Calculate net force from multiple force vectors. Supports 2D force resolution with angles, friction, gravity, normal force, and free-body diagram analysis.
The Net Force Calculator computes the resultant force from multiple force vectors acting on an object. Enter up to 6 forces with their magnitudes and directions to find the net force magnitude, direction, and resulting acceleration. The calculator resolves forces into x and y components, sums them vectorially, and displays the complete analysis. It is especially useful when you need to check a free-body diagram before solving the motion equation by hand. It gives you a clean result when the setup has more than one applied force.
Newton's Second Law states F_net = ma — the net force equals mass times acceleration. When multiple forces act on an object, only the vector sum (net force) determines its acceleration. A book on a table has gravity pulling down and the normal force pushing up — the net force is zero, so it doesn't accelerate.
Enter force magnitudes and angles, or use the common force presets (gravity, friction, applied force, tension) to build free-body diagrams. The calculator shows component breakdown, vector diagram data, and the resulting motion.
Use this calculator when you need the vector sum of several forces without manually resolving every component on paper. It is useful for free-body-diagram work, equilibrium checks, and quick acceleration estimates once the applied forces are known, especially in 2D statics and dynamics problems where the x and y components matter separately.
Fx_net = ΣFᵢcos(θᵢ). Fy_net = ΣFᵢsin(θᵢ). F_net = √(Fx² + Fy²). θ_net = atan2(Fy, Fx). Acceleration: a = F_net / m. Weight: W = mg. Friction: f = μN.
Result: F_net = 50.0 N at 30°, a = 5.0 m/s²
A 10 kg object with a 50 N applied force at 30°, gravity (98.1 N down), and normal force (98.1 N up). Gravity and normal cancel. Net = 50 N at 30°. Components: Fx = 43.3 N, Fy = 25.0 N. Acceleration = 50/10 = 5.0 m/s².
A free-body diagram (FBD) isolates an object and shows all forces acting on it. This is the essential first step in any force analysis. Common forces include: weight (mg, downward), normal force (perpendicular to surface), friction (parallel to surface, opposing motion), tension (along rope/cable, pulling), applied forces, air drag (opposing velocity), and spring forces (F = -kx).
The power of the net force approach is that complex problems with many forces reduce to a single vector equation: F_net = ma. By resolving into components, this becomes two scalar equations (x and y) that can be solved simultaneously for unknown forces or acceleration.
Newton's First Law: an object remains at rest or constant velocity unless acted on by a net force. Newton's Second Law: F_net = ma — the net force equals mass times acceleration. Newton's Third Law: for every action, there's an equal and opposite reaction (on a different object).
For connected objects (pulleys, stacked blocks), draw separate FBDs for each object and apply Newton's Second Law to each. The constraint equations (string length, contact) connect the accelerations and forces between objects.
In static equilibrium, F_net = 0 and the sum of torques about any point is zero. This is the foundation of structural engineering — every building, bridge, and machine frame is designed so that all forces balance. Even slight imbalances cause motion, which is why precision matters in structural analysis.
Net force is the vector sum of all forces acting on an object. It determines the object's acceleration via F = ma. If net force is zero, the object is in equilibrium (at rest or moving at constant velocity). Forces are vectors — both magnitude and direction matter.
For a force F at angle θ from the positive x-axis: Fx = F·cos(θ), Fy = F·sin(θ). Then sum all x-components and y-components separately. The net force magnitude = √(Fx² + Fy²), direction = atan2(Fy, Fx).
Angles are measured counterclockwise from the positive x-axis (standard mathematical convention): right = 0°, up = 90°, left = 180°, down = 270°. Gravity is typically at 270° (straight down).
Include ALL forces: gravity (mg downward), normal force (perpendicular to surface), friction (opposite to motion along surface), applied forces, tension, air resistance, spring forces. Missing a force gives wrong results — always draw a free-body diagram.
When an object is in static equilibrium (not moving) or dynamic equilibrium (constant velocity). Examples: a book on a table, a car cruising at constant speed, a hovering helicopter. Zero net force means zero acceleration, not zero velocity.
Kinetic friction: f = μₖN. Static friction: f ≤ μₛN (up to a maximum). N is the normal force, which on a flat surface equals the weight (mg). On an incline: N = mg·cos(θ). Friction always opposes motion or potential motion.