Magnitude of a Resultant from Two Components

For a planar force system, after algebraically summing the components $R_x=\sum F_{ix}$ and $R_y=\sum F_{iy}$, the magnitude of the resultant vector is obtained from the Pythagorean relation:

$$R=\sqrt{R_x^2+R_y^2}$$

This formula gives the magnitude of the vector sum of the forces. For a general force system, its moment effect must also be considered separately.