Net Force Calculator
Add several forces on one object to get the net force, its direction, the acceleration, and whether the object is in equilibrium.
⚖️ What is Net Force?
Net force is the single force that has the same effect on an object as all the forces acting on it together. Because force is a vector, with both a size and a direction, it is found by adding the individual forces as vectors, not by adding their sizes. Along one straight line that means signed addition: a 50 N push to the right and a 20 N push to the left give a net force of 30 N to the right. In two dimensions each force is split into x and y components, the components are added separately, and the result is rebuilt into a magnitude and an angle. This page does both, and it is about summing several forces. For the single relationship F = m a, with one force, one mass and one acceleration, use the force calculator.
The net force is what decides motion. Newton's second law says the acceleration of an object is its net force divided by its mass, and it points the same way as the net force. When the net force is exactly zero the object is in equilibrium: it does not accelerate, so it either stays at rest or keeps moving at a constant velocity. Real examples are everywhere. A tug of war is a sum of pulls along a rope, a box pushed across a floor is a push minus friction, a hanging sign is two cable tensions balancing a weight, and an airplane in flight is thrust, drag, lift and weight acting at once. Once you have the net force, the acceleration calculator and the kinematic equations calculator take it from there, and the impulse and momentum calculator shows what a net force does over a time interval.
A few distinctions are easy to miss. The net force is not drawn on a free-body diagram of the object, because it is the result of the drawn forces. Zero net force does not mean zero velocity. Adding magnitudes ignores direction and only works when every force points the same way. And friction is a force like any other, but kinetic friction exists only while surfaces slide, and it always points against the sliding motion. This calculator models kinetic friction for a sliding object. It does not model static friction, so it cannot tell you whether a resting box will start to move.
The vector mode adds one more idea, the equilibriant: the force you would have to add to make the net force zero. It has the same magnitude as the net force and points in the opposite direction. The calculator shows it, draws it, and plots how the net force changes as you rotate the last force through a full turn. Related vector addition for velocities is on the resultant velocity calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Tug of War
Team A pulls right with 620 N and 580 N, team B pulls left with 700 N and 450 N, on a 120 kg system
Example 2 — A Box Pushed With Friction
A 10 kg box sliding right is pushed with 50 N on a floor with a kinetic friction coefficient of 0.2
Example 3 — Three Forces in Equilibrium
Three 10 N forces at 0, 120 and 240 degrees acting on a 2 kg object
Example 4 — An Airplane in Flight
Thrust 8000 N at 0°, drag 6500 N at 180°, lift 50000 N at 90°, weight 49033.25 N at 270°, mass 5000 kg
Example 5 — Two Perpendicular Forces
30 N to the right and 40 N upward on a 5 kg object
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate net force?
Net force is the vector sum of every force on the object. Along one line, add the signed forces: right or up is positive, left or down is negative. In two dimensions, add the x components F cos(angle) and the y components F sin(angle), then take the square root of Fx squared plus Fy squared.
What is the net force when forces are balanced?
Zero. Balanced forces cancel, so the object is in equilibrium and does not accelerate. It may be at rest or moving at constant velocity. Three 10 N forces 120 degrees apart, for example, add to exactly 0 N.
How do you find acceleration from net force?
Use Newton's second law in the form a = F_net / m. A net force of 50 N on a 120 kg system gives 0.417 m/s squared. The acceleration points in the same direction as the net force.
What is the equilibriant force?
The equilibriant is the single force that balances the net force. It has the same magnitude as the net force and points in the opposite direction, so its angle is the net direction plus 180 degrees.
How does friction change the net force?
Kinetic friction has magnitude mu times m times g and points against the motion of a sliding object. Subtract it from the applied force along the direction of motion. A 10 kg box with mu 0.2 feels 19.61 N of friction.
Can the net force be smaller than every individual force?
Yes. Forces that point in partly opposite directions cancel. A 620 N and a 580 N pull to the right against 700 N and 450 N to the left leave only 50 N, far smaller than any single force.
How do you add forces at different angles?
Resolve each force into components, add all the x components and all the y components separately, then recombine them. The magnitude is the square root of the sum of the squares and the direction is atan2(Fy, Fx).
What does a negative net force mean?
It only means the net force points in the negative direction you chose, usually left or down. The size of the push is the absolute value. Always check which direction you called positive.
Is net force the same as the sum of the magnitudes?
No. The sum of magnitudes ignores direction and is only equal to the net force when every force points the same way. Direction matters, so opposite forces subtract and perpendicular forces combine by Pythagoras.
Does zero net force mean the object is not moving?
No. By Newton's first law an object with zero net force keeps its velocity, which can be zero or any constant value. A car cruising at constant speed on a flat road has balanced forces.