How to use the Stress, Strain & Young's Modulus Calculator
- 1. Choose what to findE from test readings, or the change in length for a known E.
- 2. Enter the bar dataDiameter or area, load in kN, length and the measured change.
- 3. Get the answerStress in MPa, strain, E in GPa or ΔL in mm, with the working.
Formulas
Stress σ = P / A, strain ε = ΔL / L and, within the elastic limit, E = σ / ε (Hooke's law). Rearranged, the change in length of a bar is ΔL = PL / AE.
Poisson's ratio ν = lateral strain / longitudinal strain, and the shear modulus G = E / 2(1 + ν). 1 N/mm² = 1 MPa, and 1 GPa = 1000 MPa.
Worked example and lab tips
A 20 mm steel bar, 200 mm gauge length, carries 50 kN and stretches 0.16 mm. A = π × 20² / 4 = 314.16 mm². σ = 50,000 / 314.16 = 159.15 MPa. ε = 0.16 / 200 = 0.0008. E = 159.15 / 0.0008 = 198,944 MPa ≈ 199 GPa.
- Use readings from the straight part of the load-extension graph only.
- Mild steel is close to 200 GPa and aluminium about 70 GPa, so a far-off value usually means a unit slip.
- Use the gauge length, not the full bar length.
Frequently asked questions
Can I use it for compression?
Yes. Enter the load as a negative number and the result shows shortening.
Why is my E value very different from 200 GPa?
Check units first: load in kN, area in mm², lengths in mm. Also use readings below the elastic limit.
What is true stress?
True stress uses the actual, reduced area during the test. This tool gives engineering stress, based on the original area, which is what most exams ask for.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.