Young modulus calculator: stress, strain and elongation of a rod
This Young modulus calculator uses the definitions from OpenStax University Physics: stress = F/A, strain = ΔL/L₀ and Young’s modulus E = stress ÷ strain. Example: a 2.0 m steel rod with 30 mm² cross-section carrying 550 kg (5390 N) stretches by 1.80 mm.
Example: Calculate: elongation ΔL for a material · Force F (tension or compression) 5,390 N · Cross-sectional area A 30 mm² · Original length L₀ 2 m · Material (Young’s modulus, OpenStax Table 12.1): steel (200 GPa) → Result: Elongation ΔL = 1.80 mm. Source: OpenStax University Physics Volume 1, 12.3 Stress, Strain, and Elastic Modulus: stress = F⊥/A, strain = ΔL/L₀, Y = (F⊥/A)(L₀/ΔL); Table 12.1 approximate elastic moduli; Example 12.8 (steel rod, 1.8 mm) and 12.7 (granite, 2.85 × 10⁻⁶) (read 09.10.2026). Updated: .
How it is calculated
E = stress ÷ strain = (F/A) · (L₀/ΔL). Stress is the force per cross-sectional area, strain the relative change in length. In the linear range their ratio is a material constant, Young’s modulus. Rearranged, the elongation is ΔL = (F/A) · L₀ / E. The same formulas hold for compression.
Approximate values (OpenStax Table 12.1)
| Material | E | Material | E |
|---|---|---|---|
| steel | 200 GPa | iron, nickel | 210 GPa |
| copper | 110 GPa | brass | 90 GPa |
| aluminium | 70 GPa | crown glass, marble | 60 GPa |
| granite | 45 GPa | concrete | 20 GPa |
| lead | 16 GPa | brick, hardwood | 15 GPa |
Examples
OpenStax Example 12.8: a steel rod 2.0 m long with 0.30 cm² (30 mm²) holds a 550 kg platform. The force is 550 × 9.8 = 5390 N, the stress 179.67 MPa (OpenStax: 1.8 × 10⁸ Pa) and the elongation 1.80 mm. The same rod in aluminium stretches 5.13 mm, in copper 3.27 mm. The other way round: a test bar with 50 mm² and 1 m length that stretches 1 mm under 10 kN has E = 200 GPa – steel. In Example 12.7 a granite pillar under 128.4 kPa is compressed by a strain of only 2.85 × 10⁻⁶.
How a whole beam bends is worked out by the beam deflection calculator; the stiffness of a coil spring by the spring constant calculator.
Frequently asked questions
How do you calculate Young’s modulus?
Divide stress by strain: E = (F/A) · (L₀/ΔL). 10 kN on 50 mm² over 1 m with 1 mm elongation: 200 MPa ÷ 0.001 = 200 GPa.
How much does a steel rod stretch?
ΔL = F · L₀ / (A · E). 5390 N on 30 mm² over 2.0 m with E = 200 GPa gives 1.80 mm, as in OpenStax Example 12.8.
What is the difference between stress and strain?
Stress is force per area (Pa or MPa); strain is the change in length divided by the original length and has no unit.
What is Young’s modulus of steel and aluminium?
OpenStax lists 20 × 10¹⁰ Pa (200 GPa) for steel and 7.0 × 10¹⁰ Pa (70 GPa) for aluminium, so aluminium stretches about three times as much.
Does it work for compression too?
Yes. For compression the same formulas apply with absolute values; the granite pillar in OpenStax Example 12.7 is such a case.
How exact is the result?
It is calculated for the linear elastic range with approximate table values; beyond the yield point the formula no longer holds.
Sources and legal basis
As of: · Editorial policy
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