MotionLab

Stress Calculator

The internal force per unit area a material experiences — the starting point for any structural analysis.

Force (N)

Cross-sectional area (m²)

Stress (Pa)

10,000,000

σ = F / A

What you entered

Force (N): 5000Cross-sectional area (m²): 0.0005

1
σ = F ÷ A
5000 ÷ 0.0005= 1.0000e+7 Pa

Result

Stress (Pa): 10,000,000

5000N over a 0.0005 m² area is 10,000,000 Pa of stress.

Mechanical stress from force and cross-section

Stress is force divided by cross-sectional area, in pascals. Every row here happens to reach the same order of magnitude.

Force (N)	Area (m2)	Stress (Pa)
1000	0.0001	1.0000e+7
5000	0.0005	1.0000e+7
10000	0.001	1.0000e+7
20000	0.002	1.0000e+7
500	0.00002	2.5000e+7

The first four rows deliberately hold force and area in the same proportion, giving identical stress of 10 MPa from loads varying twentyfold - stress, not force, is what determines whether a material fails. That is why a thin wire snaps under a load a thick bar carries easily. For context, structural steel yields around 250 MPa and fails near 400 to 550, so 10 MPa is a very light load for steel. Divide pascals by 1e6 for megapascals, the unit most engineering tables use.

Stress vs. everyday 'pressure'

Mechanically, stress and pressure share the same formula and units (force ÷ area) — the terminology difference is mostly about context: 'pressure' for fluids pushing on surfaces, 'stress' for solid materials under load.

Why cross-sectional area matters so much

The same applied force creates far more stress on a thin cable than a thick one — this is why engineers increase a structural member's cross-sectional area (not just its material strength) to handle higher loads safely.

Frequently asked questions

A steel cable with cross-section 0.001 m² supports a 5,000 kg elevator. What's the stress?

σ = F/A = (5000 × 9.81)/0.001 = 49,050,000 Pa = 49 MPa. Steel's yield strength is ~250 MPa, so this cable is at about 20% of its limit — a reasonable safety factor of 5.

How is stress different from force?

Force is the total load (in N). Stress is force per unit area (in Pa). A 10,000 N force on a 1 cm² wire creates 100 MPa stress, while the same force on a 100 cm² plate creates only 1 MPa. The material feels stress, not force — that's why thicker structural members are stronger.

What are common stress limits for engineering materials?

Yield stress (permanent deformation begins): mild steel ~250 MPa, aluminum 6061 ~275 MPa, titanium ~880 MPa, concrete (compression) ~30 MPa, wood ~40 MPa. Engineers design to stay well below yield — typically at 50-67% of it (safety factor 1.5-2).