Newton's Second Law Calculator (F = ma)

Newton's second law states F = ma, where F is the net force in newtons, m is mass in kilograms, and a is acceleration in m/s². Enter any two and the calculator returns the third. This is the central equation of classical mechanics — virtually every dynamics problem reduces to applying it correctly. Students sometimes plug in just one applied force, but F here means the net force, after you've added up everything pulling and pushing. Friction, gravity, tension, normal force — all included. Get the net force right and the acceleration follows.

Multiply mass in kilograms by acceleration in m/s² to get force in newtons: F = ma. So a 60 kg sprinter accelerating at 3 m/s² needs a net force of 180 N from her legs against the track. A 1500 kg car accelerating at 2 m/s² needs 3000 N from engine torque overcoming friction and drag. The newton is defined precisely as the force that gives 1 kg an acceleration of 1 m/s², so the formula is essentially the unit definition. Always check that the force you're computing is the net force, not just one of several acting.

Rearrange F = ma to m = F/a. If a 200 N net force produces 4 m/s² acceleration, the mass must be 50 kg. This is exactly how inertial mass is operationally defined: apply a known force, measure the acceleration, divide. It's also how astronauts can measure mass in zero gravity, where weighing scales don't work — they oscillate themselves on a calibrated spring and infer mass from the period. The formula assumes a constant force throughout the acceleration, so for varying forces you'd integrate or use averages.

Divide net force by mass: a = F/m. A 100 N force on a 25 kg trolley gives a = 4 m/s². The result has units of m/s² when force is in newtons and mass in kilograms. This is the form that comes up most often in everyday problems: you know what's pushing, you know what's being pushed, and you want to know how quickly it speeds up. The same force gives smaller acceleration to bigger masses, which is why a small car beats a lorry away from traffic lights even with similar engine forces.

When several forces act on an object, add them as vectors first to get the net force, then apply F_net = ma. If two forces in the same direction (say 50 N and 30 N) push a 10 kg box, F_net = 80 N and a = 8 m/s². If they're opposed, F_net = 50 − 30 = 20 N and a = 2 m/s². For two-dimensional cases, break each force into x and y components, sum each axis separately, and find the resultant. Free-body diagrams are non-negotiable here — sketch every force before you start arithmetic.

The newton is defined as kg·m/s², which is exactly what you get when you multiply mass (kg) by acceleration (m/s²). So a force of 1 N produces an acceleration of 1 m/s² on a 1 kg mass. If you stick to these SI units, F = ma works flawlessly. Mixing in grams, centimetres, or pounds-force without converting always produces a wrong answer. Some engineering work uses pound-force (lbf) and slugs, where 1 lbf accelerates 1 slug at 1 ft/s²; that's a self-consistent system, but don't blend it with metric inputs.

Mass is how much matter you have, in kilograms — it's intrinsic and unchanged anywhere in the universe. Weight is the gravitational force on that mass, in newtons, given by W = mg. So a 70 kg person has a mass of 70 kg everywhere, but a weight of about 686 N on Earth and only about 113 N on the Moon. F = ma uses mass, never weight. Confusing the two gives nonsense: a 50 kg crate has 50 kg of mass and roughly 490 N of weight, but you'd never multiply weight by acceleration in F = ma.