MotionLab

Young's Modulus Calculator

A single number describing how stiff a material is — steel's is far higher than rubber's.

Stress (Pa)

Strain

Young's modulus (Pa)

5,000,000,000

E = σ / ε

What you entered

Stress (Pa): 10000000Strain: 0.002

1
E = σ ÷ ε
10000000 ÷ 0.002= 5.0000e+9 Pa

Result

Young's modulus (Pa): 5,000,000,000

A stress of 10000000 Pa producing a strain of 0.002 gives a Young's modulus of 5,000,000,000 Pa.

Young's modulus from stress and strain

Young's modulus is stress divided by strain - the stiffness of a material, independent of the size of the sample.

Stress (Pa)	Strain	Young's modulus (Pa)	Comparable material
7e7	0.001	7.0000e+10	Aluminium, about 70 GPa
2e8	0.002	1.0000e+11	Brass or bronze range
1.1e8	0.001	1.1000e+11	Titanium, about 110 GPa
1e8	0.0005	2.0000e+11	Steel, about 200 GPa
2e8	0.001	2.0000e+11	Steel, about 200 GPa

The last two rows both give 200 GPa from different stress and strain pairs, which is exactly what makes the modulus useful - it is a property of the material rather than the specimen, so any valid test on the same steel returns the same number. Steel at around 200 GPa is roughly three times stiffer than aluminium at 70, which is why an aluminium beam of the same dimensions deflects three times as far under the same load. Stiffness is not strength: a material can be stiff and brittle, or flexible and very strong. The modulus only applies in the elastic region, before permanent deformation begins.

Stiffness, not strength

Young's modulus measures how much a material resists elastic deformation (stiffness), not how much load it can take before breaking (strength) — a material can be very stiff but still brittle and prone to snapping, like glass.

Only valid in the elastic region

This calculation assumes the material is still behaving elastically (it would spring back to its original shape if unloaded) — beyond a material's yield point, the stress-strain relationship stops being linear and this simple ratio no longer describes its behavior.

Frequently asked questions

A steel bar (E = 200 GPa) has strain of 0.001. What stress is it under?

σ = E × ε = 200 × 10⁹ × 0.001 = 200 MPa. Steel yields at ~250 MPa, so this bar is at 80% of its yield strength — functional but with limited safety margin.

Why is rubber's Young's modulus so much lower than steel's?

Rubber: E ≈ 0.01-0.1 GPa. Steel: E ≈ 200 GPa. This 2,000-20,000× difference means rubber deforms enormously under the same stress. Rubber's polymer chains uncoil easily; steel's metallic bonds resist deformation strongly. Both are useful — flexibility and rigidity serve different purposes.

How do I choose between materials based on Young's modulus?

High E (steel, titanium) for stiff structures where deflection must be minimal — bridges, building frames. Low E (rubber, foam) for vibration damping and flexibility. Medium E (wood, bone) for structures needing some give. See the stress and strain calculators for the full picture.