Enter an axial load, cross-sectional area, original length, and measured elongation to find the engineering stress, engineering strain, and Young's modulus of a material under tension. Results assume the bar is loaded within its elastic (linear) region, where Hooke's law holds.
When a material is pulled in tension it stretches, and how much it stretches for a given load tells you almost everything about its mechanical stiffness. This calculator converts a raw load–elongation measurement from a tensile test (or a design load case) into the three quantities that define elastic behaviour: engineering stress, engineering strain, and Young's modulus. It is the starting point for everything from sizing a tie-rod to interpreting a stress–strain curve.
Engineering stress is the applied force divided by the original cross-sectional area: σ = F/A₀. Because area is entered in mm² it is converted to m² (×10⁻⁶) so the result comes out in pascals, then displayed in megapascals (1 MPa = 1 N/mm²).
Engineering strain is the change in length divided by the original length: ε = ΔL/L₀. It is dimensionless and often quoted as a percentage. "Engineering" values use the original geometry throughout, which is the convention for design; "true" stress and strain instead use the instantaneous area and length and diverge once necking begins.
In the initial, straight part of the stress–strain curve, stress is proportional to strain: σ = E·ε. This is Hooke's law, and the constant of proportionality E is Young's modulus (the modulus of elasticity). Rearranged, E = σ/ε, which is what this tool computes.
Young's modulus is a material property, not a property of the part: steel is about 200 GPa, aluminium 69 GPa, copper 117 GPa, titanium 116 GPa, and most polymers 1–4 GPa. A higher modulus means a stiffer material that deflects less under the same stress.
The linear, recoverable region ends at the proportional/elastic limit, near the yield strength. Below yield, removing the load returns the part to its original length — deformation is elastic. Above yield the material deforms plastically and keeps a permanent set; the curve is no longer linear, and E = σ/ε no longer applies.
That is why this calculator is labelled for the elastic region only. If your elongation corresponds to a stress beyond yield, the computed "modulus" is just a secant slope and not the true elastic modulus.
Take a bar with F = 10,000 N, A = 100 mm², L₀ = 1000 mm, and a measured ΔL = 0.5 mm. Stress σ = 10,000 / (100×10⁻⁶) = 100 MPa. Strain ε = 0.5/1000 = 0.0005 (0.05%). Modulus E = 100 MPa / 0.0005 = 200,000 MPa = 200 GPa — consistent with structural steel.
Change any input and the others update instantly, so you can back-calculate the load needed to reach a target stress, or the elongation expected from a known modulus.
Stress is the internal force intensity carried by the material, force per unit area (σ = F/A), measured in pascals or MPa. Strain is the resulting deformation, the fractional change in length (ε = ΔL/L₀), and is dimensionless. Stress is the cause; strain is the effect, and Young's modulus links them.
The pascal is defined as one newton per square metre, so to get stress in SI base units the area must be in m². Since 1 mm² = 10⁻⁶ m², the calculator multiplies the entered area by 10⁻⁶. Conveniently, 1 N/mm² equals exactly 1 MPa, so you can also read stress directly as N divided by mm².
It is engineering (nominal) stress and strain, based on the original cross-section and original length. Engineering values are standard for design and for the early elastic region. True stress and true strain, which account for the shrinking cross-section, only differ noticeably at large plastic strains near and after necking.
The most common cause is that the elongation corresponds to a stress beyond the elastic limit, so you are measuring a slope on the plastic part of the curve rather than the true elastic modulus. Measurement noise, machine compliance, slack, or grip slip in the early loading can also flatten the apparent slope. Use small loads well within the linear region for a clean E.
Only slightly. Unlike strength and hardness, Young's modulus is governed mainly by atomic bonding and is relatively insensitive to heat treatment, cold work, or minor alloying. All steels, for instance, share a modulus near 200 GPa regardless of whether they are annealed or hardened — heat treatment changes their strength, not their stiffness.