Stress and Strain Calculator
Calculate axial stress, strain, elongation and Young’s modulus.
Please note: These are idealised textbook models using representative material data. They are for study, sizing and sanity-checking only — never for final design. Real engineering requires code-compliant analysis, verified material certificates and a qualified engineer’s sign-off.
What the Stress and Strain Calculator does
Stress is force spread over area; strain is the resulting proportional stretch. Young’s modulus links them, and because it is a material constant, a steel bar of any size stretches by the same fraction under the same stress.
Formula
σ = F ÷ Aε = ΔL ÷ LE = σ ÷ ε (Hooke’s law)ΔL = F L ÷ (A E)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Solve for | one of 3 options | Yes | — |
| Axial load | number | In some modes | Shown in 4 of the 6 modes. |
| Axial load unit | one of 5 options | In some modes | Shown in 4 of the 6 modes. |
| Allowable stress | MPa | In some modes | Accepts more than 0. Shown Solve for is Load a member can carry and Cross-section given as is Round bar diameter, or Solve for is Load a member can carry and Cross-section given as is Area directly. |
| Cross-section given as | one of 2 options | Yes | — |
| Bar diameter | number | In some modes | Shown in 3 of the 6 modes. |
| Bar diameter unit | one of 9 options | In some modes | Shown in 3 of the 6 modes. |
| Cross-sectional area | number | In some modes | Shown in 3 of the 6 modes. |
| Cross-sectional area unit | one of 5 options | In some modes | Shown in 3 of the 6 modes. |
| Original length | number | Yes | — |
| Original length unit | one of 9 options | Yes | — |
| Measured elongation | number | In some modes | Shown Solve for is Young’s modulus from a measured elongation and Cross-section given as is Round bar diameter, or Solve for is Young’s modulus from a measured elongation and Cross-section given as is Area directly. |
| Measured elongation unit | one of 9 options | In some modes | Shown Solve for is Young’s modulus from a measured elongation and Cross-section given as is Round bar diameter, or Solve for is Young’s modulus from a measured elongation and Cross-section given as is Area directly. |
| Material | one of 13 options | Yes | — |
How to use it
- Choose Solve for and Cross-section given as.
- Enter Original length.
- Fill in the remaining inputs the form shows for your choice.
- Select Calculate.
Worked example
A 10 kN load on a 20 mm diameter steel rod, 2 m long.
- Load
- 10 kN
- Diameter
- 20 mm
- Length
- 2 m
- Material
- Structural steel
A = 314.16 mm², so σ = 31.83 MPa. Strain = 31.83 ÷ 200,000 = 0.000159, giving 0.318 mm of stretch and a safety factor of 7.9.
Frequently asked questions
What is the difference between stiffness and strength?
Stiffness (Young’s modulus) is how much it stretches under load; strength (yield) is when it deforms permanently. A material can be stiff and weak, or flexible and strong.
Does a thicker bar stretch less?
Yes — stress falls with area, and strain follows stress. Doubling the diameter quarters the stress and quarters the stretch.
Method and sources
Method. Engineering stress as force over original area, strain as extension over original length, and Young's modulus as their ratio within the elastic region — Hooke's law.
Assumptions
- Uniaxial loading, uniform section, and behaviour within the proportional limit.
Limitations
- Engineering stress uses the original area. Past the point where a specimen necks, true stress diverges sharply and the engineering curve turns downward while the material is still hardening.
- Hooke's law applies only below the proportional limit; nothing here describes plastic behaviour.
- Modulus values for a material class are representative, not certified figures for a specific alloy and temper.
Sources
- Hooke's law and standard tensile-test definitions — Established mechanics of materials; material data from the supplier's certificate for a specific grade. The stress-strain relationship, and the distinction between engineering and true stress.