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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:**

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?

**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**