Definition

Stress and strain

stress = \frac{F}{A}, strain = \frac{Δ L}{L _{0}}

Statement

Stress is the internal force per unit cross-sectional area; strain is the resulting change in length as a fraction of the original length.

Symbols and units

$F$	applied force	N
$A$	cross-sectional area	m²
$Δ L, L_{0}$	elongation, original length	m

When it applies

Applies within the material's elastic region.

Derivation

Defined directly as force normalized by area, and deformation normalized by original length, so that both quantities are independent of the specimen's size:

stress = \frac{F}{A}, strain = \frac{Δ L}{L _{0}}

Worked examples

Strain in a stretched cable

A 2.000 m cable stretches to 2.004 m under load:

strain = \frac{Δ L}{L _{0}} = \frac{0.004}{2.000} = 0.002

Watch out for

Stress has units of pressure (Pa); strain is dimensionless — a common source of unit errors when the two are combined.

Connects to

Young's modulus