Newton (unit)

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

Newton
Unit system	SI derived unit
Unit of	Force
Symbol	N
Named after	Sir Isaac Newton
In SI base units:	kg ⋅ m ⋅ s^-2

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 and SI unitizing.

Definition

One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in 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 le 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 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. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on The International System of Units, section 5.2.

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	⋅	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:

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

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

=

0.102 kg × 9.80665 m/s² (0.102 kg = 102 g)

The weight of an average adult exerts a force of about 550 - 800 N.

566 N

=

57.7 kg (average adult weight in Asia) × 9.80665 m/s²

791 N

=

80.7 kg (average adult weight in North America) × 9.80665 m/s²

Bench pressing 100 pounds (45 kg) takes a little under 450 N of force.

441 N

=

45 kg × 9.80665 m/s²

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 and the thrust of an F100 fighter jet 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 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 more, 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**
	newton (SI unit)	dyne	kilogram-force, kilopond	pound-force	poundal
1 N	≡ 1 kg⋅m/s²	= 10⁵ dyn	≈ 0.10197 kp	≈ 0.22481 lb_F	≈ 7.2330 pdl
1 dyn	= 10⁻⁵ N	≡ 1 g⋅cm/s²	≈ 1.0197 × 10⁻⁶ kp	≈ 2.2481 × 10⁻⁶ lb_F	≈ 7.2330 × 10⁻⁵ pdl
1 kp	= 9.80665 N	= 980665 dyn	≡ g_n⋅(1 kg)	≈ 2.2046 lb_F	≈ 70.932 pdl
1 lb_F	≈ 4.448222 N	≈ 444822 dyn	≈ 0.45359 kp	≡ g_n⋅(1 lb)	≈ 32.174 pdl
1 pdl	≈ 0.138255 N	≈ 13825 dyn	≈ 0.014098 kp	≈ 0.031081 lb_F	≡ 1 lb⋅ft/s²
The value of g_n as used in the official definition of the kilogram-force is used here for all gravitational units.

Three approaches to mass and force units^[4]^[5]
Base	force, length, time		weight, length, time		mass, length, time
Force (F)	$F = m \cdot a = w \cdot a / g$		$F = m \cdot a / g c = w \cdot a / g$		$F = m \cdot a = w \cdot a / g$
Weight (w)	$w = m \cdot g$		$w = m \cdot g / g c ≙ m$		$w = m \cdot g$
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	lb_m	kg	lb	g	t	kg
Force (F)	lb	kp	lb_F	kp	pdl	dyn	sn	N
Pressure (p)	lb/in²	at	PSI	atm	pdl/ft²	Ba	pz	Pa

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

Fractions	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

Notes and references

↑ 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.
↑ "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.
↑ Whitbread BSc (Hons) MSc DipION, Daisy. "What weighs 100g?". Retrieved 28 August 2015.
↑ Michael R. Lindeburg (2011). Civil Engineering Reference Manual for the Pe Exam. Professional Publications. ISBN 1591263417.
↑ Wurbs, Ralph A, Fort Hood Review Sessions for Professional Engineering Exam (PDF), retrieved October 26, 2011

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 of arc neper second of arc tonne atomic units natural units

See also	Conversion of units History of the metric system Metric prefixes Proposed redefinitions Systems of measurement

Book Category Outline

Isaac Newton

Publications	De analysi per aequationes numero terminorum infinitas (1669, published 1711) Method of Fluxions (1671) De motu corporum in gyrum (1684) Philosophiæ Naturalis Principia Mathematica (1687) General Scholium (1713) Opticks (1704) The Queries (1704) Arithmetica Universalis (1707)

Other writings	Notes on the Jewish Temple Quaestiones quaedam philosophicae The Chronology of Ancient Kingdoms Amended (1728) An Historical Account of Two Notable Corruptions of Scripture (1754)

Newtonianism	Bucket argument Newton's inequalities Newton's law of cooling Newton's law of universal gravitation Post-Newtonian expansion Parameterized post-Newtonian formalism Newton–Cartan theory Schrödinger–Newton equation Gravitational constant Newton's laws of motion Newtonian dynamics Newton's method in optimization Gauss–Newton algorithm Truncated Newton method 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 Rotating spheres Newton's cannonball Newton–Cotes formulas Newton's method Newton fractal Generalized Gauss–Newton method Newton's identities Newton polynomial Newton's theorem of revolving orbits Newton–Euler equations Newton number Kissing number problem Power number Solar mass Dynamics Absolute time and space Finite difference Table of Newtonian series Impact depth Structural coloration Inertia

Life	Cranbury Park Woolsthorpe Manor Early life of Isaac Newton Later life of Isaac Newton Religious views of Isaac Newton Isaac Newton's occult studies The Mysteryes of Nature and Art Scientific revolution Copernican Revolution

Friends and family	Catherine Barton John Conduitt William Clarke Benjamin Pulleyn William Stukeley William Jones Isaac Barrow Abraham de Moivre John Keill

Discoveries and inventions	Calculus Newton disc Newton polygon Newton–Okounkov body Newton's reflector Newtonian telescope Newton scale Newton's metal Newton's cradle Sextant

Phrases	"Hypotheses non fingo" "Standing on the shoulders of giants"

Theory expansions	Kepler's laws of planetary motion Problem of Apollonius

Related	Writing of Principia Mathematica Newton (Blake) List of things named after Isaac Newton Newton (unit) Isaac Newton in popular culture Elements of the Philosophy of Newton Isaac Newton S/O Philipose

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