This is the ratio of the tensile stress ($\sigma$) to the tensile strain ($\epsilon$): $$ \begin{equation}\begin{aligned} E&=\frac{\sigma}{\epsilon}\\ \end{aligned}\end{equation} $$
The stress is the force per unit area and the strain is the percentage change in length: $$ \begin{equation}\begin{aligned} &=\frac{F/A}{\Delta l/l}\\ \end{aligned}\end{equation} $$
The SI unit for stress is the $Pa$: $$ \begin{equation}\begin{aligned} \sigma&=\frac{F}{A}\\ &\rightarrow\frac{N}{m^2}\\ &=Pa\\ \end{aligned}\end{equation} $$
Strain, however, is dimensionless: $$ \begin{equation}\begin{aligned} \epsilon &= \frac{\Delta l}{l}\\ &\rightarrow \frac{m}{m}\\ &=\text{no units}\\ \end{aligned}\end{equation} $$
Hence the unit for Young’s Modulus is the Pascal ($Pa$). Young’s Modulus answers the question: What force per unit cross-sectional area of the material causes a $100\%$ increase in the length of the material? It is the value of $\sigma$ when $\epsilon=100\%$: $$ \begin{equation}\begin{aligned} E&=\frac{\sigma}{\epsilon}\\ \therefore \sigma&=E\times \epsilon\\ \sigma&=E\times 100\%\\ \sigma&=E\\ \end{aligned}\end{equation} $$
Example Find the force required per unit area to obtain a $3\%$ increase in the length of a steel cable if its Young’s Modulus is $5000Pa$.
Solution From the formula: $$ \begin{equation}\begin{aligned} E&=\frac{\sigma}{\epsilon}\\ \therefore \sigma&=E\times \epsilon\\ &=5000Pa\times 3\%\\ &=150Pa\\ \end{aligned}\end{equation} $$