Newton (unit)

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 1kg⋅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

A newton is defined as 1kg⋅m/s2 (it is a named derived unit defined in terms of the SI base units). 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.

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.

In 1946, the General Conference on Weights and Measures (CGPM) Resolution2 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 Resolution7 adopted the name newton for this force. 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.

The newton is named afterIsaac Newton. As with everySIunit named after a person, its symbol starts with anupper caseletter (N), but when written in full, it follows the rules for capitalisation of acommon noun; i.e.,newtonbecomes 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: 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: 1kg⋅m/s2.

Examples

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

An average-sized apple with mass 200g 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 608N 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 62kg is the world average adult mass).

Kilonewtons

Large forces may be expressed in kilonewtons (kN), where 1kN = 1000N. For example, the tractive effort of a Class Y steam train locomotive and the thrust of an F100 jet engine are both around 130kN.[citation needed]

Climbing ropes are tested by assuming a human can withstand a fall that creates 12kN of force. The ropes must not break when tested against 5 such falls.

Conversion factors

Force units
vte	Newtons	Dynes	Kilograms-force kiloponds	Pounds	Poundals
1N	≡1kg⋅m⁄s2	=100000dyn	≈0.10197kgf	≈0.22481lb	≈7.23301pdl
1dyn	=1×10−5N	≡1g⋅cm⁄s2	≈1.01972×10−6kgf	≈2.24809×10−6lb	≈7.23301×10−5pdl
1kgf	=9.80665N	=980665dyn	≡gn×1kg	≈2.20462lb	≈70.9316pdl
1lb	≈4.44822N	≈444822dyn	≈0.45359kgf	≡gn×1lbm/.3048m⁄ft	≈32.1740pdl
1pdl	≈0.13825N	≈13825.5dyn	≈0.01410kgf	≈0.03108lbf	≡1lbm⋅ft⁄s2

Three approaches to units of mass and force or weight
vte 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

SI multiples of newton (N)
Submultiples	Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10−1N	dN	decinewton	101N	daN	decanewton
10−2N	cN	centinewton	102N	hN	hectonewton
10−3N	mN	millinewton	103N	kN	kilonewton
10−6N	μN	micronewton	106N	MN	meganewton
10−9N	nN	nanonewton	109N	GN	giganewton
10−12N	pN	piconewton	1012N	TN	teranewton
10−15N	fN	femtonewton	1015N	PN	petanewton
10−18N	aN	attonewton	1018N	EN	exanewton
10−21N	zN	zeptonewton	1021N	ZN	zettanewton
10−24N	yN	yoctonewton	1024N	YN	yottanewton
10−27N	rN	rontonewton	1027N	RN	ronnanewton
10−30N	qN	quectonewton	1030N	QN	quettanewton

Newton (unit)

Definition

Examples

Kilonewtons

Conversion factors

See also