Add Forces

A simple calculator for adding forces that point in different directions. The directions can also be the same, in which case the angle is 0°. The unit for all the forces is equal, for example newtons. The force resulting from both forces is calculated, as well as the angle of the resulting force to the two original forces. The formula for adding two forces is F = √ F₁² + F₂² + 2 F₁ F₂ cos(α). The angle of the total force is calculated using the law of sine in a triangle.

Please enter the first three values, i.e. both forces and the angle between them. The other three values, i.e. the resulting force and its angle to the two original forces, will be calculated.

Example: a 10 kilograms weight has a weight force of 98.1 newtons. If you pull with 50 newtons to one side, i.e. at an angle of 90 degrees, then a total force of 110.107 newtons acts on the weight and it is now hanging in an angle of about 27 degrees.

The addition of two forces can be illustrated very well graphically. Each force is drawn as an arrow that starts from the same point. Then the second force is drawn as a straight line starting from the tip of the first arrow and the first force is drawn as a straight line starting from the tip of the second arrow. This results in a parallelogram, the so-called parallelogram of forces. The resulting force is the arrow from the starting point of both forces to the opposite corner of the parallelogram. Whether the resulting force is greater than either of the two starting forces or not depends on the angle between the two, the border is at an angle of 120 degrees. If the angle is 90 degrees, as in the example above, then the parallelogram becomes a square, and the total force is then calculated using the famous Pythagorean theorem, F = √ F₁² + F₂². If both forces are the same size, then you get a rhombus. Both squares and rhombuses are special cases of the parallelogram.