Newton
SI derived unit · quantity: force
01 · Definition
The force that gives a mass of one kilogram an acceleration of one metre per second per second. A quantity built entirely from three base units, without any artefact of its own.
The definition simply restates the second law of mechanics, so it needs neither a prototype nor a calibration rig: the newton is calculated, not kept in a vault.
Uniform motion needs no force: a cart that nothing slows down rolls on by itself. Newtons are needed only where velocity changes — or where something resists the change.
02 · Conversion
Newtons, kilogram-force and pounds-force
All the coefficients are exact by definition: the kilogram-force and the pound-force are fixed through the standard acceleration of free fall.
The kilogram-force is defined as the weight of a kilogram at the standard acceleration of free fall — nine point eight zero six six five metres per second squared, exactly.
| Unit | Name | Value | Where it appears |
|---|---|---|---|
| N | newton | 1 | the base notation of force in the SI |
| kN | kilonewton | 0.001 | construction, thrust, structural loads |
| MN | meganewton | 1·10⁻⁶ | rockets, presses, bridges |
| mN | millinewton | 1 000 | laboratory measurements |
| µN | micronewton | 1·10⁶ | micromechanics, solar sails |
| kgf | kilogram-force | 0.101972 | weight of a kilogram at g₀ |
| gf | gram-force | 101.972 | pharmacy and laboratory balances |
| tf | tonne-force | 0.000101972 | cranes, engine thrust in everyday speech |
| lbf | pound-force | 0.224809 | English-language engineering |
| ozf | ounce-force | 3.59694 | small forces, springs |
| dyn | dyne | 100 000 | the CGS system, nineteenth-century physics |
| pdl | poundal | 7.23301 | the English absolute system |
| sn | sthène | 0.001 | the MTS system, France 1919–1961 |
Weight is calculated at the standard acceleration of free fall, 9.806 65 m/s²; the acceleration is given for a mass of one tonne.
03 · Orders of magnitude
from a speck of dust to a rocket at lift-offOne newton — an apple in the hand
04 · Measuring instruments
How force is measured
The most direct method: Hooke's law relates extension to force linearly, so the scale can be graduated in newtons. Cheap, visual, and accurate to about a percent.
A grid bonded to an elastic element stretches with the metal, and its resistance changes by a fraction of a percent. This is how industrial load cells and crane scales work.
National metrology institutes realise the newton with loads of known mass suspended in a controlled gravitational field. The primary standard for force, accurate to a millionth.
Quartz under load generates charge by itself, and the response keeps up with impacts lasting microseconds. This is how ballistics and crash tests are measured.
05 · Writing rules
Capital N with no full stop
The symbol comes from a surname, so the first letter is capital, while the name of the unit in running text is lower case: newton, five newtons.
The prefix kilo is written in lower case: kN, not KN. Torque is written as newton-metre, and although the dimension matches the joule, the two are never interchanged: work is scalar, torque is not.
06 · Neighbouring units
The newton stands at the root of a whole cluster of derived units: divide it by area and you get the pascal, multiply by distance and you get the joule, divide the joule by time and you get the watt.
newton per square metre
force
newton-metre of work
In neighbouring Simetrium passports: pascal for pressure, joule for work, watt for power, and kilogram — the base unit through which the newton is defined. Among the non-SI units nearby stand the pound-force and the foot-pound, still alive in English-language engineering.
07 · Historical section
How force was measured before the newton
The second law of motion was formulated without any unit of force at all: Newton wrote about proportions, not about numbers with dimensions. A unit was unnecessary — forces were compared with one another.
Engineers counted in kilogram-force — the weight of a known mass, easy to picture. Physicists preferred the centimetre-gram-second system, where the unit of force is the dyne, a hundred-thousandth of a newton.
The ninth General Conference on Weights and Measures approved the name newton for the force that accelerates a kilogram by one metre per second squared. The unit had existed before that — it simply had no name of its own.
The kilogram-force has left the documents but stayed in speech: engine thrust is still quoted in tonnes, and pressure gauges are still marked in kgf/cm². The number differs from the newton by a factor of nearly ten — enough to matter in a calculation.
The newton cannot be realised by an artefact — only computed
The kilogram had a prototype, the metre had a line on a platinum bar; the newton has no object and can have none. Force is not stored — it is produced at the moment of measurement, by hanging a known mass in a known gravitational field. That is why a deadweight machine is not a standard kept in a safe but a procedure repeated afresh each time: the mass of the loads, the local value of g and the buoyancy of air all enter the result. Below a hundred micronewtons even that fails, and force is measured by electrostatic balance — the current in a coil is compared with the pull of gravity.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived units with names of their own, and the non-SI units without which neither engineering nor everyday life gets by. Each is a separate sheet: definition, dimension, conversion, instruments, writing rules.
SI derived units with names of their own
the newton's passport is openSI base units
in terracotta — the kilogram, metre and second from which the newton is builtNon-SI units
in terracotta — units of force from other systemsPassport language
2 languages. The symbol N is international, and the name of the unit follows a surname, so it changes little: newton, Newton, نيوتن. What is translated is the description, the examples and the writing rules of each script.