Young's Modulus Axial Stress, Strain & Elongation Calculator
Hooke's Law for uniaxial elastic solids states that axial elongation ΔL of a prismatic member equals the product of axial force F and initial length L₀ divided by cross-sectional area A and Young's Modulus E.
Stretch or compression in millimeters
Applied axial force in Newtons (switch to kN)
Unstressed length in meters
Load-bearing area in square millimeters
Modulus of elasticity in Gigapascals (1 GPa = 1000 N/mm²)
Step-by-Step Calculation
Hooke's Law for uniaxial elastic solids states that axial elongation ΔL of a prismatic member equals the product of axial force F and initial length L₀ divided by cross-sectional area A and Young's Modulus E.
Real-World Reference Values
1 GPa = 1 kN/mm² = 1,000 MPa
High strength-to-weight aerospace alloys
Along fiber orientation axis
20-Row Comparison Table
Axial Elastic Elongation (mm) (ΔL (mm)) · Axial Tensile/Compressive Load (F)
| # | Axial Tensile/Compressive Load (N) | Axial Elastic Elongation (mm) (ΔL (mm)) | Δ % |
|---|---|---|---|
| 01 | 10 N | 0.00025 | -99.98% |
| 02 | 60,000.00 NCurrent | 1.5 | 0.00% |
| 03 | 151,061.43 N | 3.7765 | +151.77% |
| 04 | 226,587.15 N | 5.6647 | +277.65% |
| 05 | 302,112.87 N | 7.5528 | +403.52% |
| 06 | 377,638.59 N | 9.441 | +529.40% |
| 07 | 453,164.30 N | 11.3291 | +655.27% |
| 08 | 528,690.02 N | 13.2173 | +781.15% |
| 09 | 604,215.74 N | 15.1054 | +907.03% |
| 10 | 679,741.45 N | 16.9935 | +1032.90% |
| 11 | 755,267.17 N | 18.8817 | +1158.78% |
| 12 | 830,792.89 N | 20.7698 | +1284.65% |
| 13 | 906,318.61 N | 22.658 | +1410.53% |
| 14 | 981,844.32 N | 24.5461 | +1536.41% |
| 15 | 1,057,370.04 N | 26.4343 | +1662.28% |
| 16 | 1,132,895.76 N | 28.3224 | +1788.16% |
| 17 | 1,208,421.47 N | 30.2105 | +1914.04% |
| 18 | 1,283,947.19 N | 32.0987 | +2039.91% |
| 19 | 1,359,472.91 N | 33.9868 | +2165.79% |
| 20 | 1,434,998.63 N | 35.875 | +2291.66% |
Frequently Asked Questions
What is the axial tensile stress σ in the rod?+
Axial stress in MPa (N/mm²) is simply Force F (in Newtons) divided by Area A (in mm²): at F = 60,000 N and A = 500 mm², σ = 120 MPa.
What is engineering strain ε?+
Engineering strain is the dimensionless ratio ΔL / L₀ (or σ / E). At ΔL = 1.5 mm and L₀ = 2,500 mm, ε = 0.0006 (600 microstrain).
How is this related to Hooke's spring constant k?+
Writing F = (AE / L₀) × ΔL shows that a prismatic bar acts as a stiff spring with axial spring rate k = A × E / L₀.