Stress-Strain Calculator
Find tensile stress, strain, and Young's modulus of elasticity from force, cross-sectional area, original length, and elongation.
🔩 What is the Stress-Strain Calculator?
The stress-strain calculator turns a load test into the three numbers engineers care about most: tensile stress, strain, and Young's modulus of elasticity. You enter the force applied to a member, its cross-sectional area, its original length, and how much it stretched, and the tool returns the stress in MPa and psi, the strain as a decimal and a percent, and the elastic modulus in GPa. It handles the unit conversions so you can mix newtons with square millimetres, or pounds-force with square inches, without doing the arithmetic by hand.
Students, technicians, and design engineers use it to interpret tensile tests, verify a material against its published modulus, check that a part stays within its elastic range, and size members so they do not deflect too much under load. It is equally useful in the classroom for connecting the definitions of stress and strain to a real calculation, and in the workshop for spot-checking whether a measured stretch is consistent with the material you think you are working with.
The key idea is that stress is the cause and strain is the effect. Stress is the internal force spread over the area carrying it, while strain is the fractional change in length that results. While a material behaves elastically, the two are proportional, and their ratio is Young's modulus, a fixed property of the material. Above the elastic limit the material yields and deforms permanently, so the modulus result is only meaningful when the test point lies on the straight part of the stress-strain curve.
This tool is useful because it combines three related formulas into one clear result, keeps the units consistent, and shows the full working so you can follow exactly how force, area, length, and elongation combine into stress, strain, and stiffness.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Steel bar, 10 kN over 100 mm²
Example 2 - Brass rod, 5 kN over 50 mm²
Example 3 - Aluminium bar in imperial units
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate stress and strain?
Stress is force divided by cross-sectional area (σ = F / A), giving pascals or MPa. Strain is the change in length divided by the original length (ε = ΔL / L₀), a dimensionless ratio. For 10 kN over 100 mm², stress is 100 MPa; if a 1000 mm bar stretches 0.5 mm, strain is 0.0005 or 0.05 percent.
What is Young's modulus?
Young's modulus (E), also called the modulus of elasticity, is the ratio of stress to strain in the linear elastic region: E = σ / ε. It measures a material's stiffness. Steel is about 200 GPa, aluminium about 69 GPa, and rubber under 0.1 GPa. A higher modulus means the material resists stretching more for a given stress.
What are the units of stress and strain?
Stress has units of pressure: pascals (Pa), megapascals (MPa), or pounds per square inch (psi). One MPa equals one newton per square millimetre. Strain is a ratio of two lengths, so it has no units and is often expressed as a percent or in microstrain (parts per million).
What is the difference between stress and strain?
Stress is the internal force per unit area that a material carries under load, measured in MPa or psi. Strain is the resulting deformation, the fractional change in length, and is unitless. Stress is the cause and strain is the effect; Young's modulus links the two while the material behaves elastically.
Does this calculator work for compression as well as tension?
Yes. The formulas σ = F / A and ε = ΔL / L₀ apply to both tension and compression as long as the deformation is elastic. Enter the axial load and the resulting change in length, whether the member is being stretched or squeezed, and read off stress, strain, and modulus.
What is the elastic limit and why does it matter?
The elastic limit is the highest stress a material can take and still return to its original shape when unloaded. Below it, stress and strain are proportional and Young's modulus is constant. Above it, the material yields and deforms permanently, so E no longer applies and the calculator's modulus result is not meaningful.
How do I find Young's modulus from a stress-strain graph?
Young's modulus is the slope of the straight, initial portion of the stress-strain curve. Take two points on that linear region, then divide the change in stress by the change in strain. This calculator does the same thing from a single load-and-elongation measurement, assuming the point lies in the elastic region.
What is a typical Young's modulus for common materials?
Approximate values are: structural steel about 200 GPa, cast iron 100 to 170 GPa, aluminium 69 GPa, copper 117 GPa, glass 50 to 90 GPa, concrete 30 GPa, wood 9 to 13 GPa, and rubber below 0.1 GPa. Comparing your calculated modulus to these helps confirm the material and that the load is elastic.