Newton (unit)

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Illustration on One Newton, 2018-07-06.png
Visualization of one newton of force
General information
Unit system SI derived unit
Unit of Force
Named after Sir Isaac Newton
1 N in ...... is equal to ...
   SI base units   1 kgms −2
   British Gravitational System   0.2248089 lbf

The newton (symbol: N) is the International System of Units (SI) derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.


See below for the conversion factors.


One newton is 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. [1] The units "metre per second squared" can be understood as change in velocity per time, i.e. an increase of velocity by 1 metre per second every second.

In 1946, Conférence Générale des Poids et Mesures (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. [2] The MKS system then became the blueprint for today's SI system of units. The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units.

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.

In more formal terms, Newton's second law of motion states that the force exerted on an object is directly proportional to the acceleration hence acquired by that object, namely: [3]

where the proportionality constant represents the mass of the object undergoing an acceleration . As a result, the newton may be defined in terms of kilograms (), metres (), and seconds () as


At average gravity on Earth (conventionally, g = 9.80665  m/s2 ), a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force, which we measure as the apple's weight. [4]

1 N = 0.10197 kg × 9.80665 m/s2    (0.10197  kg  = 101.97 g).

The weight of an average adult exerts a force of about 608 N.

608 N = 62 kg × 9.80665 m/s2 (where 62 kg is the world average adult mass). [5]

Commonly seen as kilonewtons

It is common to see forces 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.

One kilonewton, 1 kN, is equivalent to 102.0  kgf, or about 100 kg of load under Earth gravity.

1 kN = 102 kg × 9.81 m/s2.

So for example, a platform that shows it is rated at 321 kilonewtons (72,000 lbf), will safely support a 32,100 kilograms (70,800 lb) load.

Specifications in kilonewtons are common in safety specifications for:

Units of force
(SI unit)
dyne kilogram-force,
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 dyngn ⋅ (1 kg)≈ 2.2046 lbf≈ 70.932 pdl
1 lbf≈ 4.448222 N≈ 444822 dyn≈ 0.45359 kpgn ⋅ (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 is used here for all gravitational units.
Three approaches to units of mass and force or weight [6] [7]
2nd law of motion m = F/aF = Wa/gF = ma
Acceleration (a)ft/s2m/s2ft/s2m/s2ft/s2 Gal m/s2m/s2
Mass (m) slug hyl pound-masskilogram pound gram tonne kilogram
Force (F),
weight (W)
pound kilopond pound-forcekilopond poundal dyne sthène newton
Pressure (p) pounds per square inch technical atmosphere pounds-force per square inch atmosphere poundals per square foot barye pieze pascal
Standard prefixes for the metric units of measure (multiples)
Prefix nameN/A deca- hecto- kilo- mega- giga- tera- peta- exa- zetta- yotta-
Prefix symbolda-h-k-M-G-T-P-E-Z-Y-
Standard prefixes for the metric units of measure (submultiples)
Prefix nameN/A deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Prefix symbold-c-m-μ-n-p-f-a-z-y-

See also

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