Free-Body Diagram
Build a free-body diagram, resolve each force into Fx and Fy, then get ΣFx, ΣFy, |F_net|, direction, and optional a = F_net/m with step-by-step working.
Key formula
ΣFx, ΣFy → |F_net|; a = F_net/m
How do you find net force from a free-body diagram?
Resolve each force: Fx = F cosθ, Fy = F sinθ. Add components to get ΣFx and ΣFy. Then |F_net| = √(ΣFx² + ΣFy²). If mass m is known, a = F_net / m (and ax = ΣFx/m, ay = ΣFy/m).
About this tool
A free-body diagram lists every external force on one object. This tool resolves each arrow into Fx and Fy, then returns ΣFx, ΣFy, |F_net|, direction, and optional a = F_net/m.
Inputs and assumptions
Force magnitudes in newtons and angles from +x (0° right, 90° up). Optional mass in kilograms for acceleration.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: pushed box
Weight 49 N down, normal 49 N up, push 20 N at 0°, friction 8 N at 180°. ΣFx = 12 N, ΣFy = 0, |F_net| = 12 N. With m = 5 kg, a = 2.4 m/s² to the right.
Example 2: box at rest
Weight and normal equal and opposite. ΣFx = ΣFy = 0, so |F_net| = 0 (equilibrium).
Frequently asked questions
What is a free-body diagram?
An FBD shows one object as a point or box with every external force drawn as an arrow from that object. Internal forces inside the object are omitted.
How do you calculate net force from an FBD?
Break each force into Fx = F cosθ and Fy = F sinθ, sum the components, then |F_net| = √(ΣFx² + ΣFy²). Direction is atan2(ΣFy, ΣFx) from +x.
Which way is 0° on this calculator?
0° points right (+x) and 90° points up (+y), measured counterclockwise. Weight on a flat surface is usually 270° (straight down).