Force Calculator

F = ma. Newton's second law says the net force on an object equals its mass times its acceleration. Force is in newtons, mass in kilograms, acceleration in meters per second squared.

Worked example, the one above: a 1,500 kg car accelerating at 2.5 m/s² needs a net force of F = 1,500 × 2.5 = 3,750 N, about 843 pounds-force. Turned around, the same law gives the other two: m = F / a and a = F / m. Push 3,750 N on a 750 kg trailer and it accelerates at 5 m/s².

Why a newton is kg·m/s². The newton is defined by this law: one newton is the force that gives one kilogram an acceleration of one meter per second squared. So kg × m/s² is not something that happens to equal newtons; it is what a newton is. Every unit this calculator uses builds on it. A joule is a newton acting through a meter, N·m, which is kg·m²/s². A watt is a joule per second. A newton-second, the unit of impulse, is kg·m/s, which is also the unit of momentum. Following the units through a calculation is the fastest way to catch a mistake: if the answer to an energy question does not come out in kg·m²/s², something is wrong.

Newton's laws of motion. The first law: an object stays at rest or keeps moving in a straight line at constant speed unless a net force acts on it. Motion does not need a force; changing it does. The second law: the net force equals mass times acceleration, F = ma, or more generally the rate of change of momentum. The third law: when one body pushes on another, the other pushes back with an equal and opposite force. Those two forces act on different bodies, which is why they do not cancel: the road pushes the car forward exactly as hard as the tires push the road back.

Net force is the common mistake. F in F = ma is the sum of every force on the object. A car's engine force minus rolling resistance and drag is what accelerates it; at a steady 100 km/h the engine is still pushing hard, the net force is zero, and so is the acceleration.

Weight is F = ma with a = g. An object's weight is its mass times the local acceleration of gravity, W = mg. With standard gravity, 9.80665 m/s², a 70 kg person weighs 686.5 N. The pound-force is defined the same way, as the weight of one pound under standard gravity. That is why on Earth a pound weighs a pound-force and the two get used interchangeably. On the Moon the mass is the same and the weight is about a sixth.

The other modes. Kinetic energy, KE = ½mv², is the work needed to bring a mass from rest to speed v. Gravitational potential energy, PE = mgh, is the work done lifting a weight mg through a height h. Work, W = Fd cos θ, counts only the part of a force that points along the motion. Power, P = W / t, is how fast that work is done. Momentum, p = mv, is what the second law conserves: a force F acting for a time Δt changes momentum by F·Δt. Friction, F = μN, is a coefficient times the force pressing two surfaces together, and pressure, P = F / A, is a force spread over an area.

What this calculator does not do: it treats forces and accelerations as constant, ignores friction and air resistance unless you put them into the net force yourself, and is classical mechanics throughout: accurate at everyday speeds, wrong near the speed of light.