Newton (unit)

The newton, symbol N, is the coherent derived unit of force in the International System of Units (SI). One newton is the force that gives a body with a mass of one kilogram an acceleration of one metre per second squared. Its expression in SI base units is therefore 1 N = 1 kg·m·s⁻². The unit is named after Isaac Newton, whose laws of motion established a central framework for classical mechanics. (nist.gov)

Definition and physical meaning

The definition corresponds to the second of Newton’s laws of motion. For a body of constant mass, observed in an inertial reference frame, the relationship is

where $\mathbf{F}_{\mathrm{net}}$ is the resultant external force and $\mathbf{a}$ is acceleration. Expressing mass in kilograms and acceleration in metres per second squared gives force in newtons. The newton’s dimensions are $MLT^{-2}$, where $M$, $L$, and $T$ represent mass, length, and time. Its coherence means that no additional numerical conversion factor is needed in this equation when coherent SI units are used. (nist.gov)

For example, a net force of 6 N acting on a 2 kg body produces an acceleration of 3 m/s². “Net” is essential: several forces may act simultaneously, and it is their vector sum—not necessarily any individual force—that determines the acceleration. A force expressed in newtons need not cause motion; an opposing force can balance it. These are consequences of the mechanical relationship underlying the unit, rather than additional parts of its definition. (nist.gov)

Historical adoption and SI foundations

In 1948, the ninth General Conference on Weights and Measures (CGPM) adopted the name newton for the unit of force in the metre–kilogram–second system. When the SI was established in 1960, the newton became one of its named derived units. Its name supplies a convenient designation for a combination of base units, rather than introducing a separate base quantity. (bipm.org)

The revised SI, effective from May 20, 2019, retained the relationship $\mathrm{N}=\mathrm{kg\,m\,s^{-2}}$. However, the kilogram ceased to be defined by an international material prototype and became defined through a fixed numerical value of the Planck constant. Together with the definitions of the metre through the speed of light and the second through a caesium atomic transition, this anchors the newton in the SI’s defining constants. It did not change the unit’s intended magnitude. (nist.gov)

Force, mass, and weight

The newton measures force, not mass. In scientific usage, weight is a force associated with gravity, commonly calculated near a planetary surface as $W=mg$. Mass is expressed in kilograms; weight is expressed in newtons. Consequently, the same mass can have different weights in different gravitational fields. Everyday references to “weight in kilograms” usually describe mass rather than force. (nvlpubs.nist.gov)

The conventional standard acceleration of gravity is exactly $g_{\mathrm n}=9.80665\ \mathrm{m/s^2}$. Under that acceleration, a 1 kg mass has a weight of 9.80665 N; a 100 g mass has a weight of 0.980665 N, approximately one newton. Standard gravity is a reference value, not the actual acceleration at every location. Local gravitational acceleration must be distinguished from it in precise force measurements. (nvlpubs.nist.gov)

Common exact conversions include:

The kilogram-force and pound-force use standard gravity in their definitions; neither should be confused with a unit of mass. (nvlpubs.nist.gov)

Notation and related units

In running English text, the unit name is lowercase: newton, with plural newtons. Its symbol is an upright capital N, remains unchanged in the plural, and is separated from the numerical value by a space: 25 N, not “25 Ns.” SI prefixes attach directly to the symbol, as in mN for millinewton ($10^{-3}$ N), kN for kilonewton ($10^3$ N), and MN for meganewton ($10^6$ N). Capitalization matters: mN and MN differ by a factor of one billion. (bipm.org)

The newton also appears in units for related physical quantities:

• Pressure and mechanical stress: one pascal is one newton per square metre, $1\ \mathrm{Pa}=1\ \mathrm{N/m^2}$.
• Work and energy: one joule equals one newton metre, $1\ \mathrm{J}=1\ \mathrm{N\,m}$.
• Torque: its coherent SI unit is the newton metre, N·m. Although dimensionally identical to the joule, it is normally written N·m to distinguish torque from energy.
• Momentum and impulse: the newton second, N·s, is equivalent to kg·m/s. (nist.gov)

Realization and measurement

In metrology, a definition must be translated into experimentally realizable forces. Deadweight machines generate reference forces using calibrated masses and measured local gravitational acceleration. Precision work also accounts for air buoyancy. These reference forces provide calibration for instruments such as load cells and proving rings, connecting their readings to SI standards through metrological traceability. (nist.gov)

Other realization methods are useful at very small force scales. NIST’s small-force research uses electrostatic force balances and forces arising from photon momentum. Such methods support calibration of sensitive force sensors, including those used in atomic force microscopy. The definition of the newton is exact, but any practical force realization or measurement has a finite measurement uncertainty. (nist.gov)