Stress and Strain Calculator
Axial stress, strain, elongation and Young's modulus for round bars, tubes and plates, with yield safety factor, Poisson contraction and SI or US units.
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About this toolWhat is the Stress and Strain Calculator?
Pull on a steel rod and it gets longer by an amount you can predict with three numbers: the load, the cross-section and the material's Young's modulus. This calculator does that sum for a solid round bar, a round tube, a rectangular bar or any known area, and reports the stress, the strain, the change in length and how far the stress sits below yield. A 10 mm A36 rod carrying 10 kN over 1 m, the default case, sees 127.3 MPa, stretches 0.637 mm and has a safety factor of 1.96 against yielding.
It works in three directions. Give it a load and a modulus and it returns stress, strain and elongation. Give it a measured load and extension from a tensile test and it back-calculates Young's modulus. Give it the stretch you can tolerate and it tells you the load that produces it. Material presets fill in typical E, yield strength and Poisson's ratio for common steels, stainless, aluminium, titanium, copper and brass, and every value stays editable.
Switch between SI (kN, mm, MPa, GPa) and US customary (lbf, in, ksi) at any time; the inputs convert in place so the bar stays the same size.
- Three solve modes: stress and elongation from load, modulus from test data, and load from target elongation
- Round bar, tube, rectangle or known area, in tension or compression
- Typical E, yield and Poisson ratio presets for eight engineering metals, all editable
- Safety factor against yield, lateral strain, diameter change and axial stiffness EA/L
- SI and US customary units that convert in place, plus a stress-strain sketch, copy and share link
How to use the Stress and Strain Calculator
- Choose SI or US units and what you want to solve for: stress and elongation from a load, modulus from test data, or load from a target elongation.
- Pick tension or compression and the cross-section, then enter its dimensions and the original length of the bar.
- Enter the axial load, the measured or target elongation, or both, depending on the mode.
- Choose a material preset or type your own modulus, yield strength and Poisson ratio.
- Read stress, strain, elongation, safety factor and lateral contraction. The sketch shows where your bar sits on the elastic line relative to yield.
Worked examples
Steel tie rod
Input
10 mm round A36 bar, 1,000 mm long, 10 kN tension
Output
σ = 127.3 MPa, ε = 0.000637 (637 µε), ΔL = 0.637 mm, safety factor 1.96
The stress is about half of yield, so the elastic answer holds. The bar gets 0.0017 mm thinner across its diameter at the same time.
Finding E from a tensile test
Input
12.5 mm aluminium specimen, 50 mm gauge length, 20 kN gives 0.118 mm extension
Output
σ = 163.0 MPa, ε = 0.00236, E = 69.1 GPa
The answer matches the handbook 68.9 GPa for 6061-T6, a good sign that the extensometer and load cell agree.
Aluminium rod in US units
Input
1/2 in round 6061-T6, 24 in long, 3,000 lbf
Output
σ = 15,279 psi, ΔL = 0.0367 in, safety factor 2.62
An identical steel rod would stretch only about 0.0126 in under the same load, because E is roughly three times higher.
Short stainless tube in compression
Input
50 mm OD x 40 mm ID tube, 500 mm long, 20 kN, 304 stainless
Output
A = 706.9 mm², σ = −28.3 MPa, shortening 0.073 mm, safety factor 7.6
Crushing is not the concern here; a longer tube would buckle first, which the column buckling calculator checks.
Background and insight
Engineering stress is load divided by the original cross-section, σ = F/A, and engineering strain is change in length over original length, ε = ΔL/L₀. Below the proportional limit most metals follow Hooke's law, σ = Eε, so elongation is ΔL = FL₀/(AE). Thomas Young described the modulus that carries his name in 1807; in modern units structural steel sits near 200 GPa (29,000 ksi) and aluminium alloys near 69 GPa (10,000 ksi), which is why an aluminium bar of the same size stretches about three times as much.
