BREAKING NEWS
Newton (unit)

## Summary

The newton (symbol: N) is the unit of force in the International System of Units (SI). It is defined as ${\displaystyle 1\ {\text{kg}}\cdot {\text{m/s}}^{2}}$, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second squared.

newton
Visualization of one newton of force
General information
Unit systemSI
Unit offorce
SymbolN
Named afterSir Isaac Newton
Conversions
1 N in ...... is equal to ...
SI base units   1 kgms−2
CGS units   105 dyn
Imperial units   0.224809 lbf

It is named after Isaac Newton in recognition of his work on classical mechanics, specifically his second law of motion.

## Definition

A newton is defined as ${\displaystyle \mathrm {1\ kg{\cdot }m/s^{2}} }$  (it is a named derived unit defined in terms of the SI base units).[1]: 137  One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.[2]

The units "metre per second squared" can be understood as measuring a rate of change in velocity per unit of time, i.e. an increase in velocity by 1 metre per second every second.[2]

In 1946, the General Conference on Weights and Measures (CGPM) Resolution 2 standardized the unit of force in the MKS system of units to be the amount needed to accelerate 1 kilogram of mass at the rate of 1 metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name newton for this force.[3] The MKS system then became the blueprint for today's SI system of units.[4] The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units.[3]

The newton is named after Isaac Newton. As with every SI unit named for a person, its symbol starts with an upper case letter (N), but when written in full, it follows the rules for capitalisation of a common noun; i.e., newton becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

The connection to Newton comes from Newton's second law of motion, which states that the force exerted on an object is directly proportional to the acceleration hence acquired by that object, thus:[5]

${\displaystyle F=ma,}$

where ${\displaystyle m}$  represents the mass of the object undergoing an acceleration ${\displaystyle a}$ . When using the SI unit of mass, the kilogram (${\displaystyle {\text{kg}}}$ ), and SI units for distance metre (${\displaystyle {\text{m}}}$ ), and time, second (${\displaystyle {\text{s}}}$ ) we arrive at the SI definition of the newton: ${\displaystyle \mathrm {1\ kg{\cdot }m/s^{2}} .}$

## Examples

At average gravity on Earth (conventionally, ${\displaystyle g={9.80665}\ {\text{m/s}}^{2}}$ ), a kilogram mass exerts a force of about 9.8 newtons.

• An average-sized apple at 200 g exerts about two newtons of force at Earth's surface, which we measure as the apple's weight on Earth.
${\displaystyle 0.200{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=1.961{\text{ N}}.}$
${\displaystyle 62{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=608{\text{ N}}}$  (where 62 kg is the world average adult mass).[6]

## Kilonewtons

Large forces may be expressed in kilonewtons (kN), where 1 kN = 1000 N. For example, the tractive effort of a Class Y steam train locomotive and the thrust of an F100 jet engine are both around 130 kN.[citation needed]

Climbing ropes are tested by assuming a human can withstand a fall that creates 12 kN of force. The ropes must not break when tested against 5 such falls.[7]: 11

## Conversion factors

Units of force
newton dyne kilogram-force,
kilopond
pound-force poundal
1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl
1 dyn = 10–5 N  1 g⋅cm/s2  1.0197×10−6 kp  2.2481×10−6 lbf  7.2330×10−5 pdl
1 kp = 9.80665 N = 980665 dyn  gn × 1 kg  2.2046 lbf  70.932 pdl
1 lbf  4.448222 N  444822 dyn  0.45359 kp  gn × 1 lb  32.174 pdl
1 pdl  0.138255 N  13825 dyn  0.014098 kp  0.031081 lbf  1 lb⋅ft/s2
The value of gn as used in the official definition of the kilogram-force (9.80665 m/s2) is used here for all gravitational units.
Three approaches to units of mass and force or weight[8][9]
Base Force Weight Mass
2nd law of motion m = F/a F = Wa/g F = ma
System BG GM EE M AE CGS MTS SI
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 Gal m/s2 m/s2
Mass (m) slug hyl pound-mass kilogram pound gram tonne kilogram
Force (F),
weight (W)
pound kilopond pound-force kilopond poundal dyne sthène newton
Pressure (p) pound per square inch technical atmosphere pound-force per square inch standard atmosphere poundal per square foot barye pieze pascal
Standard prefixes for the metric units of measure (multiples)
Prefix name N/A deca hecto kilo mega giga tera peta exa zetta yotta ronna quetta
Prefix symbol da h k M G T P E Z Y R Q
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024 1027 1030
Standard prefixes for the metric units of measure (submultiples)
Prefix name N/A deci centi milli micro nano pico femto atto zepto yocto ronto quecto
Prefix symbol d c m μ n p f a z y r q
Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24 10−27 10−30