# 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.^{[1]} 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.

This SI unit is named after Isaac Newton. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (N). However, when an SI unit is spelled out in English, it should always begin with a lower case letter (*newton*)—except in a situation where *any* word in that position would be capitalized, such as at the beginning of a sentence or in material using title case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on *The International System of Units*, section 5.2.

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:^{[2]}

F |
= | m |
⋅ | a |

1 N | = | 1 kg | ⋅ | m/s^{2} |

where the following symbols are used for the units: N for newton, kg for kilogram, m for metre, and s for second.

where is force, is mass, is length and is time.

## Examples

At average gravity on earth, (conventionally *g* = 9.80665 m/s^{2}), 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.^{[3]}

- 1 N = 0.102 kg × 9.80665 m/s
^{2}( kg = 102 g) 0.102

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/s
^{2} - 791 N = 80.7 kg (average adult weight in North America) × 9.80665 m/s
^{2}

Bench pressing 100 pounds (45 kg) takes a little under 450 N of force.

- 441 N = 45 kg × 9.80665 m/s
^{2}

## 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/s
^{2}

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

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 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} as used in the official definition of the kilogram-force is used here for all gravitational units. |

Base | force, length, time | weight, length, time | mass, length, time | |||||
---|---|---|---|---|---|---|---|---|

Force (F) |
F = m⋅a = w⋅a/g |
F = m⋅a/g_{c} = w⋅a/g |
F = m⋅a = w⋅a/g | |||||

Weight (w) |
w = m⋅g |
w = m⋅g/g_{c} ≙ m |
w = m⋅g | |||||

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 | lb_{m} | kg | lb | g | t | kg |

Force (F) |
lb | kp | lb_{F} | kp | pdl | dyn | sn | N |

Pressure (p) |
lb/in^{2} | at | PSI | atm | pdl/ft^{2} | Ba | pz | Pa |

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 | 10^{0} |
10^{1} |
10^{2} |
10^{3} |
10^{6} |
10^{9} |
10^{12} |
10^{15} |
10^{18} |
10^{21} |
10^{24} | |

Fractions | 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 | 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

## Notes and references

- ↑ International Bureau of Weights and Measures (1977),
*The international system of units*(330–331) (3rd ed.), U.S. Dept. of Commerce, National Bureau of Standards, p. 17, ISBN 0745649742. - ↑ "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. - ↑ Whitbread BSc (Hons) MSc DipION, Daisy. "What weighs 100g?". Retrieved 28 August 2015.
- ↑ Michael R. Lindeburg (2011).
*Civil Engineering Reference Manual for the Pe Exam*. Professional Publications. ISBN 1591263417. - ↑ Wurbs, Ralph A,
*Fort Hood Review Sessions for Professional Engineering Exam*(PDF), retrieved October 26, 2011