Young's modulus (modulus of elasticity) E, three-way solver: E = σ/ε — plus axial elongation δ = FL/AE with full inverse solver, unit conversions, and reference material values.
E = σ / εδ = F·L / (A·E)Valid only in the linear-elastic region (below yield). Strain ε is dimensionless (ΔL/L); 1 µε = 10⁻⁶.
Assumes uniform axial load on a prismatic bar in the elastic range. For beams in bending use a beam deflection tool.
Values are typical / reference at room temperature — real materials vary by alloy, temper, temperature, and (for wood) grain direction. Always use the datasheet value for design.
| Material | E (typical) | Notes · source |
|---|
A steel sample is under a tensile stress σ = 250.0000 MPa and shows a strain ε = 0.00125 (1250.0 µε).
A steel rod (E = 200.0000 GPa), length L = 2 m, cross-section A = 50 mm², is pulled by F = 10 kN.
Young's modulus (E), also called the modulus of elasticity, is the ratio of tensile stress to tensile strain in the linear-elastic region: E = σ/ε. It measures stiffness — a higher E means less deformation under the same load. Because strain is dimensionless, E has the same units as stress (Pa, typically GPa).
Divide the stress by the strain: E = σ/ε. Example: a stress of 250.0000 MPa producing a strain of 0.00125 gives E = 250.0000 MPa / 0.00125 = 200.0000 GPa. Mode 1 of this calculator does this with full unit support (Pa, kPa, MPa, GPa, psi, ksi for stress; ratio, %, ‰, mε, με for strain).
Rearrange Hooke's law: ε = σ/E. Example: a stress of 250.0000 MPa on steel with E = 200.0000 GPa gives ε = 250.0000 MPa / 200.0000 GPa = 0.00125, which is 1250.0 με (microstrain).
Use δ = F·L/(A·E). Example: a 10 kN pull on a 2 m steel rod (E = 200.0000 GPa) with 50 mm² cross-section gives δ = 2.0000 mm. Mode 2 of this calculator also solves the inverse problems — force, length, area, or E — from a known elongation.
1 psi = 6894.757293168 Pa and 1 ksi = 1000 psi. Examples: 29,000,000 psi = 199.9480 GPa; 300 ksi = 2.0684 GPa; and 200 GPa = 29007.5475 ksi. Mode 1 converts between Pa, kPa, MPa, GPa, psi, and ksi automatically.
Microstrain is strain expressed in parts per million: 1 με = 10⁻⁶. For example, 1250.0 με = 0.00125 = 0.1250 %. Small strains are easier to read in με, which is why this calculator offers ratio, %, ‰, mε, and με units.
About 200 GPa for carbon steel (typical range 200–210 GPa). Stainless steel is about 193 GPa, aluminium alloys about 70–72 GPa, and copper about 110–128 GPa. These are typical reference values at room temperature — real materials vary by alloy, temper, and temperature, so always use the datasheet value for design. Mode 3 lists reference values with their sources.
This tool computes Young's modulus E from stress and strain (E = σ/ε) and axial elongation (δ = FL/AE). For converting between elastic constants — E, shear modulus G, bulk modulus K, Poisson's ratio ν, and Lamé constants — use the elastic constants converter at https://nrtechstudio.com/tools/elastic-constants/.
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