Newton (unit)

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. One newton is 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.

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

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

newton
Visualization of one newton of force
General information
Unit system	SI derived unit
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
British Gravitational System	0.2248089 lbf

See below for the conversion factors.

Definition

One newton is 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.[1] The units "metre per second squared" can be understood as change in velocity per time, i.e. an increase of velocity by 1 metre per second every second.

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.[2] 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 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.

In more formal terms, Newton's second law of motion states that the force exerted by an object is directly proportional to the acceleration of that object, namely:[3]

${\displaystyle F=ma}$

where the proportionality constant, ${\displaystyle m}$, represents the mass of the object undergoing an acceleration, ${\displaystyle a}$. As a result, the newton may be defined in terms of kilograms (${\displaystyle {\text{kg}}}$), metres (${\displaystyle {\text{m}}}$), and seconds (${\displaystyle {\text{s}}}$) by

${\displaystyle 1\ {\text{N}}=1{\frac {{\text{kg}}\cdot {\text{m}}}{{\text{s}}^{2}}}}$.

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.[4]

1 N = 0.10197 kg × 9.80665 m/s²    (0.10197 kg = 101.97 g)

The weight of an average adult exerts a force of about 608 N.

608 N = 62 kg × 9.80665 m/s² (where 62 kg is the world average adult mass)[5]

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 locomotive and the thrust of an F100 jet engine are both around 130 kN.

One kilonewton, 1 kN, is equivalent to 102.0 kgf, or about 100 kg of load under Earth gravity.

1 kN = 102 kg × 9.81 m/s²   

So for example, a platform that shows it is 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 other items used 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.

Units of force

	newton (SI unit)	dyne	kilogram-force, kilopond	pound-force	poundal
1 N	≡ ​^1 kg⋅m⁄s^2	= 10^5 dyn	≈ 0.10197 kp	≈ 0.22481 lbf	≈ 7.2330 pdl
1 dyn	= 10^–5 N	≡ ​^1 g⋅cm⁄s^2	≈ 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⁄s^2
The value of gn 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[6][7]

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/s^2	m/s^2	ft/s^2	m/s^2	ft/s^2	Gal	m/s^2	m/s^2
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)	pounds per square inch	technical atmosphere	pounds-force per square inch	atmosphere	poundals 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
Prefix symbol		da	h	k	M	G	T	P	E	Z	Y
Factor	10^0	10^1	10^2	10^3	10^6	10^9	10^12	10^15	10^18	10^21	10^24

Standard prefixes for the metric units of measure (submultiples)

Prefix name	N/A	deci	centi	milli	micro	nano	pico	femto	atto	zepto	yocto
Prefix symbol		d	c	m	μ	n	p	f	a	z	y
Factor	10^0	10^–1	10^–2	10^–3	10^–6	10^–9	10^–12	10^–15	10^–18	10^–21	10^–24

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

References

1. "Newton | unit of measurement". Encyclopedia Britannica. Retrieved 2019-09-27.
2. International Bureau of Weights and Measures (1977), The International System of Units (3rd ed.), U.S. Dept. of Commerce, National Bureau of Standards, p. 17, ISBN 0745649742.
3. "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 2007-06-18.
4. Whitbread BSc (Hons) MSc DipION, Daisy. "What weighs 100g?". Retrieved 28 August 2015.
5. Walpole, Sarah Catherine; Prieto-Merino, David; Edwards, Phillip; Cleland, John; Stevens, Gretchen; Roberts, Ian (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.
6. Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
7. 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.