Stress and Strain Calculator
Find the normal stress, strain and Young's modulus of a bar or specimen under an axial load. Enter the force, the cross-section (or its area) and the original and changed length; the calculator also gives true stress and strain, Poisson's ratio, and how the same part would behave in steel, aluminum, titanium, plastics and more.
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In the square of the dimension unit (mm², in², …)
Shorter than L₀ means compression
Negative for compression
For lateral strain and Poisson's ratio (dimension unit)
How to use the Stress and Strain Calculator
- Enter the force and its unit. Use a negative value for compression.
- Describe the cross-section: pick round, tube or rectangle and type its dimensions, or enter the area directly.
- Enter the original length and either the final length or the change in length.
- Optionally pick a material to see a safety factor, and add the final diameter for Poisson's ratio.
- Read stress, strain and E, then compare with other materials in the table below.
Stress, strain and Young's modulus explained
When a bar is pulled or pushed along its axis, the load spreads over its cross-section. Stress is that load per unit area, strain is how much the bar stretches relative to its length, and in the elastic range the two are proportional. The constant of proportionality is the modulus of elasticity (Young's modulus), a property of the material, not of the part.
| Quantity | Formula | Typical units |
|---|---|---|
| Normal stress | σ = F ÷ A | MPa (N/mm²), psi, ksi |
| Engineering strain | ε = ΔL ÷ L₀ = (L − L₀) ÷ L₀ | unitless, %, µε |
| Young's modulus (Hooke's law) | E = σ ÷ ε | GPa, Msi |
| Elongation under load | ΔL = F L₀ ÷ (A E) | mm, in |
| Poisson's ratio | ν = −εlateral ÷ εaxial | unitless |
| True stress / strain | σt = σ(1 + ε), εt = ln(1 + ε) | MPa / unitless |
Typical material properties
| Material | Young's modulus E | Yield strength | Poisson's ratio |
|---|---|---|---|
| Structural steel (A36) | 200 GPa (29,000 ksi) | 250 MPa (36 ksi) | 0.26 |
| Stainless steel 304 | 193 GPa | 215 MPa | 0.29 |
| Aluminum 6061-T6 | 68.9 GPa (10,000 ksi) | 276 MPa (40 ksi) | 0.33 |
| Titanium Ti-6Al-4V | 114 GPa | 880 MPa | 0.34 |
| Copper, annealed | 117 GPa | ≈ 70 MPa | 0.34 |
| Gray cast iron | ≈ 100 GPa (varies widely) | brittle, ≈ 200 MPa tensile | 0.26 |
| Concrete | ≈ 30 GPa | ≈ 30 MPa compressive | 0.2 |
| Nylon 6/6 | ≈ 2.8 GPa | ≈ 70 MPa | 0.39 |
Values are rounded typical figures for comparison; always check the specification of the exact grade you use.
Tips for accurate results
- Stay in the elastic range. E = σ ÷ ε only holds on the straight part of the stress-strain curve, below the yield point.
- Measure small changes carefully. Steel at its working stress stretches only about 0.1%, so a 1% error in ΔL gives a 1% error in E. Use an extensometer or strain gauge rather than a ruler.
- Use the net area at holes or notches, where stress is highest, and remember stress concentrations can raise local stress further.
- Compression members can buckle long before the material reaches its compressive strength; slender columns need a buckling check.
Frequently asked questions
What is the formula for stress and strain?
Normal stress is force divided by cross-section area, σ = F ÷ A, measured in pascals (N/m²), MPa (N/mm²) or psi. Engineering strain is the change in length divided by the original length, ε = ΔL ÷ L₀, and has no unit.
How do I calculate Young's modulus from stress and strain?
Divide stress by strain in the elastic (straight-line) region: E = σ ÷ ε. A steel rod stressed to 159 MPa that stretches 0.08% (ε = 0.0008) has E ≈ 199 GPa, close to the textbook 200 GPa for steel.
What is the difference between engineering and true stress?
Engineering stress uses the original area; true stress uses the actual, shrinking area. For constant volume, true stress = σ(1 + ε) and true strain = ln(1 + ε). They are almost identical for small elastic strains and only diverge after significant plastic stretching.
What units should I use?
Any consistent set works. 1 MPa equals 1 N/mm² and about 145.04 psi; 1 GPa is 1,000 MPa or about 0.145 Msi (million psi). The calculator converts all forces, dimensions and lengths for you.
What is microstrain?
Microstrain (µε) is strain multiplied by one million. Strain gauges usually report it: 1,000 µε means 0.1% elongation, or 1 mm of stretch over a 1 m length.
What is Poisson's ratio?
Poisson's ratio ν is the negative ratio of lateral strain to axial strain. When a bar is stretched it gets slightly thinner; for most metals ν is between 0.25 and 0.35, and it cannot exceed 0.5 for an isotropic material.
Are the material values exact?
No. They are typical room-temperature values for common grades and tempers, meant for comparison and estimates. Real strength depends on the alloy, heat treatment, product form and test standard, so use certified data sheets or design codes for final design.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.