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Enter the magnitudes and directions of x and y forces in the magnitude of the resultant forces calculator and hit the calculate button.

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.

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:

There are different formulas for both magnitude and direction.

**For magnitude:**

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.

**Example:**

A car is being pushed by **10 newtons** in the forward direction (0^{o}) and by **7 newtons** from a 90 degrees angle.

**Solution:**

**Step 1:** Identify the values.

Magnitude of F_{1} = 10N

Magnitude of F_{2} = 7N

Angle of F_{1} = 0^{o}

Angle of F_{2 }= 90^{o}

**Step 2:** Find the x and y components of the resultant force.

X-component of F_{1}= 10cos(0) = 10

Y-component of F_{1} = 10sin(0) = 0

X-component of F_{2} = 7cos(90) = 0

Y-component of F_{2} = 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)

**θ**_{R} = 34.99^{o} ≈** 35**^{o}

**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**