Newton's Second Law Calculator
From a mass and an acceleration, get the net force in newtons — the single equation behind how every push and pull changes motion.
Two inputs, one answer
Enter the mass and the acceleration and the calculator returns the force (m × a) straight away.
Use SI units
Mass in kilograms (kg), acceleration in metres per second squared (m/s²) — then the force comes back in newtons (N).
What is Newton's second law?
Mass and acceleration in, force out
Newton's second law is the equation that links the three core quantities of motion: force, mass, and acceleration. It says the net force on an object equals its mass multiplied by its acceleration, written F = m × a. Once you know the mass and the acceleration, the force is fixed — it is the total push or pull needed to make that mass speed up, slow down, or change direction at that rate. That makes mass and acceleration the two inputs you need for everything from sizing a rocket engine to working out the impact force in a crash or the weight of an object under gravity.
Enter the mass in kilograms and the acceleration in metres per second squared to get the force instantly.
One short formula, built from the mass (m) and the acceleration (a).
force = mass × accelerationThe force is simply the mass times the acceleration (m × a). The unit of force is the newton (N), defined so that 1 N gives a 1 kg mass an acceleration of 1 m/s² — that is, 1 N = 1 kg·m/s². Because force is proportional to acceleration, doubling the acceleration of a fixed mass doubles the force, and for a fixed force a heavier object accelerates less.
Suppose a mass of 10 kg accelerates at 9.80665 m/s² — the acceleration of Earth's gravity.
Multiply mass by acceleration
10 × 9.80665 = 98.0665 N — the net force on the mass.
Recognise the result
Because the acceleration here is g, this force is exactly the weight of the 10 kg mass — the pull of gravity on it.
Sense-check the size
1 N is roughly the weight of a small apple, so 98 N is about the weight of 100 apples — a reasonable feel for 10 kg.
The force you get is what changes an object's motion — it is the net push or pull, in newtons, needed to give that mass that acceleration. The key insight is that the same force affects different masses differently: applied to a lighter object it produces a larger acceleration, applied to a heavier one a smaller acceleration, because acceleration equals force divided by mass. Weight is just a special case of this law: gravity applies the force F = m × g, where g is 9.80665 m/s² on Earth, which is why a 10 kg mass weighs about 98 N. Mass measures how much matter an object has and never changes, but the force — and therefore the weight — depends entirely on the acceleration involved. Reach for this number whenever you need to know how hard you must push to get a given motion, or how hard a moving object pushes back.
The formula is exact for a constant mass, but a couple of practical points are worth keeping in mind.
Constant mass and SI units
F = m × a assumes the mass stays constant; for systems that lose or gain mass (a rocket burning fuel, for instance) the full form uses the rate of change of momentum instead. This tool also gives the magnitude of the net force only — real problems may involve several forces in different directions that must be added as vectors first. Keep the inputs in kilograms and metres per second squared so the force comes back in newtons.