1) Understanding elastic modulus in practice
Elastic modulus (E) describes axial stiffness in the elastic range. It is the slope of the linear part of the stress–strain curve, so higher E means less strain at the same stress. This calculator helps compare stiffness values and check lab data.
2) Units and conversions you should expect
Stress and modulus share the same dimension (pressure). Use Pa for fundamentals, then scale to kPa, MPa, or GPa. Key conversions: 1 GPa = 10^9 Pa = 1000 MPa, and 1 psi ≈ 6894.76 Pa.
3) From force and deformation to stiffness
With force and geometry, the calculator forms σ = F/A and ε = ΔL/L₀. It then computes E = σ/ε, matching common tensile-test workflows using a load cell and an extensometer. Keep ε small (often 0.0005–0.002 for metals) to stay elastic.
4) Using stress–strain data directly
If you already have σ and ε from a test report, enter them directly to estimate modulus. For best accuracy, use values from the same linear segment of the curve or compute σ/ε using a point near the origin. Mixing linear and nonlinear points skews results.
5) Typical modulus ranges for common materials
Typical ranges help validate results: steels about 190–210 GPa, aluminum alloys 65–75 GPa, copper 100–130 GPa, and many glasses 60–75 GPa. Normal concrete is often 20–40 GPa. Many polymers are 0.5–3 GPa, while elastomers may be 10–100 MPa.
6) Why linear region selection matters
Modulus is defined for linear elasticity. Yielding, microcracking, and viscoelasticity introduce curvature, so a single-point ratio becomes a tangent estimate. In practice, labs often fit a straight line to an elastic strain window and report its slope as E.
7) Measurement quality: area, gauge length, and strain
Geometry and strain measurement drive uncertainty. Area errors propagate directly to σ, so measure diameter or width carefully and use consistent units. Gauge length L₀ should match the measurement span. If ΔL is near instrument resolution, repeatability improves by increasing L₀ or sensor precision.
8) Reporting results for labs and design checks
When reporting results, include E, stress, strain, units, and the input mode used. Also note temperature, strain rate, and specimen condition because they shift modulus for many materials. Export CSV for spreadsheets or PDF for lab notes to preserve an auditable summary.