Definition · Plain-language
Units of force
The SI unit of force is the newton; it is the force that gives a one-kilogram mass an acceleration of one metre per second squared.
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The newton, the SI unit
The SI unit of force is the newton, symbol N, named after Isaac Newton. It is a derived unit, defined through his second law of motion: one newton is the force that gives a mass of one kilogram an acceleration of one metre per second squared. Written in base units, a newton is therefore a kilogram metre per second squared. Force itself is simply a push or a pull — anything that can change an object’s motion. Because force has both a size and a direction, it is a vector quantity, which the unit alone does not capture but the full description does.
Force, mass and acceleration
The newton is inseparable from Newton’s second law, force equals mass times acceleration. This says the force needed to accelerate an object is proportional both to its mass and to the acceleration desired: a heavier object, or a quicker change in motion, demands more force. A two-kilogram mass accelerating at three metres per second squared experiences a force of six newtons. The law also explains why mass and force are different quantities with different units — mass in kilograms is the amount of matter, force in newtons is what acts to change its motion.
Weight and other force units
The most familiar force in daily life is weight — the gravitational pull on an object, equal to its mass times the acceleration of gravity. Near the Earth’s surface, where gravity is about 9.8 metres per second squared, a one-kilogram mass has a weight of about 9.8 newtons. This is why scientists insist that weight, a force, is properly given in newtons, not kilograms. Older and non-SI units of force still appear in some contexts — the kilogram-force, the pound-force and the dyne — but all convert to newtons, the single coherent SI unit.
Key facts
At a glance
- SI unit: the newton (N)
- Newton defined: accelerates 1 kg at 1 m/s²
- In base units: kilogram metre per second squared (kg·m·s⁻²)
- Governing law: force = mass × acceleration
- Weight: a force; 1 kg weighs about 9.8 N on Earth
- Other units: kilogram-force, pound-force, dyne all convert to newtons
Common misconceptions
What people often get wrong
Often heard: Force is measured in kilograms.
Actually: The kilogram is the unit of mass, not force. Force is measured in newtons. Saying something "weighs 5 kilograms" describes its mass; its weight as a force is about 49 newtons.
Often heard: Weight and mass are the same and share a unit.
Actually: They differ. Mass is the amount of matter, in kilograms; weight is the gravitational force on that mass, in newtons. Weight changes with gravity, mass does not.
Often heard: A larger force always means a larger acceleration.
Actually: Only for a fixed mass. Force equals mass times acceleration, so the same force produces less acceleration on a heavier object. Both mass and force determine the resulting motion.
Going deeper
