Force Calculator — Newton's second law (F = ma)

How it works

Newton's second law of motion links force, mass and acceleration. The net force on an object equals its mass times the acceleration that force produces:

F = m × a

The net force is what matters — the single force left over once every push and pull on the object is added together. For a given force, a heavier object accelerates less; for a given mass, a bigger force means more acceleration.

This calculator is unit-agnostic but works in SI by default: mass in kilograms (kg) and acceleration in metres per second squared (m/s²) give a force in newtons (N), where one newton is the force that accelerates 1 kg at 1 m/s². Acceleration may be negative — a decelerating object has a force opposing its motion — so the force can come out negative too, indicating direction.

Worked example

OpenStax's lawn-mower example runs the law in reverse: a net force of 51 N on a 24 kg mower gives an acceleration of 51 ÷ 24 = 2.125 m/s². Feed that acceleration back in and the force returns: 24 × 2.125 = 51 N. The other presets show a 10 kg object in free fall (10 × 9.8 = 98 N of weight) and a 1000 kg car pushed at 3 m/s² (3000 N).

Frequently asked questions

What is Newton's second law?

It states that the net force on an object equals its mass times its acceleration, F = ma. It is the quantitative link between the forces acting on something and how its motion changes — more force gives more acceleration, more mass gives less.

What is a newton?

The newton (N) is the SI unit of force: one newton accelerates a one-kilogram mass at one metre per second squared (1 N = 1 kg·m/s²). It is named after Isaac Newton and is roughly the weight of a small apple on Earth.

What is the difference between mass and weight?

Mass is the amount of matter in an object (kilograms) and does not change; weight is the gravitational force on that mass (newtons) and depends on gravity. Weight is mass times g, so a 10 kg mass weighs about 98 N on Earth (g ≈ 9.8 m/s²) but less on the Moon.

Can the force be negative?

Yes. A negative result means the net force points in the opposite direction to the one you called positive — for example a braking force that decelerates a moving object. Enter a negative acceleration and the force flips sign accordingly.

How do I find acceleration if I know the force?

Rearrange the law to a = F ÷ m. Newton's second law can be read in any of three ways: F = ma, a = F/m, or m = F/a, so knowing any two of the three quantities gives the third.

Does this include friction or gravity automatically?

No — F = ma uses the **net** force, the sum of all forces already combined. If friction, gravity or other forces act, add them up (with their directions) first, then enter that net acceleration. The calculator does not know what forces are present.