How to use this calculator
Enter the axial force (positive for tension, negative for compression), the cross-sectional area and the length. Pick a material to fill in Young’s modulus and yield strength, or type your own. Units can be mixed freely.
Formulas
Worked example
50 kN on a 500 mm², 2 m steel bar (the default)
- σ = 50,000 N / 500 mm² = 100 MPa (tension).
- ε = 100 MPa / 200,000 MPa = 5 × 10⁻⁴, or 500 µε.
- δ = εL = 5 × 10⁻⁴ × 2,000 mm = 1.0 mm.
- n = 250 / 100 = 2.5 against yield.
Assumptions and limits
- The bar is straight, prismatic and loaded through the centroid of its cross-section.
- The material is linear elastic: stress stays below the proportional limit.
- Stress is averaged over the section. Holes and notches raise local stress by a factor Kt.
- Compression members may buckle long before they yield.
Frequently asked questions
What is the difference between stress and strain?
Stress is force per unit area (Pa, psi). Strain is the stretch per unit length and has no units. Young’s modulus links the two in the elastic range.
How do I handle a bar with several sections?
Find δ for each segment with its own force, area and length, then add them: δ = Σ FᵢLᵢ/(AᵢEᵢ).
What does axial stiffness mean?
k = AE/L is the force needed per unit of stretch. It lets you treat the bar as a spring, for example in statically indeterminate problems.
For education and preliminary checks only. Have a qualified engineer verify any design before it is built.