Stress, strain and Young's modulus calculator
Choose what to find, enter the force, the cross-section (as an area or a round bar diameter), the original length and the elongation or the modulus. The calculator applies σ = F/A, ε = ΔL/L₀ and E = σ/ε and shows stress in MPa and psi.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: Young’s modulus, elongation or force.
- Enter the cross-section as an area in mm² or the diameter of a round bar.
- Enter the original length and the two other known values (force, ΔL or E).
- Read the result with the stress in MPa and psi and the strain.
- Stress: σ = F / A (N/mm² = MPa).
- Strain: ε = ΔL / L₀.
- Hooke’s law for a bar: E = σ / ε, so ΔL = F × L₀ / (A × E) and F = E × A × ΔL / L₀.
- Round bar area: A = π × d² / 4.
1 MPa = 145.04 psi; 1 GPa = 1,000 MPa.
Worked examples
Young’s modulus: 10 kN on 100 mm², a 1,000 mm length stretches 0.5 mm: σ = 10,000 ÷ 100 = 100 MPa (14,504 psi), ε = 0.5 ÷ 1,000 = 0.0005, E = 100 ÷ 0.0005 = 200,000 MPa = 200 GPa.
Elongation: 5,000 N on an aluminium bar of 50 mm² and 2,000 mm, E = 70 GPa: σ = 100 MPa, ε = 100 ÷ 70,000 = 0.001429, ΔL = 2.8571 mm.
Force: a 10 mm steel rod (A = 78.54 mm²), 500 mm long, stretched 1 mm with E = 200 GPa: ε = 0.002, σ = 400 MPa, F = 400 × 78.54 = 31.416 kN.
Tips
- Use the original length and area (engineering stress and strain); the bar narrows slightly under tension.
- Gauge length: in a test, ΔL is measured between gauge marks, not over the whole specimen.
- Compare stress with the material’s yield strength to make sure you are in the elastic range.
Frequently asked questions
What is the difference between stress and strain?
Stress is force per unit area, σ = F / A, measured in pascals (N/mm² = MPa). Strain is the relative change in length, ε = ΔL / L₀, a pure number often given in percent or microstrain.
How do I calculate Young's modulus?
Divide stress by strain in the elastic range: E = σ / ε. A bar of 100 mm² under 10 kN has σ = 100 MPa; if a 1,000 mm length stretches 0.5 mm, ε = 0.0005 and E = 200,000 MPa = 200 GPa, typical of steel.
What Young's modulus do common materials have?
Roughly 200 GPa for steel, 70 GPa for aluminium alloys and 110–120 GPa for copper. Plastics are far lower, usually a few GPa. Use the figure for your exact material when precision matters.
Does this work beyond the yield point?
No. σ = Eε holds only in the elastic, linear part of the stress-strain curve. Past the yield point strain grows faster than stress and the bar does not return to its length.