Newton (unit)

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. 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.

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.

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:

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 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.

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	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

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)

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)

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 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