Stress and Strain Calculator
Stress σ = F ÷ A, strain ε = ΔL ÷ L and Young's modulus E = σ ÷ ε for a bar or wire in tension or compression: find the modulus, the extension or the force.
Result…
How it's calculated
σ = F ÷ A, with A = π d² ÷ 4 or w × t ε = ΔL ÷ L E = σ ÷ ε = F L ÷ (A ΔL) ΔL = F L ÷ (A E)
Stress is the force carried per unit of cross-section area; strain is the stretch per unit of length and has no unit. In the elastic range they are proportional (Hooke's law), and the constant is Young's modulus E. Give any three of force, area, length, extension and modulus to find the rest. Material presets are single values from Engineering ToolBox (engineeringtoolbox.com); grades and alloys differ, so enter a measured or supplier value when you have one. Unit factors are exact: 1 psi = 6894.757… Pa, 1 ksi = 1000 psi, 1 lbf = 4.4482216152605 N, 1 in = 25.4 mm.
Your numbers, step by step
About the Stress and Strain calculator
This stress and strain calculator links the force on a bar or wire to how much it stretches. It finds stress σ = F ÷ A, strain ε = ΔL ÷ L and Young's modulus E = σ ÷ ε, and it can solve for the modulus from a test, the extension under a load, or the force that causes a given extension. The cross-section can be round (from a diameter), rectangular (width × thickness) or an area you already know. Results come in MPa, GPa, kPa, psi, ksi or millions of psi, and forces in N, kN, lbf or kip. A few material moduli are offered as single values taken from Engineering ToolBox, or you can enter your own. Students, makers and technicians can use it to check a tensile test or size a rod, with every step shown.
How to use it
- Choose what to “Solve for”: Young's modulus, extension or force.
- Pick the “Cross-section” and enter the diameter, the width and thickness, or the area.
- Enter the “Original length” and, depending on the mode, the “Force” or the “Extension (change in length)”.
- For extension or force, choose a “Material” or enter your own “Young's modulus”.
- Pick the “Stress unit” and “Modulus unit”, then read the stress, strain and answer.
Worked example
A structural steel rod (E = 200 GPa) 12 mm in diameter and 2 m long carries 20 kN. Its area is π × 12² ÷ 4 ≈ 113.1 mm², so the stress is 20 000 ÷ 113.1 ≈ 176.8 MPa. The strain is 176.8 ÷ 200 000 ≈ 0.000884, and the extension is 0.000884 × 2000 mm ≈ 1.77 mm.
Updated
Questions people ask
How do I calculate Young's modulus from a tensile test?
Divide the stress by the strain: E = (F ÷ A) ÷ (ΔL ÷ L). Use a point on the straight part of the curve, well below yield, and keep the units consistent.
What is the difference between stress and strain?
Stress is force per unit area and has pressure units such as MPa or psi. Strain is the change in length divided by the original length, so it has no unit; it is often quoted as a percentage or in microstrain.
Why is my answer off by a factor of a million?
Usually a unit mix-up: a diameter in mm treated as metres, or stress in MPa compared with a modulus in GPa. Pick each unit in the calculator rather than converting by hand.
Does Young's modulus change between grades of the same metal?
A little. The presets are single published figures, while real values vary with alloy, heat treatment and, for wood and plastics, grain direction and temperature. Use a supplier or test value when it matters. For a spring constant instead of a material property, use the Hooke's law calculator.
Can I use this stress calculator to design a structure?
No. It only covers the elastic stretch of a straight member under an axial load. Yield strength, buckling, fatigue, joints and safety factors all matter in a real design, so have an engineer check anything load-bearing.