Stress is how hard a material is being pulled, and strain is how far it has stretched. Stress is force divided by area, in MPa or psi; strain is the change in length divided by the original length, a pure ratio usually quoted in microstrain. If you measured a length change, use the first mode to get strain and solve for either length. If you know the load, use the force and area mode: enter the force, the cross-section and the material, and the calculator returns the stress, the strain, the elongation and the factor of safety against yield. The two are linked by Young's modulus, but only while the material stays elastic, so the calculator stops at yield rather than give you a number that no longer applies.
Example Result
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Stress and strain are linked by Young's modulus, but only while the material stays elastic. Below yield, a bar returns to its length when unloaded; beyond it, E × ε no longer gives the stress.
| Symbol | Meaning |
|---|---|
| σ | Normal stress = F ÷ A (MPa, psi) |
| ε | Engineering strain = ΔL ÷ L₀ (dimensionless, µε) |
| E | σ = E × ε, up to yield only |
| ΔL | Elongation = F L₀ ÷ (A E) |
| ε_y | Yield strain = σ_y ÷ E |
| SF | Factor of safety = σ_y ÷ σ, above 1 |
| τ, γ | Direct shear: τ = V ÷ A, γ = τ ÷ G |
1A 2 m steel rod stretches 1.5 mm. E = 200 GPa, S275 steel.
ε = 1.5 ÷ 2,000 = 0.00075; σ = 200,000 × 0.00075
750 µε (0.075%), 150 MPa
That is below the 275 MPa yield of S275 steel, so the rod returns to its length when unloaded. With a Poisson's ratio of 0.3 the sideways strain is −225 µε.
280 kN on a 600 mm² bar, 1 m long, E = 200 GPa, yield 250 MPa.
σ = 80,000 ÷ 600; ε = 133.3 ÷ 200,000; 250 ÷ 133.3
133.3 MPa, 667 µε, 0.67 mm over 1 m, safety factor 1.87
310,000 lbf on 1.5 in², E = 29,000,000 psi.
σ = 10,000 ÷ 1.5; ε = 6,667 ÷ 29,000,000
6,667 psi (46 MPa), 230 µε
The line σ = E ε holds only to yield. Multiply a strain by E beyond that point and you get a stress the material does not have. A reading of 1,500 µε on S275 has passed yield: the part has a permanent set, and E × ε no longer gives the stress. Use the calculator's safety factor, not a bare multiplication.
| Steel | Minimum yield | E | Yield strain |
|---|---|---|---|
| S275 | 275 MPa | 210 GPa | 1,310 µε |
| S355 | 355 MPa | 210 GPa | 1,690 µε |
| ASTM A36 | 250 MPa (36 ksi) | 200 GPa | 1,250 µε |
Engineering strain divides by the original length; true strain adds up the small stretches, ε_true = ln(1 + ε). They agree closely in the elastic range and part ways in forming and tensile tests.
| Engineering strain | True strain |
|---|---|
| 0.002 | 0.0020 |
| 0.05 | 0.0488 |
| 0.20 | 0.1823 |
A foil gauge changes resistance in proportion to strain: ΔR ÷ R = GF × ε, where the gauge factor GF is close to 2 for metal foil gauges. A 350 Ω gauge at 1,000 µε changes by only 0.70 Ω, which is why gauges are read through a bridge circuit.
A strain or stress figure from this page is not a design check. Members that carry people or heavy loads need a design by a qualified engineer.
| Quantity | Unit | In SI base units (m) |
|---|---|---|
| Length | 1 mm | 0.001 m |
| 1 cm | 0.01 m | |
| 1 m | 1 m | |
| 1 in | 0.0254 m | |
| 1 ft | 0.3048 m | |
| Strain (dimensionless) | Decimal | ε (e.g. 0.002) |
| Percent | ε × 100 (e.g. 0.2%) | |
| Microstrain (με) | ε × 10⁶ (e.g. 2000 με) |
Pick a mode: strain from lengths, stress and strain from a force and area, direct shear, or solve for a length.
Choose the units.
Enter the known values. Add E and the yield strength to get the strain and the safety factor.
Press Calculate. Strain is shown as a decimal, a percentage, and in microstrain; lengths are shown in your chosen unit plus common conversions.
Use Copy Result to save the calculation, or Reset to clear all fields.
Deepen your understanding with the FlowUtil Strain engineering guide, glossary definitions and reference table.
Read the Strain Guide