What this calculator does
This is mechanical stress, not the everyday sense of the word: the stress formula in engineering is force divided by the cross-sectional area it acts over, and it describes how hard a material is being pushed or pulled per unit of area, not how someone feels. It is one of the first equations covered in materials and structural engineering, because it is what gets compared against a material's strength to check whether a part will hold.
How to calculate stress comes down to that one division: bigger force over the same area means more stress, and the same force spread over a bigger area means less. This calculator takes a force and an area and returns the stress in megapascals, pascals and psi, so the result can be checked against whichever unit a datasheet or textbook is using.
The formula
Divide the applied force by the cross-sectional area it acts over. With force in newtons and area in square millimetres, the result in megapascals falls out directly, because 1 newton per square millimetre is exactly 1 megapascal. The same figure is also shown in pascals and psi for reference.
| Term | Meaning |
|---|---|
| Stress (σ) | Force divided by the cross-sectional area it acts over: σ = F / A. |
| Force | The load applied to the material, in newtons. |
| Cross-sectional area | The area of the slice the force is spread across, at right angles to the force. |
| Pascal | The SI unit of stress and pressure: 1 pascal = 1 newton per square metre. |
The inputs explained
| Field | What to enter |
|---|---|
| Applied force (N) | The applied force, in newtons. |
| Cross-sectional area (mm²) | The cross-sectional area the force is spread across, in square millimetres. |
When to use it
Sizing a bolt, cable or bracket
Comparing the stress a part will see under a given load against the material's known yield strength is the basic check for whether that part is strong enough, or oversized.
Comparing two cross-sections carrying the same load
The same force produces very different stress depending on how much area it is spread across, which is the whole reason structural members are made thicker in high-load areas.
Converting between stress units on a datasheet
Material strength figures are quoted in MPa, psi or pascals depending on the source; working out stress in all three avoids a unit-conversion mistake when comparing against a spec.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How stress changes as force increases, at a fixed area
The same 50 mm² area, carrying a range of applied forces.
| Applied force | Stress (σ) | Stress in psi |
|---|---|---|
| 1,000 N | 20.00 MPa | 2,901 psi |
| 2,500 N | 50.00 MPa | 7,252 psi |
| 5,000 N | 100.00 MPa | 14,504 psi |
| 7,500 N | 150.00 MPa | 21,756 psi |
| 10,000 N | 200.00 MPa | 29,008 psi |
| 15,000 N | 300.00 MPa | 43,511 psi |
How stress changes as the cross-sectional area increases, at a fixed force
A fixed 5,000 N load, spread across a range of cross-sectional areas.
| Cross-sectional area | Stress (σ) | Stress in psi |
|---|---|---|
| 10 mm² | 500.00 MPa | 72,519 psi |
| 25 mm² | 200.00 MPa | 29,008 psi |
| 50 mm² | 100.00 MPa | 14,504 psi |
| 75 mm² | 66.67 MPa | 9,669 psi |
| 100 mm² | 50.00 MPa | 7,252 psi |
| 150 mm² | 33.33 MPa | 4,835 psi |
Questions
What is the formula for stress?
Stress equals force divided by cross-sectional area, σ = F / A. With force in newtons and area in square metres, the result is in pascals; with area in square millimetres, the result in megapascals comes out directly, since 1 N/mm² equals 1 MPa.
Is stress the same as pressure?
They share the same formula and units, but describe different situations. Pressure usually refers to a fluid or gas pushing on a surface from all directions; stress describes internal force within a solid material, which can pull, push or shear rather than just push.
How is stress different from strain?
Stress is the force per unit area applied to a material; strain is the resulting deformation, usually expressed as a fraction of the original length. The two are related by the material's stiffness, but stress alone does not tell you how much a part will stretch or bend.
What stress level is safe for a given material?
That depends on the specific material's yield strength, which this calculator does not assume, since quoting a generic safe figure would be misleading across different materials and applications. Compare the calculated stress against the actual yield or tensile strength for the material in question, usually with a safety factor applied.
For the area itself on a circular, rectangular or pipe-shaped section, see the cross-sectional area calculator.