Stress formula
Stress is the internal force a material carries spread over its cross-sectional area. It is what you compare against a material strength to decide whether a part will hold, which is why force alone is never the whole story.
Variables
| σ | Normal stress | psi or Pa |
| F | Applied force (axial) | lb or N |
| A | Cross-sectional area | in² or m² |
Rearranged
A = F / σ
Worked example
A steel rod with a cross-section of 0.0005 m² carries an axial pull of 10,000 N.
Divide force by area: 10,000 / 0.0005 = 20,000,000 Pa.
Stress is force per unit area, so a thin rod and a thick rod under the same load are not equally safe. Compare the result against the material yield or ultimate strength, applying a factor of safety, to judge whether a part survives.
Need material strengths to compare against?
See the Yield Strength Chart and Ultimate Tensile Strength Chart.
Tensile, compressive, and shear stress
Normal stress acts perpendicular to a surface and is either tensile, pulling the material apart, or compressive, pushing it together. Shear stress acts parallel to the surface instead. The same formula, force over area, applies to all of them; what changes is the direction of the force and which area resists it.
Why stress, not force, predicts failure
A material fails when the internal stress reaches its strength, not when the force reaches some fixed number. Spreading the same force over a larger area lowers the stress, which is why thicker members carry more. This is why every strength check converts loads into stresses before comparing them to the material limit.
FAQ
What is the formula for stress?
Stress equals force divided by area, written sigma = F / A. The result is in pascals (SI) or psi.
What is the difference between stress and pressure?
Both are force over area, but pressure is an external load applied to a surface, while stress is the internal reaction carried within the material.
How do I know if a part is safe?
Compare the calculated stress to the material yield or ultimate strength. Keep the stress below the strength by a factor of safety suited to the application.