About the Stress & Strain Calculator
This stress and strain calculator handles the basic axial-load relationships for a bar, rod, wire or test specimen. In measure mode you enter the applied force, the cross-section and the measured change in length, and it returns the engineering stress, the strain and the resulting Young's modulus (modulus of elasticity). In predict mode you pick a material (or enter its modulus) and it tells you how much the bar will stretch or shorten under the load.
It is aimed at mechanical and civil engineering students working through tensile-test labs and homework, and at designers checking whether a rod, hanger or bolt will stretch more than is acceptable. Results are given in both metric (MPa, GPa) and US customary (psi, ksi) units.
The calculation assumes a straight, prismatic member loaded along its axis and linear-elastic behaviour (Hooke's law). Once stress passes the material's yield strength, strain is no longer proportional to stress and the predicted elongation will be too small. Engineering stress uses the original cross-section, not the necked-down area.
How to use the stress & strain calculator
- 1Choose whether you measured the stretch (to find Young's modulus) or know the material (to predict the stretch).
- 2Pick metric or US units and enter the axial force.
- 3Describe the cross-section by diameter, width × thickness, or area.
- 4Enter the original length and either the measured change in length or the material.
- 5Read the stress, strain and modulus or elongation, and compare stress with the yield strength.
Formula and method
Normal (engineering) stress is the axial force divided by the original cross-sectional area. Engineering strain is the change in length divided by the original length, a dimensionless ratio often quoted in microstrain (millionths). In the elastic range, stress and strain are proportional (Hooke’s law), and the constant of proportionality is Young’s modulus E.
Inputs are converted to newtons and square millimetres so that stress comes out in MPa (N/mm²); 1 MPa = 145.04 psi and 1 GPa = 145.04 ksi. In predict mode the calculator rearranges Hooke’s law to find strain = σ ÷ E and elongation = strain × L₀. Typical moduli: steel about 200 GPa, aluminum about 69 GPa and titanium alloy about 114 GPa.
- σ
- Normal stress (MPa or psi)
- F
- Axial force
- A
- Original cross-sectional area
- ε
- Engineering strain (dimensionless)
- ΔL
- Change in length
- L₀
- Original (gauge) length
- E
- Young's modulus (modulus of elasticity)
Worked examples
10 kN on a 10 mm steel rod that stretched 0.065 mm
The rod’s area is π/4 × 10² = 78.54 mm², so stress = 10,000 ÷ 78.54 = 127.3 MPa. Strain = 0.065 ÷ 100 = 0.00065, and E = 127.3 ÷ 0.00065 ≈ 195,900 MPa ≈ 195.9 GPa — consistent with steel.
Predict stretch of a 1/2" × 2" aluminum bar under 5,000 lbf
The area is 2 × 0.5 = 1 in², so stress = 5,000 psi (34.47 MPa). With E = 68.9 GPa (about 9,993 ksi), strain = 5,000 ÷ 9,993,000 ≈ 0.0005, and a 48 in bar stretches about 0.024 in.
2,000 N on a 1 mm diameter steel wire, 2 m long
A 1 mm wire has an area of only 0.785 mm², so the stress is 2,000 ÷ 0.785 ≈ 2,546 MPa — beyond the strength of all but high-strength music wire. If it stayed elastic with E = 200 GPa, it would stretch 2,546 ÷ 200,000 × 2,000 ≈ 25.5 mm.
Frequently asked questions
What is the difference between stress and strain?+
Stress is the internal force per unit area in a material (MPa or psi). Strain is the resulting deformation — change in length divided by original length — and has no units. Stress is the cause, strain the effect.
How do you calculate Young's modulus?+
Divide stress by strain in the linear (elastic) part of the stress–strain curve: E = (F ÷ A) ÷ (ΔL ÷ L₀). For example, 127 MPa of stress producing 0.00065 strain gives E ≈ 196 GPa.
What is Young's modulus of steel?+
Most carbon and alloy steels have a Young's modulus of about 200 GPa (29,000 ksi), and it barely changes with heat treatment or strength. Stainless steels are around 190–200 GPa, aluminum alloys about 69 GPa and titanium alloys about 110–115 GPa.
What units is strain measured in?+
Strain is dimensionless (mm/mm or in/in). Because the values are small, it is often given as a percentage or in microstrain (µε), where 1,000 µε equals 0.1% strain.
Does this work for compression?+
Yes, for short members the same formulas apply in compression, with the length decreasing instead of increasing. For long, slender columns, buckling usually governs before the material yields, so use a column buckling calculation as well.
What is engineering stress versus true stress?+
Engineering stress uses the original cross-section; true stress uses the actual, shrinking cross-section during a tensile test. They are almost identical in the elastic range but diverge after yielding and necking.