Newton (unit)

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The newton (symbol: N) is the unit of force in the International System of Units (SI). In SI base units, it is defined as ${\displaystyle 1\ {\text{kg}}\cdot {\text{m/s}}^{2}}$, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second squared.

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

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

Definition

A newton is defined as ${\displaystyle \mathrm {1\ kg{\cdot }m/s^{2}} }$ (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 1 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 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.^[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 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.

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] $${\displaystyle F=ma,}$$ where ${\displaystyle m}$ represents the mass of the object undergoing an acceleration ${\displaystyle a}$. When using the SI unit of mass, the kilogram (${\displaystyle {\text{kg}}}$), and SI units for distance metre (${\displaystyle {\text{m}}}$), and time, second (${\displaystyle {\text{s}}}$) we arrive at the SI definition of the newton: ${\displaystyle \mathrm {1\ kg{\cdot }m/s^{2}} .}$

Examples

At average gravity on Earth (conventionally, ${\displaystyle g={9.80665}\ {\text{m/s}}^{2}}$), a kilogram mass exerts a force of about 9.81 newtons.

• 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.

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

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

${\displaystyle 62{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=608{\text{ N}}}$ (where 62 kg is the world average adult mass).^[6]

Kilonewtons

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

Units of force

v t e	newton	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 (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]

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	standard atmosphere	poundal per square foot	barye	pieze	pascal

Standard prefixes for the metric units of measure (multiples)

• v
• t
• e

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

• v
• t
• e

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

• 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

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. "Newton | unit of measurement". Encyclopædia Britannica. 17 December 2020. Archived from the original on 27 September 2019. Retrieved 27 September 2019.
3. 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 g_c". Industrial & Engineering Chemistry. 61 (4): 53–59. doi:10.1021/ie50712a010.