Enter the forces and angles/directions of up to 5 different forces into the calculator. The calculator will evaluate and display the resultant force.

Resultant Force Formula

The following equation is used to calculate the resultant force acting on an object.

Fxy = Sqrt ((Fx)^2 + (Fy)^2) 
A = tan^{-1} (Fy/Fx) 
  • Where Fxy is the magnitude of the resultant force
  • Fx is the sum of the x-components of forces
  • Fy is the sum of the y-components of forces
  • A is the resultant angle

For example, if there’s a force of 10 Newtons acting in the positive x-direction and a force of 5 newtons acting in the -x direction, the result is 10 + (-5) = 5 newtons in the positive x-direction.

Resultant Force Definition

A resultant force is also known as the net force acting on an object. It’s the sum of all forces and their directions.

The calculator above can solve for up to 5 different forces and angles. If you require less, simply leave them blank.

Resultant Force Example

How to calculate resultant force?

Example #1:

The first step in solving for a resultant force is determining the forces and angles acting on the object. The following forces and angles will be used for this problem.

  1. 20N @ 5 degrees
  2. 10N @ 62 degrees
  3. 5N @ 65 degrees
  4. 12N @ 27 degrees
  5. 6N @ 30 degrees

The next step is to calculate the X and Y components of each force. For the X-component this is done by multiplying the force by the cosine of the angle. For the Y-component this is done by multiplying the force by the sine of the angle.

Doing this yields the following X and Y components of force.

  1. X = 19.92 N , Y = 1.743 N
  2. X = 4.694 N , Y = 8.829 N
  3. X = 2.113 N , Y = 4.531 N
  4. X = 10.692 N , Y = 5.447 N
  5. X = 5.195 N , Y = 3.000 N

Next, we sum all of the X components together and all of the y components together. This yields 42.61 N and 23.55 N respectively.

Next, we must calculate the magnitude of the resulting force using the formula F = Sqrt (Fx^2 + Fy^2). Inputting the values above yields a magnitude of 48.693 N.

Finally, the angle of the force is calculated using the formula tan^-1 ( Fy/Fx) = 28.92 degrees.

Example #2:

This next example will involve only 3 different forces and angles, but some of the forces will have angles greater than 90 degrees. Those are as follows:

  1. 20 N @ 110 degrees
  2. 30 N @ 34 degrees
  3. 40 N @ 140 degrees

As done previously, first we calculate the x and y components. These are found to be:

  1. X = -6.840 N , Y = 18.793 N
  2. X = 24.871 N, Y = 16.775 N
  3. X = -30.641 N , Y = 25.711 N

The resulting sums of these are found to be -12.61N and 61.28.

Next, we calculate the magnitude from these. The magnitude is calculated to be 62.563.

Finally, we calculate the angle using the y and x components of force. This is calculated to be 101.63 degrees.

Resultant in Physics

In physics, a resultant is the equivalent combination of the vectors of some property. This can be anywhere from velocity, to force, to acceleration. The only requirement is that the property being analyzed can be displayed as a vector.

For the calculator on this page specifically, the resultant being analyzed is force, however, you can technically input any property value in the force sections and the result should be correct.

The method for calculating the resultant, whether it be force or velocity, is the same.

Resultant Properties

If a resultant force is 0, then the object being analyzed will not undergo any acceleration.

It will stay still, or keep moving in the same direction and speed as it was previously.

The magnitude of these resultant forces will always be positive. This is due to the nature of the formula for calculating the magnitude which can be seen above.

The angle will also always be positive since it’s calculated as rotating from the x-axis. However, the individual components of the resultant can be negative such as a force of -10 newtons in the x-direction.

Units of Resultant Force

The SI standard units for resultant forces are newtons (N).

The English standard units are pound-force (lb-f).