Case 1
- Pulling force
- 1000N
- Cross-sectional area
- 0.0001m²
- Original length
- 2m
- Change in length
- 0.001m
20,000,000,000Pa
Open with these valuesYoung's Modulus Calculator
20,000,000,000Pa
Result: 20,000,000,000 PaYoung's modulus is stress divided by strain: the force per square metre divided by the fraction of its length the sample gained. Strain goes in as a ratio, not a percentage — 1 mm on a 2 m bar is 0.0005, not 0.05. The answer is in pascals; steel sits near 200 GPa, that is 2e11 Pa.
Worked examples
Case 2
- Pulling force
- 500N
- Cross-sectional area
- 0.00005m²
- Original length
- 3m
- Change in length
- 0.002m
15,000,000,000Pa
Open with these valuesCase 3
- Pulling force
- 0.145N
- Cross-sectional area
- 0.00002m²
- Original length
- 0.5m
- Change in length
- 0.0001m
36,250,000Pa
Open with these valuesHow it's calculated
E = stress ÷ strain = (F × L₀) ÷ (A × ΔL)
- StepEnter the tensile force in newtons.
- StepEnter the cross-section the force acts on — a 1 cm bar is 0.0001 m².
- StepEnter the unstretched length and how much it gained, both in metres.
- ResultRead the modulus in pascals; divide by 1e9 for gigapascals.
Reference table
| Force, area, length, stretch | Stress on the sample | Modulus (Pa) |
|---|---|---|
| 0.145, 0.00002, 0.5, 0.0001 | 7250 Pa | 36250000 |
| 10000, 0.001, 5, 0.01 | 10 MPa | 5000000000 |
| 1500, 0.0003, 2.5, 0.0015 | 5 MPa | 8333333333.33 |
| 500, 0.00005, 3, 0.002 | 10 MPa | 15000000000 |
| 1000, 0.0001, 2, 0.001 | 10 MPa | 20000000000 |
| 2000, 0.0002, 1, 0.0005 | 10 MPa | 20000000000 |
Questions
How do I calculate Young's modulus?
Divide the tensile stress by the tensile strain: E = (F × L₀) ÷ (A × ΔL). Use newtons for force, square metres for area and metres for both lengths to get pascals. A 1000 N pull on a 0.0001 m² bar that stretches 0.001 m from an original 2 m gives 20 GPa.
What is Young's modulus?
Young's modulus, or the modulus of elasticity, measures how stiff a material is — how strongly it resists being stretched or compressed. It is the ratio of tensile stress, force per unit area, to tensile strain, the relative change in length. It is measured in pascals and usually quoted in gigapascals.
Is strain a ratio or a percentage?
A ratio. A bar 2 m long that gains 1 mm has a strain of 0.001 ÷ 2 = 0.0005, not 0.05 percent. Entering a percentage here makes the modulus come out a hundred times too small.
What is the difference between stress and strain?
Stress is the force spread over the cross-section, σ = F ÷ A, measured in pascals. Strain is the relative stretch, ε = ΔL ÷ L₀, and is a dimensionless ratio. Young's modulus is stress divided by strain, so it says how much stress a given amount of stretch costs.
What are typical values?
Steel is roughly 200 GPa, copper about 110 GPa, aluminium around 69 GPa, glass near 70 GPa, and rubber only about 0.01 to 0.1 GPa. A higher modulus means the material stretches less under the same stress.
Does Young's modulus always apply?
Only within the elastic region, where stress and strain stay proportional and the material springs back to its original shape. Beyond the elastic limit it deforms permanently and one modulus no longer describes it. This calculator assumes small, reversible deformations.
Sources and last check
Information, not professional advice.