Stress and strain describe what happens inside a material when it is pulled or pushed. Stress is the force carried by each unit of cross-sectional area; strain is how much each unit of length stretches. Their ratio in the elastic range, Young’s modulus, is one of the most useful material properties in engineering. This calculator works in both directions: it turns load-test readings into stress, strain and modulus, or uses a known modulus to predict how far a bar will stretch, and it compares the stress with the material’s yield strength.
How to use the stress, strain and Young’s modulus calculator
- Choose what to find: all three values from a test, the stretch of a bar from its material, stress only or strain only.
- Enter the axial force in N, kN, lbf, kip or kgf.
- Describe the cross-section: a round bar’s diameter, a rectangle’s width and thickness, or the area directly.
- Enter the original length L0 and, for test data, the measured change in length ΔL.
- To predict stretch, pick a material such as A36 steel or 6061-T6 aluminum, or enter a custom modulus.
Stress and strain formulas
One megapascal is one newton per square millimeter, which makes metric arithmetic easy: newtons divided by mm² give MPa directly. In US units, pounds divided by square inches give psi, and 1 ksi = 1,000 psi ≈ 6.895 MPa. The relation E = σ/ε is Hooke’s law for materials; the linear part of a stress–strain curve is its graph.
Worked examples
Tensile test on a 10 mm steel bar (the default)
Area = π × 10² ÷ 4 = 78.54 mm². Stress = 10,000 N ÷ 78.54 mm² = 127.3 MPa (18,470 psi).
Strain = 0.127 mm ÷ 200 mm = 0.000635 (635 µε).
Young's modulus = 127.3 MPa ÷ 0.000635 = 200.5 GPa — right on the 200 GPa (29,000 ksi) expected for steel.
Predicting the stretch of a hanger rod. A 3/4 in A36 rod, 10 ft long, carries 5 kip. Area = 0.4418 in², stress = 11,320 psi (78.03 MPa), and ΔL = 5,000 × 120 ÷ (0.4418 × 29,000,000) = 0.0468 in (1.19 mm). The yield safety factor is 36,000 ÷ 11,320 = 3.18.
Typical material properties
| Material | Young’s modulus E | Yield strength |
|---|---|---|
| Structural steel, ASTM A36 | 29,000 ksi (200 GPa) | 36 ksi (250 MPa) |
| Structural steel, ASTM A992 | 29,000 ksi (200 GPa) | 50 ksi (345 MPa) |
| Stainless steel 304, annealed | 28,000 ksi (193 GPa) | 30 ksi (205 MPa) |
| Aluminum 6061-T6 | 10,000 ksi (69 GPa) | 35 ksi (241 MPa) minimum |
| Titanium Ti-6Al-4V | 16,500 ksi (114 GPa) | 120 ksi (827 MPa) minimum |
| Douglas fir-larch No. 2 lumber | 1,600 ksi (11 GPa) | — |
| Concrete, f′c = 4,000 psi | 3,605 ksi (24.9 GPa) | — |
Steel yields are ASTM specification minimums; the concrete modulus uses the ACI 318 expression 57,000√f′c psi; the lumber value is a reference design value. Aluminum stretches about three times as much as steel under the same stress, which is why aluminum structures need deeper sections for the same stiffness.
Engineering versus true stress
These formulas use the original area and length, giving engineering stress and strain — the standard for design and for small elastic deformations. Once a ductile metal yields and begins to neck, its actual cross-section shrinks, and true stress (force over current area) rises above engineering stress. Compression members also need a buckling check, because a slender column can fail by bowing sideways at a stress far below yield.
For a beam bending under load rather than a bar in tension, use the beam deflection calculator. The Hooke’s law calculator handles springs, and the pressure converter translates between MPa, psi and other stress units.
Results are for estimation. Load-bearing parts must be designed with appropriate safety factors and checked by a qualified engineer under the applicable codes and standards.
Frequently asked questions
What is the formula for stress?
Stress σ = F ÷ A, the axial force divided by the cross-sectional area. A 10 kN pull on a 10 mm diameter bar (78.54 mm²) gives σ = 10,000 N ÷ 78.54 mm² = 127.3 MPa, about 18,500 psi.
What is strain and does it have units?
Strain ε = ΔL ÷ L₀, the change in length divided by the original length. Because it is a length over a length it has no units, though it is often written as a percentage or in microstrain (µε, millionths). Stretching 200 mm by 0.127 mm is a strain of 0.000635, or 635 µε.
How do I calculate Young's modulus?
Divide stress by strain within the elastic range: E = σ ÷ ε. With 127.3 MPa and 0.000635, E = 200.5 GPa, which matches structural steel. Use readings from the straight, early part of a load test, before the material starts to yield.
How much does a steel rod stretch under load?
ΔL = FL₀ ÷ (AE). A 3/4 in A36 steel rod 10 ft long carrying 5,000 lbf stretches 5,000 × 120 ÷ (0.4418 × 29,000,000) ≈ 0.047 in, about 1.2 mm, at a stress of about 11,300 psi — less than a third of its 36 ksi yield strength.
What is the difference between Young's modulus and yield strength?
Young's modulus measures stiffness — how much a material stretches per unit of stress — and is nearly the same for all steels. Yield strength measures how much stress it takes to bend the material permanently, and varies widely with alloy and heat treatment. A high-strength steel is not stiffer than mild steel, only stronger.