Normal Stress Calculator: Force per Area

What does this quantity describe?

The average normal stress in a cross-section under tension or compression is force relative to the bearing area: σ = F/A. It describes internal material loading, independent of the part's absolute size.

An elevator cable and a rigging chain for the same load can be sized very differently: a thinner cable experiences higher stress than a thicker one at the same load. That's why standards for passenger elevators mandate safety factors of about 8 to 10 times breaking load, while general lifting equipment is often designed to a minimum factor of 5.

Formula and variables

σ = F / A

• σ = F / A
• F = σ · A
• A = F / σ

Choose the inputs correctly

Enter two of the three quantities. Stress requires force and area, force requires stress and area, area requires force and stress. Use the actual bearing net area; holes or notches must be subtracted where applicable.

How to use the calculator

Select the target quantity and enter the two known values with units. Compare the result against the material's allowable stress (yield strength divided by a safety factor) afterward, not directly against tensile strength.

Worked example

Given F = 10,000 N and A = 100 mm², substitution gives σ = 10,000 N / 100 mm² = 100 MPa.

Understand the result and units

A stress of 100 MPa means a force of 100 newtons acts on every square millimetre of the considered cross-section. Whether this is safe depends on the material: for structural steel with a yield strength of about 235-355 MPa, this stress sits well within the elastic range, while for many aluminium alloys it can already be close to yield.

The SI unit is the pascal (Pa = N/m²), but N/mm² (equal to MPa) is more practical in engineering, since 1 N/mm² = 1 MPa. Component tables often use N/mm² because it matches typical millimetre dimensions directly.

What safety factors are typical for load-bearing cables and chains?

For passenger elevators, standards such as EN 81 and ASME A17.1 mandate safety factors of about 8:1 to 10:1 against the breaking load of the suspension means. General lifting and rigging equipment is often instead designed to a minimum safety factor of about 5:1. The required factor depends on the risk to people, load type (static or dynamic), and the applicable standard, and does not substitute for verification against the rules governing the specific application.

Typical applications

Stress calculations are used to design tension members, cables, chains, bolted joints, rigging equipment, and components under simple tension or compression.

Assumptions, limits and common mistakes

The formula gives an area-averaged stress for a concentric, uniformly distributed load. Notches, holes, section changes or off-centre force application create local stress concentrations well above this calculated average, requiring a separate notch-factor or FEA analysis.

Common mistake: Do not compare calculated stress directly against tensile strength — compare it against the allowable stress (usually yield strength divided by a safety factor). Also, do not use the unweakened gross cross-section for notched or drilled sections, since actual stress at the notch can be considerably higher than the average.