Free-Body Diagram Builder

What a free-body diagram shows

A free-body diagram isolates one body and draws every external force acting on it. This builder treats the forces as a concurrent system — all acting through the body's centre of mass — so the body translates without rotating and the resultant is the plain vector sum of the forces.

• Enter each force by magnitude in newtons and direction in degrees counter-clockwise from the +x axis.
• Drag any arrow tip to rotate that force and watch the resultant follow.
• Weight is a first-class force: add it once and it tracks the mass as W = m·g.
• Start from a worked scenario — a box pushed across a floor, a sign hung from two cables, or three ropes pulling a ring.
• Switch to the motion tab to run the body as a rigid box in a closed container, with the floor supplying its own normal and Coulomb friction forces.

Equations used

The tool resolves every force into components, sums them, and applies Newton's second law:

• ΣFx = Σ Fᵢ·cos θᵢ
• ΣFy = Σ Fᵢ·sin θᵢ
• |F net| = √(ΣFx² + ΣFy²)
• Direction: θ = atan2(ΣFy, ΣFx)
• Acceleration: a = F net / m

Reading the diagram

The compass ring gives the angle of every arrow at a glance, and the scale bar in the corner states how many newtons a given length represents. When the resultant is not along an axis, a dashed rectangle shows ΣFx and ΣFy as the two legs whose vector sum is the resultant. When the forces cancel, the body is marked as being in equilibrium.

Frequently asked questions

How do you find the net force from a free-body diagram?

Resolve each force into x and y components using F·cos θ and F·sin θ, add the components separately to get ΣFx and ΣFy, then combine them: the magnitude of the net force is √(ΣFx² + ΣFy²) and its direction is atan2(ΣFy, ΣFx). This builder does that continuously as you edit or drag the forces.

What does equilibrium mean on a free-body diagram?

Equilibrium means the forces cancel: ΣFx = 0 and ΣFy = 0, so the net force is zero. By Newton's second law the acceleration is then also zero, which means the body either stays at rest or keeps moving in a straight line at constant velocity. It does not mean the body is necessarily stationary.

Should weight be included in a free-body diagram?

Yes. Weight, W = m·g, acts on every body in a gravitational field and points straight down, so it belongs on the diagram unless the problem explicitly says to ignore gravity. On Earth g is 9.81 m/s², so a 2 kg body has a weight of about 19.6 N. This tool computes weight from the mass you enter so the two can never disagree.

How much force is needed to make a box start sliding?

The box stays put while the applied force is below the maximum static friction, f_max = μ·N, where μ is the coefficient of friction and N is the normal force. On level ground with no vertical acceleration N equals the weight m·g, so a 2 kg box on a surface with μ = 0.5 needs more than 0.5 × 19.6 = 9.8 N before it moves. Once sliding, kinetic friction of about the same size opposes the motion, so the net accelerating force is the applied force minus μ·N.

What is the difference between normal force and weight?

Weight is the gravitational pull on the body and always acts downward. The normal force is the contact force a surface exerts on the body, perpendicular to that surface. On flat level ground with no vertical acceleration they are equal in magnitude and opposite in direction, but they are separate forces with separate causes, and on a slope or in a lift they are not equal.