modulus Calculator — Stress, Strain & Stiffness [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/young-modulus-calculator
TG we-Calculate Editorial Team. "Young's Modulus Calculator — Stress, Strain & Stiffness." TG we-Calculate. 2026. https://we-calculate.com/calculator/young-modulus-calculator.
TG we-Calculate Editorial Team, "Young's Modulus Calculator — Stress, Strain & Stiffness," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/young-modulus-calculator
@misc{wecalculate_young_modulus_calculator, title = {Young's Modulus Calculator — Stress, Strain & Stiffness}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/young-modulus-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?