# Young's Modulus

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Young's modulus, abbreviated as Yo or E, also called elastic modulus, modulus of elasticity, and tension modulus, Young's modulus of elasticity, measures the stiffness of an elastic material.  The ratio of the longitudinal stress applied to a body or substance to the resulting longitudinal strain within the elastic limits.

## Young's Modulus formula

 $$\large{ E = \frac{ \sigma }{ \epsilon } }$$ $$\large{ E = \frac{ \frac{ F }{ w^2 } }{ \frac{ l_f }{ l_i } } }$$

### Where:

 Units English Metric $$\large{ E }$$ = Young's modulus $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ F }$$ = force $$\large{lbf}$$ $$\large{N}$$ $$\large{ l_f }$$ = final length $$\large{in}$$ $$\large{mm}$$ $$\large{ l_i }$$ = 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 $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ w }$$ = width $$\large{in}$$ $$\large{mm}$$

## Related formula

 $$\large{ E = \frac{ S }{ \alpha \; \Delta T } }$$ (Restrained Anchored Pipe Stress)

### Where:

$$\large{ E }$$ = Young's modulus

$$\large{ S }$$ = restrained anchored pipe stress

$$\large{ \Delta T }$$ = temperature differential

$$\large{ \alpha }$$ = thermal expansion coefficient