Newton (unit)

Not to be confused with Newton scale, a rarely used non-SI temperature scale.

SI unit of force

Newton
Visualization of one newton of force
General information
Unit system	SI derived unit
Unit of	Force
Symbol	N
Named after	Sir Isaac Newton
Conversions
1 N in ...	... is equal to ...
SI base units	1 kg⋅m⋅s−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.

Contents

• 
  1 Definition
  


• 
  2 Examples
  


• 
  3 Commonly seen as kilonewtons
  


• 
  4 Conversion factors
  


• 
  5 See also
  


• 
  6 Notes and references
  

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.

In dimensional analysis:

F=MLT2{displaystyle {mathsf {F}}={frac {mathsf {ML}}{{mathsf {T}}^{2}}}}

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

Examples

At average gravity on Earth (conventionally, 7000980665000000000♠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 = 0.10197 kg × 9.80665 m/s²    (6999101970000000000♠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)^[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 lb_f), will safely support a 32,100 kilograms (70,800 lb) load.

Specifications in kilonewtons are common in safety specifications for:

• the holding values of fasteners, Earth anchors, and other items used in the building industry.


• working loads in tension and in shear.


• 
  rock climbing equipment.


• 
  thrust of rocket engines and launch vehicles
  


• clamping forces of the various moulds in injection moulding machines used to manufacture plastic parts.

Conversion factors

Units of force

v t e	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]

v t e Base	Force		Weight		Mass
2nd law of motion	m = F/a		F = W ⋅ a/g		F = m ⋅ a
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

• v


• t


• e

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

See also

• Force gauge


• 
  International System of Units (SI)


• 
  Joule, SI unit of energy, 1 newton exerted over a distance of 1 metre


• 
  Kilogram-force, force exerted by Earth's gravity at sea level on one kilogram of mass


• Kip (unit)


• 
  Pascal, SI unit of pressure, 1 newton acting on an area of 1 square metre
  


• Orders of magnitude (force)


• Pound (force)


• Sthène


• 
  Newton metre, SI unit of torque
  

Notes and references

1. 
   ^ International Bureau of Weights and Measures (1977), The international system of units (330–331) (3rd ed.), U.S. Dept. of Commerce, National Bureau of Standards, p. 17, ISBN 0745649742..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
   


2. 
   ^ "Table 3. Coherent derived units in the SI with special names and symbols". The International System of Units (SI). International Bureau of Weights and Measures. 2006. Archived from the original on 2007-06-18.
   


3. 
   ^ Whitbread BSc (Hons) MSc DipION, Daisy. "What weighs 100g?". Retrieved 28 August 2015.
   


4. 
   ^ Walpole, Sarah Catherine; Prieto-Merino, David; Edwards, Phillip; Cleland, John; Stevens, Gretchen; Roberts, Ian (2012). "The weight of nations: an estimation of adult human biomass". BMC Public Health (12): 439. doi:10.1186/1471-2458-12-439.
   


5. 
   ^ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
   


6. 
   ^ Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant g_c". Industrial & Engineering Chemistry. 61 (4): 53–59. doi:10.1021/ie50712a010.
   

v t e SI units
Base units	ampere candela kelvin kilogram metre mole second
Derived units with special names	becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber
Other accepted units	astronomical unit bar dalton day decibel degree of arc electronvolt hectare hour litre minute minute and second of arc neper tonne atomic units natural units
See also	Conversion of units Metric prefixes 2019 redefinition Systems of measurement
Book Category Portal

v t e Sir Isaac Newton
Publications	Fluxions (1671) De Motu (1684) Principia (1687; writing) Opticks (1704) Queriess (1704) Arithmetica (1707) De Analysi (1711)
Other writings	Quaestiones (1661–65) "standing on the shoulders of giants" (1675) Notes on the Jewish Temple (c. 1680) "General Scholium" (1713; "hypotheses non fingo" ) Ancient Kingdoms Amended (1728) Corruptions of Scripture (1754)
Contributions	Calculus fluxion Impact depth Inertia Newton disc Newton polygon Newton–Okounkov body Newton's reflector Newtonian telescope Newton scale Newton's metal Newton's cradle Spectrum Structural coloration
Newtonianism	Bucket argument Newton's inequalities Newton's law of cooling Newton's law of universal gravitation post-Newtonian expansion parameterized gravitational constant Newton–Cartan theory Schrödinger–Newton equation Newton's laws of motion Kepler's laws Newtonian dynamics Newton's method in optimization Apollonius's problem truncated Newton method Gauss–Newton algorithm Newton's rings Newton's theorem about ovals Newton–Pepys problem Newtonian potential Newtonian fluid Classical mechanics Newtonian fluid Corpuscular theory of light Leibniz–Newton calculus controversy Newton's notation Rotating spheres Newton's cannonball Newton–Cotes formulas Newton's method generalized Gauss–Newton method Newton fractal Newton's identities Newton polynomial Newton's theorem of revolving orbits Newton–Euler equations Newton number kissing number problem Newton's quotient Parallelogram of force Newton–Puiseux theorem Absolute space and time Newtonian series table
Personal life	Woolsthorpe Manor (birthplace) Cranbury Park (home) Early life Later life Religious views Occult studies Scientific revolution Copernican revolution
Relations	Catherine Barton (niece) John Conduitt (nephew-in-law) Isaac Barrow (professor) William Clarke (mentor) Benjamin Pulleyn (tutor) John Keill (disciple) William Stukeley (friend) William Jones (friend) Abraham de Moivre (friend)
Depictions	Newton by Blake (monotype) Newton by Paolozzi (sculpture)
Namesake	Isaac Newton Institute Isaac Newton Medal Isaac Newton Telescope Isaac Newton Group of Telescopes Newton (unit)

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