# Resultant Force Calculator



An online resultant force calculator is presented.

## Resultant Force

The resultant force due to several forces $\vec {F}_1, \vec {F}_2, ...$ acting on an object is the force $\vec {R}f$ that has the same physical effects as the different forces acting on that object.
Mathematically, the resultant $\vec {R}f$ force is given by the vector
addition of all forces acting on the object. $\vec {R}f = \vec {F}_1 + \vec {F}_2 + ....$ Given the magnitude and direction of each force, the calculator presented below, calculates the
components of each given force, then add the $x$ components of the forces $\vec {F}_1, \vec {F}_2, ...$ to obtain the $x$ component of $R_{fx}$ and then add the $y$ components of the forces $\vec {F}_1, \vec {F}_2, ...$ to obtain the $y$ components of $R_{fy}$,
The magnitude $|\vec {R}f|$ and direction $\theta$ of the resultant force $\vec {R}f$ are given by $|\vec {R}f| = \sqrt { ( R_{fx} )^2 + ( R_{fy} )^2}$ $\theta = \tan^{-1} \left({\frac{R_{fy}}{R_{fx}}}\right)$ with $\theta$ is in the range $[0 , 2\pi)$ taking into account the quadrant where the components of the resultant $\vec {R}f$ are.

## Use of the Resultant Force Calculator

1 - Enter the magnitude $|F_i|$ and the direction of each force.
Important
A) The direction is the angle measured from the positive side of the x axis and is in degrees.
B) The magnitudes and directions of the four forces $\vec {F}_1, \vec {F}_2, \vec {F}_3, \vec {F}_4,$ in the diagram above are used as the default values when you start this page. The directions given by different angles have all been converted to angles from the positive x axis to the force represented by a vector in the diagram above.
2 - Click "Calculate" to obtain $R_{fx}$ and $R_{fy}$ which are the x and y components of the resultant $\vec {R}f$, its magnitude and its direction $\theta$ defined above.

 $|F_1|$ = 20 N       Direction of $F_1$ = 40 degrees $|F_2|$ = 27 N       Direction of $F_2$ = 109 degrees $|F_3|$ = 40 N       Direction of $F_3$ = 195 degrees $|F_4|$ = 60 N       Direction of $F_4$ = 330 degrees $|F_5|$ = N       Direction of $F_5$ = degrees