# 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.

Newton
Visualization of one newton of force
General information
Unit systemSI derived unit
Unit ofForce
SymbolN
Named afterSir Isaac Newton
Conversions
1 N in ...... is equal to ...
SI base units   1 kgms−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]

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 lbf), will safely support a 32,100 kilograms (70,800 lb) load.

Specifications in kilonewtons are common in safety specifications for:

## Conversion factors

Units of force
newton
(SI unit)
dynekilogram-force,
kilopond
pound-forcepoundal
1 N ≡ 1 kgm/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl
1 dyn = 105 N ≡ 1 gcm/s2 ≈ 1.0197 × 106 kp ≈ 2.2481 × 106 lbf ≈ 7.2330 × 105 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 lbft/s2
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 BGGM EEM AECGSMTSSI
Acceleration (a) ft/s2m/s2 ft/s2m/s2 ft/s2Galm/s2m/s2
Mass (m) slughyl pound-masskilogram poundgramtonnekilogram
Force (F),
weight (W)
poundkilopond pound-forcekilopond poundaldynesthènenewton
Pressure (p) pounds per square inchtechnical atmosphere pounds-force per square inchatmosphere poundals per square footbaryepiezepascal
Standard prefixes for the metric units of measure
Multiples Prefix name deca hecto kilo mega giga tera peta exa zetta yotta
Prefix symbol da h k M G T P E Z Y
Factor 100 101 102 103 106 109 1012 1015 1018 1021 1024

Submultiples Prefix name           deci centi milli micro nano pico femto atto zepto yocto
Prefix symbol d c m μ n p f a z y
Factor 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24

## 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 gc". Industrial & Engineering Chemistry. 61 (4): 53–59. doi:10.1021/ie50712a010.
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