# Newton (unit)

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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.

Newton
Visualization of one newton of force
General information
Unit systemSI derived unit
Unit ofForce
SymbolN
Named afterSir Isaac Newton
Conversions
1 N in ...... is equal to ...
SI base units   1 kgms−2
British Gravitational System   0.2248089 lbf

See below for the conversion factors.

## Definition

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.

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.[1] 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.

This SI unit is named after Isaac Newton. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (N). However, when an SI unit is spelled out in English, it is treated as a common noun and should always begin with a lower case letter (newton)—except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.

Newton's second law of motion states that F = ma, where F is the force applied, m is the mass of the object receiving the force, and a is the acceleration of the object. The newton is therefore:[2]

 F = m ⋅ a 1 N = 1 kg ⋅ 1 m/s2

where the following symbols are used for the units: N for newton, kg for kilogram, m for metre, and s for second.

${\displaystyle {\mathsf {F}}={\frac {\mathsf {ML}}{{\mathsf {T}}^{2}}}}$

where ${\displaystyle {\mathsf {F}}}$  is force, ${\displaystyle {\mathsf {M}}}$  is mass, ${\displaystyle {\mathsf {L}}}$  is length and ${\displaystyle {\mathsf {T}}}$  is time.

## Examples

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.[3]

1 N = 0.102 kg × 9.80665 m/s2    (0.102 kg = 102 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)[4]

## 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 fighter jet engine are both around 130 kN.

One kilonewton, 1 kN, is 102.0 kgf, or about 100 kg of load.

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:

## Conversion factors

Units of force
newton
(SI unit)
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 is used here for all gravitational units.
Three approaches to units of mass and force or weight[5][6]
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 atmosphere poundal per square foot barye pieze pascal

Standard prefixes for the SI units of measure

Multiples Prefix name deca hecto kilo mega giga tera peta exa zetta yotta
Prefix symbol da h k M G T P E Z Y
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024

Submultiples Prefix name           deci centi milli micro nano pico femto atto zepto yocto
Prefix symbol d c m μ n p f a z y
Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24