Mechanical Stress Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
Mechanical stress is calculated with σ = F ÷ A, where F is the applied force in newtons and A is the cross-sectional area in square millimeters. For a force of 1,000 N on a 50 mm² section, the stress is 20 MPa.
Explanation
Mechanical stress (denoted σ, the Greek letter sigma) measures the intensity of a force relative to the surface it's applied to: for the same force, a smaller section experiences higher stress, which is why a thin part breaks more easily than a thick part under the same load. It's expressed in pascals (Pa) in the international system, but the megapascal (MPa, equivalent to newtons per square millimeter, N/mm²) is the more practical unit in mechanical engineering, since values in pascals alone tend to be very large. This calculator assumes simple tension or compression stress, uniformly distributed across the section — the most basic case in strength of materials. It doesn't cover bending, shear, or torsional stress, which follow different formulas. Comparing the result to the yield strength of the material used (a value specific to each material, not covered by this tool) tells you whether the part stays within its elastic deformation range or risks deforming plastically. For the density of a material, another useful parameter in design work, see our density calculator.
Example: a force of 1,000 N on a 50 mm² section
Inputs
Force: 1,000 N. Section area: 50 mm².
Calculation
Stress = force ÷ area = 1,000 ÷ 50 = 20.
Result
The mechanical stress on this section is 20 MPa.
Frequently asked questions
What's the difference between stress and force?
Force (in newtons) measures the action exerted in absolute terms, regardless of the surface it's applied to. Stress (in MPa) relates that force to the section's area: two parts subjected to the same force but with different cross-sections experience different stress, which is why a wider section better withstands the same load.
How do I know if a part will break under this stress?
You need to compare the calculated stress to the yield strength (or ultimate strength) of the material used, a value that depends on the specific material (steel, aluminum, wood...) and is found in a mechanical properties table. This calculator only gives the applied stress, not that limit, which varies too much from one material to another to generalize.
Does this calculator cover bending or torsion?
No, it's limited to simple tension or compression stress (uniform axial force on a straight cross-section). Bending, shear, and torsion follow different formulas that involve the part's geometry (notably its moment of inertia), which aren't covered by this tool.