Young Modulus Calculator
Get stress, strain, and Young modulus E in metric or imperial units.
What it does
Pull a bar and it gets longer; squeeze it and it gets shorter. Inside the elastic range that shape change stays proportional to the load, and the constant of proportion is Young modulus E. Engineers use E to size rods, cables, and columns before anything is built.
The tool above runs the three numbers at once. Enter force, cross section, stretch, and starting length in metric or imperial. It returns stress, strain, and E in matching units. Defaults describe a steel like bar at 5000 N on 100 mm2, so the page opens solved at 50.00 MPa, 0.000250 strain, and 200.0 GPa.
Units decide the reading path. Metric stress in MPa comes straight from newtons over mm2, and E in GPa follows after dividing by strain. Imperial stress in psi comes from lbf over in2, with E reported in ksi. Both paths share one definition of strain: stretch over starting length, with lengths first brought into one unit.
The worked example is worth reading slowly because each step checks the next. Stress 50 MPa over strain 0.00025 gives 200 GPa, the textbook neighborhood for steel. If your result lands near 70 GPa, think aluminum; near 110 GPa, think copper alloys; far below 1 GPa, think polymers or rubber.
Use the table for typical E values, then test your bar. The page fits straight line behavior only, so bent, buckled, or yielded pieces need stronger models. Within range it answers the practical question fast: is this stretch normal for this load, or is something soft.
How to use
- Pick metric or imperial.
- Enter the axial force.
- Enter the cross sectional area.
- Enter the measured stretch and the starting length.
- Read stress, strain, and E.
- Compare E with the table to name the material family.
Formula
- F
- Axial pull or push.
- A
- Cross section: mm2 metric, in2 imperial.
- Stretch
- Measured stretch under load.
- Length
- Starting length before load.
- E
- Stiffness: GPa metric, ksi imperial.
Metric stress lands in MPa (N/mm2) and E in GPa; imperial stress lands in psi with E in ksi. Strain has no units. The formulas assume a uniform bar, small stretch, and room temperature behavior inside the elastic range.
Worked example
Example: steel bar in tension
A 5000 N pull acts on a 100 mm2 bar. It stretches 0.5 mm over a 2 m length. Find stress, strain, and E.
- Stress = force / area = 5000 N / 100 mm2 = 50.00 MPa.
- Length in mm = 2 m x 1000 = 2000 mm.
- Strain = 0.5 / 2000 = 0.000250.
- E = stress / strain = 50 / 0.00025 = 200000 MPa.
- Convert: 200000 MPa = 200.0 GPa.
- That matches steel, so the numbers are sane.
Reference table
| Material | E (GPa) | E (ksi) |
|---|---|---|
| Rubber | 0.01 to 0.1 | 1 to 15 |
| Aluminum | 69 | 10000 |
| Copper | 110 to 128 | 16000 to 18500 |
| Iron | 211 | 30600 |
| Steel | 200 | 29000 |
Limits
- Linear elastic range only; no yield or creep.
- Uniform straight bars; no bending or buckling.
- Room temperature values; heat softens metals.
- Gross area only; holes and notches raise local stress.
Common mistakes
- Mixing mm2 with m2 in one division.
- Using diameter where area is required.
- Entering stretch in cm while length stays in m.
- Reading E from a yielded test curve.
- Comparing E across unit systems without converting.
Try it yourself
Quick checks. Answers sit tucked under each question.
Imperial defaults: 1124 lbf, 0.155 in2, 0.0197 in over 6.56 ft?
Stress = 7,252 psi. Strain = 0.000250. E = 28,977.0 ksi.
Force 2500 N on the same bar with 0.25 mm stretch?
Stress = 25.00 MPa. Strain = 0.000125. E = 200.0 GPa, still steel.
What if stretch doubles at the same load?
Strain doubles to 0.0005 while stress stays 50 MPa, so E stays 200 GPa; E is a material constant, not a load result.
Questions
What is Young modulus?
Stiffness in tension: E = stress / strain, with stress = force / area and strain = stretch / length. Steel sits near 200 GPa.
Stress versus strain versus modulus?
Stress is force per area (MPa or psi). Strain is fractional stretch with no units. Modulus links them: stress = E x strain.
How do units work here?
Use one system per run. Metric divides newtons by mm2 for MPa; imperial divides lbf by in2 for psi. The tool converts each side correctly.
What is typical for steel?
Near 200 GPa in metric or 29000 ksi imperial. Aluminum sits near 70 GPa and rubber far below 1 GPa.
Does it cover compression?
Yes, when squeeze is small and uniform: use absolute values of load and shortening with the same formulas.
Does it cover plastic stretch?
No. Past yield the curve bends and E no longer predicts shape. This page fits the linear range only.