The presets are typical room-temperature values from MatWeb and ASM handbook data: ASTM A36 with a 250 MPa (36 ksi) specified minimum yield, 6061-T6 at 276 MPa, 7075-T6 at 503 MPa, annealed 304 stainless at 215 MPa and Ti-6Al-4V at 880 MPa. Modulus barely changes with heat treatment, but yield strength changes a great deal, so take yield from the specification or the mill certificate for anything that matters.
Poisson's ratio links the stretch to the thinning that comes with it: lateral strain is −ν times axial strain. For a steel bar with ν around 0.26 to 0.30 the diameter shrinks by roughly a quarter of the axial strain, which is small but measurable with strain gauges.
Common use cases
Tie rods, hangers and bolts
Check the stress and stretch in a rod that carries a known tension, and how much margin it has before yielding.
Tensile test reports
Turn a load and extensometer reading into Young's modulus to check a material or a test setup.
Preload and fit-up
Find the load needed to stretch a bolt or a stay by a set amount, or the elongation a given preload produces.
Teaching mechanics of materials
Show students how stress, strain and modulus relate, with Poisson contraction and the yield line on one screen.
Tips and limitations
- Above the yield strength the result is wrong in a non-conservative way: the bar stretches far more than the linear formula predicts. The calculator warns when that happens.
- Stress concentrations at holes, threads and shoulders can raise local stress by a factor of two or three. Use net area at a hole and a stress concentration factor for fatigue.
- For threaded rods use the tensile stress area from the thread standard, not the nominal diameter, or you will understate the stress by 20% or more.
- Long members in compression usually fail by buckling well below yield. Check slenderness separately.
- Modulus falls with temperature. Eurocode 3 Part 1-2 reduces the stiffness of structural steel by 10% at 200 °C and 30% at 400 °C, and aluminium loses strength much sooner.
Frequently asked questions
How do you calculate stress and strain?
Stress is the axial load divided by the cross-section area, σ = F/A, in N/mm² (MPa) or psi. Strain is the change in length divided by the original length, ε = ΔL/L₀, and has no units. A 10 kN load on a 10 mm round bar gives 10,000 / 78.54 = 127.3 MPa.
How do you find Young's modulus from stress and strain?
Divide stress by strain in the elastic region: E = σ/ε. From a tensile test this is E = (F/A) / (ΔL/L₀). Use readings well below yield, since the slope bends once the material starts to yield.
What is the formula for elongation of a bar under load?
ΔL = F L₀ / (A E), where F is the axial force, L₀ the original length, A the cross-section area and E the modulus of elasticity. Keep units consistent: newtons, millimetres and N/mm² give millimetres.
What is Young's modulus of steel and aluminium?
Carbon and alloy steels are close to 200 GPa (29,000 ksi) and austenitic stainless about 193 GPa. Aluminium alloys are about 69 to 72 GPa (10,000 to 10,400 ksi), titanium alloys about 110 to 115 GPa, and copper about 115 to 120 GPa.
What is a good factor of safety against yield?
It depends on the code and how well the loads are known. Steel building design often works out to about 1.5 to 1.7 on yield for static loads, machine parts commonly use 2 to 4, and lifting equipment is often higher. Use the factor your governing code or standard requires.
What does Poisson's ratio tell you?
It is the ratio of lateral contraction to axial extension. With ν = 0.3, a bar stretched by 0.1% gets 0.03% thinner. Most metals fall between 0.26 and 0.34, rubber approaches 0.5, and cork is close to zero.
Is strain given in percent or microstrain?
Both are common. Strain is dimensionless, so 0.001 is the same as 0.1% or 1,000 microstrain (µε). Strain gauge readings usually come in microstrain, while tensile test elongation at break is quoted in percent.
Is there an in-depth guide to the Stress and Strain Calculator?
Yes. “Stress, Strain and Young's Modulus: Hooke's Law for Real Bars” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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