Newton (unit)

A newton is defined as 1 kg⋅m/s² (it is a named derived unit defined in terms of the SI base units).^[1] 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.^[2]

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.^[2]

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.^[3] The MKS system then became the blueprint for today's SI system of units.^[4] The newton thus became the standard unit of force in the Système international d'unités (SI), or International System of Units.^[3]

The newton is named after Isaac Newton. As with every SI unit named after 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:^[5] where represents the mass of the object undergoing an acceleration . 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/s².

At average gravity on Earth (conventionally, = 9.806 m/s²), a kilogram mass exerts a force of about 9.81 N.

• A 40lb stone lifted at 1.5 m/s² will exert a force of 180N.^[6]
• The Sun exerts N on the Earth, and vice versa.^[7]
• A small apple with mass 100 g exerts about one newton of force at Earth's surface, which we measure as the apple's weight on Earth.^[8]

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.^{[citation needed]}

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.^[9]

• Force gauge – Instrument for measuring force
• International System of Units – Modern form of the metric system
• joule – SI unit of energy
• kilogram-force – Weight on earth of a one-kilogram mass
• kip (unit) – US customary unit of force
• newton-metre – SI unit of torque
• Orders of magnitude (force) – Comparison of a wide range of physical forces
• Pascal (unit) – SI derived unit of pressure
• pound (force) – Unit of force
• sthène – Obsolete unit of force; same as 1 kilonewton

1. ^ Bureau International des Poids et Mesures (2019). The International System of Units (SI) (PDF) (9 ed.). Bureau International des Poids et Mesures (BIPM). p. 137. Archived from the original on 30 September 2021. Retrieved 22 September 2021.
2. ^ a b "Newton | unit of measurement". Encyclopædia Britannica. 17 December 2020. Archived from the original on 27 September 2019. Retrieved 27 September 2019.
3. ^ a b The International System of Units (SI) (1977 ed.). U.S. Department of Commerce, National Bureau of Standards. 1977. p. 17. ISBN 9282220451. Archived from the original on 11 May 2016. Retrieved 15 November 2015.
4. ^ David B. Newell; Eite Tiesinga, eds. (2019). The International System of Units (SI) (PDF) (NIST Special publication 330, 2019 ed.). Gaithersburg, MD: NIST. Retrieved 30 November 2019.
5. ^ "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 18 June 2007.
6. ^ Moebs, William; Ling, Samuel J.; Sanny, Jeff (19 September 2016). "5.4 Mass and Weight - University Physics Volume 1 | OpenStax". openstax.org. OpenStax. Retrieved 13 October 2026.
7. ^ Mahajan, Sanjoy (2020). A student's guide to Newton's laws of motion. New York: Cambridge University Press. ISBN 978-1-108-47114-5.
8. ^ "Things That Weigh a Newton - The Physics Factbook". hypertextbook.com. Retrieved 13 October 2026.
9. ^ Bright, Casandra Marie. "A History of Rock Climbing Gear Technology and Standards." (2014).
10. ^ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
11. ^ 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.