Force Calculator (F = ma) & Weight

Understanding the force calculator — concept and principle

Force is what changes an object's motion. This calculator applies Newton's second law to find the net force needed to give a mass a chosen acceleration, and also shows the object's weight on Earth and the force in kilogram-force (kgf) and pound-force (lbf). It is handy for physics homework, sizing actuators and motors, and converting between metric and imperial force units.

Push 10 kg with 20 N and it gains 2 m/s of speed every second.

How it is calculated

Force: F = m × a, where m is mass in kilograms and a is acceleration in m/s². The result is in newtons; 1 N = 1 kg·m/s².
Weight on Earth: W = m × g, with standard gravity g = 9.80665 m/s².
kgf: F ÷ 9.80665, since 1 kgf is the weight of 1 kg under standard gravity.
lbf: F ÷ 4.4482216, since 1 lbf = 4.4482216 N.

The principle

Newton's second law says the net force on a body equals its mass times its acceleration. Mass measures how much an object resists changes in motion (inertia): the same push accelerates a light cart more than a heavy one. The newton is defined from this law, so 1 N is exactly the force that gives 1 kg an acceleration of 1 m/s². Weight is simply the special case where the acceleration is that of free fall, g. The value 9.80665 m/s² is a conventional standard adopted in 1901; actual gravity varies from about 9.78 m/s² at the equator to about 9.83 m/s² at the poles.

Worked example

Inputs: m = 10 kg, a = 2 m/s².
Force: F = 10 × 2 = 20 N.
Weight: W = 10 × 9.80665 = 98.0665 N.
In kgf: 20 ÷ 9.80665 ≈ 2.0394 kgf.
In lbf: 20 ÷ 4.4482216 ≈ 4.4962 lbf.

Each point is the calculator re-run with only “Mass (kg)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Mass (kg)	Force (N)
2.5	5
5	10
7.5	15
10	20
12.5	25
15	30
20	40

How to read the result

The 20 N is the net force, the sum of all forces after friction, drag and gravity components are accounted for. To accelerate the 10 kg mass at 2 m/s² up a slope or against friction, the applied force must be larger. Comparing F with W is useful: here the accelerating force is about 20% of the object's weight, a gentle push. As a feel for scale, 1 N is roughly the weight of a 102 g object, and 1 kgf is about 9.8 N.

Common mistakes

Treating kilograms as a unit of force; kg is mass, N or kgf is force.
Using applied force instead of net force when friction or gravity also act.
Confusing mass with weight when working on the Moon or other planets, where g differs.
Mixing pounds (mass, lb) with pound-force (lbf).

Keep in mind: F = ma holds for speeds much lower than light and in non-accelerating reference frames. The calculator assumes standard gravity; precise work at a specific location may need local g.

Frequently asked questions

How many newtons is 1 kg?

A 1 kg mass weighs about 9.81 N on Earth (exactly 9.80665 N under standard gravity), which is also 1 kgf.

What is the difference between mass and weight?

Mass is the amount of matter and does not change with location; weight is the gravitational force on that mass and does change, for example to about one sixth on the Moon.

What force does it take to stop a car?

Multiply the car's mass by the deceleration. A 1,500 kg car braking at 5 m/s² needs a net braking force of 7,500 N.

Sources: Isaac Newton, Philosophiæ Naturalis Principia Mathematica, 1687 · BIPM, The International System of Units (SI Brochure), 9th edition, 2019 · NIST Special Publication 811, Guide for the Use of the International System of Units

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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