Resultant Force Calculator

What is a Resultant Force?

In the real world, objects are rarely pushed by just one force. Imagine two people pushing a car. One is pushing from the back, and one is pushing from the side.

The car won't move straight, and it won't move sideways. It will move diagonally. The Resultant Force (or Net Force) is that single diagonal force that represents the combined effect of all individual forces acting on the object.

Scalar vs. Vector

To understand forces, you must understand vectors.

• Scalar: Has only magnitude (Size). Example: Temperature (20°C), Mass (10kg).
• Vector: Has both magnitude AND direction. Example: Velocity (60mph North), Force (10N at 45°).

You cannot add vectors like normal numbers. 10N + 10N does not always equal 20N. If they are pulling in opposite directions, 10N + 10N = 0N.

How to Add Vectors (The Component Method)

Our calculator uses the most accurate method for vector addition: breaking them down into X (Horizontal) and Y (Vertical) components.

Step 1: Find Components

Using trigonometry (SOH CAH TOA):

• $F_x = F \times \cos(\theta)$
• $F_y = F \times \sin(\theta)$

Step 2: Sum the Components

Add all the X's together and all the Y's together.

• $R_x = F_{1x} + F_{2x}$
• $R_y = F_{1y} + F_{2y}$

Step 3: Calculate Resultant Magnitude

Use the Pythagorean Theorem on the totals.

Result = $\sqrt{R_x^2 + R_y^2}$

Step 4: Calculate Resultant Angle

Use the inverse tangent function.

Angle = $\tan^{-1}(R_y / R_x)$

The "Tip to Tail" Method

This is a visual way to estimate the result. Draw the first vector arrow. Then, draw the second vector starting from the tip (arrowhead) of the first one.

The Resultant is the line drawn from the Start of the first vector to the Tip of the last vector. The visualizer in our calculator demonstrates exactly this geometry.

Real World Examples