How to calculate force

Newton's second law is one short equation: force equals mass times acceleration. Here is how to use it, in both directions, with the units that trip people up.

By the Calculator Den team · Updated 2026-11-02

Force is one of the first things you calculate in physics, and it comes from one short equation. Newton's second law says that the force on an object equals its mass multiplied by its acceleration, usually written F = ma. Learn that, the units that go with it, and how to rearrange it, and you can handle most introductory force problems.

How to calculate force: the formula F = ma

Newton's second law links three quantities:

F = m × a

where F is the net force, m is the mass, and a is the acceleration. In plain words, the force needed to accelerate something is bigger if the object is heavier, and bigger if you want it to speed up faster. Push a shopping trolley and a loaded truck with the same effort and the trolley accelerates far more, because the same force spread across more mass gives less acceleration. To find the force, multiply the mass by the acceleration. A 10 kg box accelerating at 2 m/s² needs a force of 10 × 2 = 20 newtons.

The units (and what a newton is)

Getting the units right is where most mistakes happen. In the standard (SI) system, mass is in kilograms (kg), acceleration is in metres per second squared (m/s²), and force comes out in newtons (N). One newton is defined as exactly the force that accelerates 1 kg at 1 m/s², so a newton is really just a shorthand for one kg·m/s². If you put mass in kilograms and acceleration in m/s², your answer is automatically in newtons. Mixing units, such as grams with metres, is the classic error, so convert everything to kilograms and metres first.

Rearranging it: solving for mass or acceleration

The same equation answers three questions depending on what you know. Rearrange F = ma and you get:

m = F ÷ a (to find mass)
a = F ÷ m (to find acceleration)

So if a 50 N force makes an object accelerate at 5 m/s², its mass is 50 ÷ 5 = 10 kg. If a 200 N force acts on a 40 kg object, its acceleration is 200 ÷ 40 = 5 m/s². One equation, three forms; pick the one that leaves your unknown on its own. A quick sports example of the force form: a 0.45 kg football kicked to accelerate at 40 m/s² feels a force of 0.45 × 40 = 18 N from your foot.

How to calculate weight as a force

A common point of confusion is the difference between mass and weight. Mass is how much matter an object contains, measured in kilograms, and it never changes. Weight is the force of gravity pulling on that mass, and it is a force measured in newtons. It is just F = ma with acceleration set to g, the acceleration due to gravity, about 9.81 m/s² on Earth:

Weight = m × g

So a 70 kg person has a weight of 70 × 9.81 = 687 N on Earth. On the Moon, where g is about 1.6 m/s², the same person still has a mass of 70 kg but a weight of only about 112 N. This is why you would feel lighter on the Moon: your mass is unchanged, but the gravitational force pulling on it is roughly a sixth as strong. (Astronauts in orbit float for a different reason, continuous free fall, not weaker gravity.)

Net force: when more than one force acts

The F in F = ma is the net force, the overall push once every force on the object is added up, taking direction into account. Real objects usually have several forces on them at once: your push, friction resisting it, gravity, the ground pushing back. To use F = ma, first combine them into one net force. Forces in the same direction add; forces in opposite directions subtract.

Say you push a 20 kg crate with 100 N, and friction resists with 40 N in the opposite direction. The net force is 100 − 40 = 60 N, so the acceleration is 60 ÷ 20 = 3 m/s². If the forces had been balanced, say 40 N of push against 40 N of friction, the net force would be zero and the crate would not accelerate at all, which is Newton's first law: no net force, no change in motion.

A worked example

Put it together. A 1,200 kg car accelerates from a standstill at 3 m/s². Ignoring friction, the driving force the engine must provide is F = m × a = 1,200 × 3 = 3,600 N. If the road also provides 400 N of resistance, the engine has to overcome that too, so it must push with 3,600 + 400 = 4,000 N to get the same 3 m/s², because only the net 3,600 N goes into accelerating the car. Keeping track of which forces help and which resist is most of the work in any force problem.

Force is a vector, and other force formulas

Force has a direction as well as a size, which is why the net force depends on which way each force points. A negative answer simply means the force acts opposite to the direction you called positive, so pick one positive direction (usually the way the object moves) and stick to it to avoid sign errors.

F = ma is the backbone, but a few related formulas describe specific forces. Friction is roughly F = μN, the coefficient of friction times the normal force pressing the surfaces together. An object moving in a circle needs a centripetal force pulling it inward. And in some engineering contexts you will meet pound-force (lbf) instead of newtons. All of these still obey F = ma underneath; they just name a particular force. If your units are awkward, convert first: a 500 g ball at 4 m/s² is 0.5 kg × 4 = 2 N, not 500 × 4.

Common mistakes to avoid

Three slips account for most wrong answers. The first is units: putting mass in grams, or using a speed in km/h where acceleration in metres per second squared is needed, gives a number that is not in newtons, so convert to kilograms and m/s² first. The second is confusing weight with mass, using a weight in newtons where the formula wants a mass in kilograms; if you are told something "weighs 20 N", its mass is 20 ÷ 9.81, about 2 kg, not 20. The third is forgetting that F is the net force: plugging in only your push and ignoring friction or gravity will overstate the acceleration. Combine all the forces first, then divide by the mass.

The bottom line

Force is mass times acceleration, F = ma, with mass in kilograms, acceleration in m/s², and force in newtons. Rearrange it to m = F ÷ a or a = F ÷ m when those are the unknowns, remember that weight is just this equation with g in place of a, and always use the net force when several forces act. To check a calculation or solve for any of the three quantities at once, put your numbers into our force calculator. If you are moving on through mechanics, our explainers on kinetic energy and density cover the next pieces.