Newton (unit)

Unit of force in physics

"Newtons" redirects here. For the snack, see Newtons (cookie).

newton

Visualization of one newton of force

General information
Unit system| SI
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
CGS units|  105 dyn
Imperial units|  0.224809 lbf

The newton (symbol: N) is the unit of force in the International System of Units (SI). Expressed in terms of SI base units, it is 1 kg⋅m/s2, the force that accelerates a mass of one kilogram at one metre per second squared.

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

## Definition

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A newton is defined as 1 kg⋅m/s2 (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 one 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 one kilogram of mass at the rate of one 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 after 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] F = m a , {\displaystyle F=ma,} where  m {\displaystyle m} represents the mass of the object undergoing an acceleration  a {\displaystyle a} . When using the SI unit of mass, the kilogram (kg), and SI units for distance metre (m), and time, second (s) we arrive at the SI definition of the newton: 1 kg⋅m/s2.

## Examples

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At average gravity on Earth (conventionally,  g n {\displaystyle g_{\text{n}}} = 9.80665 m/s2), a kilogram mass exerts a force of about 9.81 N.

* An average-sized apple with mass 200 g exerts about two newtons of force at Earth's surface, which we measure as the apple's weight on Earth.

0.200 kg × 9.80665 m/s 2 = 1.961 N . {\displaystyle 0.200{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=1.961{\text{ N}}.}

* An average adult exerts a force of about 608 N on Earth.

62 kg × 9.80665 m/s 2 = 608 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

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A carabiner used in rock climbing, with a safety rating of 26 kN when loaded along the spine with the gate closed, 8 kN when loaded perpendicular to the spine, and 10 kN when loaded along the spine with the gate open.

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

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Units of force

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| newton | dyne | kilogram-force,
kilopond  | pound-force | poundal

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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 (9.80665 m/s2) 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[8][9]

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Base  | Force  | Weight  | Mass

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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 | standard atmosphere | poundal per square foot | barye | pieze | pascal
Standard prefixes for the metric units of measure (multiples)

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Prefix name  | N/A  | deca | hecto | kilo | mega | giga | tera | peta | exa | zetta | yotta | ronna | quetta

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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)

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Prefix name  | N/A  | deci | centi | milli | micro | nano | pico | femto | atto | zepto | yocto | ronto | quecto

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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

## See also

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* Force gauge
* International System of Units (SI)
* Joule, SI unit of energy, 1 newton exerted over a displacement 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

## References

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1. ^ Bureau International des Poids et Mesures (2019). The International System of Units (SI) (PDF) (9 ed.). Bureau International des Poids et Mesures (BIPM). p. 137\. Archived from the original on 30 September 2021. Retrieved 22 September 2021.
2. ^ a b "Newton | unit of measurement". Encyclopædia Britannica. 17 December 2020. Archived from the original on 27 September 2019. Retrieved 27 September 2019.
3. ^ a b The International System of Units (SI) (1977 ed.). U.S. Department of Commerce, National Bureau of Standards. 1977. p. 17\. ISBN 9282220451. Archived from the original on 11 May 2016. Retrieved 15 November 2015.
4. ^ David B. Newell; Eite Tiesinga, eds. (2019). The International System of Units (SI) (PDF) (NIST Special publication 330, 2019 ed.). Gaithersburg, MD: NIST. Retrieved 30 November 2019.
5. ^ "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 18 June 2007.
6. ^ Walpole, Sarah Catherine; Prieto-Merino, David; et al. (18 June 2012). "The weight of nations: an estimation of adult human biomass". BMC Public Health. 12 (12): 439. doi:10.1186/1471-2458-12-439. PMC 3408371. PMID 22709383.
7. ^ Bright, Casandra Marie. "A History of Rock Climbing Gear Technology and Standards." (2014).
8. ^ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987\. doi:10.1021/ie50367a028.
9. ^ Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant gc". Industrial & Engineering Chemistry. 61 (4): 53–59\. doi:10.1021/ie50712a010.

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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
* dalton
* day
* decibel
* degree of arc
* electronvolt
* hectare
* hour
* litre
* minute
* minute and second of arc
* neper
* tonne

See also|

* Conversion of units
* Metric prefixes
* Historical definitions of the SI base units
* 2019 revision of the SI
* System of units of measurement

* Category

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Sir Isaac Newton

Publications|

* Fluxions (1671)
* De Motu (1684)
* Principia (1687)
* Opticks (1704)
* Queries (1704)
* Arithmetica (1707)
* De Analysi (1711)

Other writings|

* Quaestiones (1661–1665)
* "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
* 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
* 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
* Luminiferous aether
* Newtonian series
* table

Personal life|

* Woolsthorpe Manor (birthplace)
* Cranbury Park (home)
* Early life
* Later life
* Apple tree
* 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)
* Roger Cotes (student)
* William Whiston (student)
* John Keill (disciple)
* William Stukeley (friend)
* William Jones (friend)
* Abraham de Moivre (friend)

Depictions|

* Newton by Blake (monotype)
* Newton by Paolozzi (sculpture)
* Isaac Newton Gargoyle
* Astronomers Monument

Namesake|

* Newton (unit)
* Newton's cradle
* Isaac Newton Institute
* Isaac Newton Medal
* Isaac Newton Telescope
* Isaac Newton Group of Telescopes
* XMM-Newton
* Sir Isaac Newton Sixth Form
* Statal Institute of Higher Education Isaac Newton
* Newton International Fellowship

Categories|

Isaac Newton
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