# 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 1 kg⋅m/s$^2$, 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 1 kg⋅m/s$^2$ (it is a named derived unit defined in terms of the SI base units).$^{:137}$ 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.
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) Resolution 2 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 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 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.
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: $F=ma,$ where $m$ represents the mass of the object undergoing an acceleration $a$. 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: 1 kg⋅m/s$^2$.

## Examples

At average gravity on Earth (conventionally, $g_{\text{n}}$ = 9.80665 m/s$^2$), a kilogram mass exerts a force of about 9.81 N.
* 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.
    $0.200{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=1.961{\text{ N}}.$
* An average adult exerts a force of about 608 N on Earth.
    $62{\text{ kg}}\times 9.80665{\text{ m/s}}^{2}=608{\text{ N}}$ (where 62 kg is the world average adult mass).

## Kilonewtons

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.
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.$^{:11}$

## Conversion factors

Units of force :
| vte | newton | dyne | kilogram-force, kilopond | pound-force | poundal |
| 1 N | ≡ 1 kg⋅m/s$^2$ | = 10$^5$ dyn | ≈ 0.10197 kp | ≈ 0.22481 lb$_F$ | ≈ 7.2330 pdl |
| 1 dyn | = 10$^{−5}$ N | ≡ 1 g⋅cm/s$^2$ | ≈ 1.0197×10$^{−6}$ kp | ≈ 2.2481×10$^{−6}$ lb$_F$ | ≈ 7.2330×10$^{−5}$ pdl |
| 1 kp | = 9.80665 N | = 980665 dyn | ≡ g$_n$ × 1 kg | ≈ 2.2046 lb$_F$ | ≈ 70.932 pdl |
| 1 lb$_F$ | ≈ 4.448222 N | ≈ 444822 dyn | ≈ 0.45359 kp | ≡ g$_n$ × 1 lb | ≈ 32.174 pdl |
| 1 pdl | ≈ 0.138255 N | ≈ 13825 dyn | ≈ 0.014098 kp | ≈ 0.031081 lb$_F$ | ≡ 1 lb⋅ft/s$^2$ |
| The value of g$_n$ (9.80665 m/s$^2$) 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 :
| vte Base | Force | Force | Weight | Weight | Mass | Mass | Mass | Mass |
| 2nd law of motion | m = ⁠F/a⁠ | m = ⁠F/a⁠ | F = ⁠W ⋅ a/g⁠ | F = ⁠W ⋅ a/g⁠ | F = m ⋅ a | F = m ⋅ a | F = m ⋅ a | 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) | 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) vte :
| 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 | 10$^0$ | 10$^1$ | 10$^2$ | 10$^3$ | 10$^6$ | 10$^9$ | 10$^{12}$ | 10$^{15}$ | 10$^{18}$ | 10$^{21}$ | 10$^{24}$ | 10$^{27}$ | 10$^{30}$ |
Standard prefixes for the metric units of measure (submultiples) vte :
| 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 | 10$^0$ | 10$^{−1}$ | 10$^{−2}$ | 10$^{−3}$ | 10$^{−6}$ | 10$^{−9}$ | 10$^{−12}$ | 10$^{−15}$ | 10$^{−18}$ | 10$^{−21}$ | 10$^{−24}$ | 10$^{−27}$ | 10$^{−30}$ |