What formula does the calculator use?

It uses Hooke's law in the linear-elastic region: E = σ/ε.

What units should I use for Young's modulus and stress?

Enter both Young's modulus and stress in MPa. The modulus result also includes a GPa reading.

What unit is used for strain?

Strain is dimensionless and is entered as a ratio such as 0.001.

Which values are required?

Enter the two known positive values needed for the selected calculation direction.

Can this calculator be used beyond the elastic region?

No. The calculation is intended for the linear-elastic region where Hooke's law applies.

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Young's Modulus Calculator

Solve Young's modulus (modulus of elasticity) in the linear-elastic region using E = σ/ε (Hooke's law). Three directions: modulus E = σ/ε, stress σ = E·ε, strain ε = σ/E. Pick the unknown, supply the other two positive values. Result in MPa with a GPa reading (e.g. steel ≈ 200 000 MPa).

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2 examples

Modulus: σ=200 MPa, ε=0.001 → E = 200000 MPa (200 GPa)

E = σ/ε = 200/0.001 = 200000 MPa = 200 GPa. Typical carbon-steel stiffness.

{"result":"Young's modulus E = σ/ε = 200/0.001 = 200000.0000 MPa (= 200.0000 GPa).","metadata":{"input":{"solveFor":"modulus","stress":200,"strain":0.001},"result":{"solveFor":"modulus","modulus":200000,"modulusUnit":"MPa","modulusGPa":200,"stress":200,"strain":0.001}}}

Strain: E=210000 MPa, σ=210 MPa → ε = 0.001

ε = σ/E = 210/210000 = 0.001. Solving for the unknown strain from modulus and stress.

{"result":"Strain ε = σ/E = 210/210000 = 0.001000.","metadata":{"input":{"solveFor":"strain","E":210000,"stress":210},"result":{"solveFor":"strain","strain":0.001,"strainUnit":"-","modulus":210000,"stress":210}}}

Inputs

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5 options

SettingsAdjust formats, ranges, numbers, and modes.5

Solve forselectOptionalYoung's Modulus E (MPa)numberOptionalYoung's modulus in MPa. Required when solving for stress or strain. Typical: steel ≈ 200000–210000, aluminum ≈ 70000.Stress σ (MPa)numberOptionalNormal stress in MPa. Required when solving for modulus or strain.Strain εnumberOptionalDimensionless strain (ΔL/L₀). Required when solving for modulus or stress. Typically very small (1e-4 – 1e-3).Decimal PlacesnumberOptional

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Young's Modulus Calculator

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Examples

1. Calculate modulus from stress and strain

2. Calculate strain from modulus and stress

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