Force Calculator (F = ma)
Solve Newton's second law F = ma for force, mass, or acceleration, with the result in newtons, pounds-force, and as a multiple of gravity.
How to use this calculator
- 1Choose whether to find force, mass, or acceleration.
- 2Enter the two quantities you know, in kilograms and metres per second squared.
- 3Read the force in newtons, pounds-force, and g's.
How it works
Newton's second law
F = m × a F = force (newtons), m = mass (kg), a = acceleration (m/s²) rearranged: m = F ÷ a, a = F ÷ m 1 newton = 1 kg·m/s² ≈ the weight of a small apple weight = mass × g (a special case with a = 9.81)
Newton's second law is the definition of force: the force on an object equals its mass times its acceleration. It says that a given push accelerates a light object more than a heavy one, and that to accelerate anything you must apply a force proportional to how quickly you want its velocity to change. Weight is just this law applied to gravity — your weight in newtons is your mass times g, the acceleration gravity would give you in free fall.
Worked example
To accelerate a 1,000 kg car at 3 m/s², the engine must supply F = 1000 × 3 = 3,000 newtons of driving force. That same 3,000 N applied to a 500 kg car would accelerate it twice as fast, at 6 m/s², because acceleration is force divided by mass.
Force Calculator (F = ma): the complete guide
What a force actually is
Newton's second law, F = ma, is not just a formula to plug numbers into — it is the definition of force itself. A force is whatever causes a mass to accelerate, and its size is exactly the mass times the acceleration it produces. This is why the unit of force, the newton, is defined as one kilogram-metre per second squared: it is the force that gives one kilogram an acceleration of one metre per second squared.
The law captures two everyday intuitions precisely. The same push moves a light object more easily than a heavy one (bigger mass, smaller acceleration), and a bigger push produces a bigger acceleration. What Newton added was that these are exactly proportional — double the force and you double the acceleration; double the mass and you halve it.
Weight is a force, mass is not
Newton's second law clears up the constant confusion between mass and weight. Mass, in kilograms, is the amount of matter and never changes. Weight is a force, in newtons — specifically the force gravity exerts, which is mass times the gravitational acceleration g. Your weight is just F = ma with a set to 9.81 m/s², the acceleration you would have if you fell freely.
This is why weight changes with location while mass does not. On the Moon, g is about 1.62 m/s², so the same mass weighs about a sixth as much — the mass is identical, but the force gravity applies is smaller. Bathroom scales read weight (a force) and label it as mass (kilograms), which works only because everyone using them shares the same Earth gravity.
g-force and the feeling of acceleration
Because weight and acceleration are both governed by this law, accelerations are often quoted in 'g's — multiples of Earth's gravitational acceleration. Pulling 2 g in a fast car or a fighter jet means accelerating at twice 9.81 m/s², and it means the seat pushes on you with twice your normal weight. This is why acceleration feels like a force: your body's inertia resists the change, and the resistance registers as apparent weight.
The concept sets real physical limits. Trained pilots can briefly withstand around 9 g before blood is forced from the brain and they black out; sustained accelerations above a few g are dangerous. Roller coasters are designed around brief peaks of 4–5 g. Expressing acceleration in g's, as the calculator does, turns an abstract metres-per-second-squared figure into something you can feel — how many times heavier than normal it would make you.
Frequently asked questions
What is Newton's second law?
Force equals mass times acceleration, F = ma. It defines force as what causes a mass to accelerate, and says a given force produces less acceleration on a heavier object. Rearranged, it gives mass (F ÷ a) or acceleration (F ÷ m).
What is the difference between mass and weight?
Mass is the amount of matter, in kilograms, and never changes. Weight is a force, in newtons — the pull of gravity on that mass, equal to mass × g. Weight changes with location (less on the Moon); mass does not. Scales read weight but label it as mass.
What is a newton?
The SI unit of force: one newton is the force that accelerates a one-kilogram mass at one metre per second squared (1 kg·m/s²). It's roughly the weight of a small apple on Earth — a handy way to picture the size of the unit.
What does g-force mean?
It expresses acceleration as a multiple of Earth's gravity (9.81 m/s²). Pulling 3 g means accelerating at three times that, and feeling three times your normal weight. It's a natural way to describe the accelerations in vehicles, aircraft, and rides, because it maps onto how heavy you feel.