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Resultant Force Calculator
Enter the magnitudes and directions of x and y forces in the magnitude of the resultant forces calculator and hit the calculate button.
Resultant force Calculator
The resultant force calculator finds the magnitude and the direction of the resultant force. You can find the resultant for up to 2 force vectors.
If you have three vectors e.g a, b, and c, first enter the a and b vectors and then add the resultant vector of a and b and the c vector.
What is the resultant force?
The resultant force is the net force acting on an object that is under multiple forces. Since force is a vector quantity, the resultant force has both magnitude and direction.
The resultant force can be displayed in the vector form as follows:
Resultant force formula:
There are different formulas for both magnitude and direction.
For magnitude, it is important to know the angle between the vectors.
And for direction/angle:
Typically for finding the magnitude, the angle is calculated first.
How to find the resultant force?
A car is being pushed by 10 newtons in the forward direction (0o) and by 7 newtons from a 90 degrees angle.
Step 1: Identify the values.
Magnitude of F1 = 10N
Magnitude of F2 = 7N
Angle of F1 = 0o
Angle of F2 = 90o
Step 2: Find the x and y components of the resultant force.
X-component of F1= 10cos(0) = 10
Y-component of F1 = 10sin(0) = 0
X-component of F2 = 7cos(90) = 0
Y-component of F2 = 7sin(90) = 7
Step 3: Find summation fx and fy.
Σfx = 10 +0 = 10
Σfy = 0 + 7 = 7
Step 4: Find the angle.
θ = tan-1 (7/10)
θ= tan-1 (0.7)
θR = 34.99o ≈ 35o
Step 5: Put the values in the magnitude formula.
|R| = ½ [(10)2 + (7)2 - cos (35)]
|R| = ½ [100 + 49 - 0.819… ]
|R| = ½ [ 149 - 0.819… ]
|R| = ½ [ 148.093… ]
|R| = 12.2 N