# Elastic Modulus

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Elastic modulus (Young's modulus), abbreviated as $$\lambda$$ (Greek symbol lambda), also called modulus of elasticity, is the ratio of the stress applied to a body or substance to the resulting strain within the elastic limits.

## Elastic Modulus formulas

 $$\large{ \lambda = \frac { \sigma } { \epsilon } }$$ $$\large{ E = \frac{ \sigma \left( F_i\;-\;F_f \right) l_i }{ \left( \delta_i\;-\;\delta_f \right)\;A_c } }$$

### Where:

 Units English Metric $$\large{ \lambda }$$  (Greek symbol lambda) = elastic modulus $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ A_c }$$ = area cross-section $$\large{in^2}$$ $$\large{mm^2}$$ $$\large{ \delta_f }$$  (Greek symbol delta) = final deformation $$\large{in}$$ $$\large{mm}$$ $$\large{ \delta_i }$$  (Greek symbol delta) = initial deformation $$\large{in}$$ $$\large{mm}$$ $$\large{ F_f }$$ = final force $$\large{lbf}$$ $$\large{N}$$ $$\large{ F_i }$$ = initial force $$\large{lbf}$$ $$\large{N}$$ $$\large{ l_i }$$ = initial length $$\large{in}$$ $$\large{mm}$$ $$\large{ \epsilon }$$  (Greek symbol epsilon) = strain $$\large{\frac{in}{in}}$$ $$\large{\frac{mm}{mm}}$$ $$\large{ \sigma }$$  (Greek symbol sigma) = stress $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$