Newton (unit)

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Not to be confused with Newton scale, a rarely used non-SI temperature scale.
Unit system SI derived unit
Unit of Force
Symbol N 
Named after Sir Isaac Newton
In SI base units: 1 N = 1 kgm/s2

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.


One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared.

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/s2

where the following symbols are used for the units:

N: newton
kg: kilogram
m: metre
s: second.

In dimensional analysis:

{\mathsf F} = \frac{\mathsf {ML}} {{\mathsf T}^2}


F: force
M: mass
L: length
T: time.


The gravity of Earth would impart a downward acceleration, g = 9.8 m/s2, to objects on its surface, were those objects not held in place by an upward force, measurable in newtons, felt as the weight of an object. It will be shown in the following examples, where the acceleration is due to gravity, g ≅ 10 m/s2,

1 kg × g = 9.8 N ≅ 10N

that the following approximate force-relations hold:

  • 1 kg is about 10 N of force
  • 1/10 of a kg is about 1 N
  • 100 kg is about a kN

One newton is about 100 grams (3.5 oz) of mass, or about half a medium-sized apple.[3]

1 N = 0.102 kg × 9.81 m/s2    (0.102 kg ≅ 100 g)

The average adult will feel 664 N of force, his own weight, pushing up on his feet.

664 N = 67.7 kilograms (149 lb) × 9.8 m/s2

1 kilogram (2.2 lb) is about ten newtons of force, because 98.1 ≅ 100.

1 N = 1 kg × g
1 daN = 1 kg × 10 g = 98.1 m/s2
The SI abbreviation daN stands for ten newtons, or a decanewton. The 1 kilogram-force (9.8 N; 2.2 lbf) in this example is a good enough approximation that "a daN per kilogram" is a rule of thumb with only about a 2% over-estimate.

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

441 N = 45 kg × 9.81 m/s2

In another example, we start with the fact that the calculation of an amount of work done is the force applied times the distance moved. So we can have 1 N⋅m of work. Now the Work-Energy Theorem states that the work done on a body is equal to the change in energy of the body, measured in joules, and we say 1 N⋅m = 1 J.

Bench pressing 100 pounds (45 kg) upward 26 inches (66 cm) imparts about 450 N × 23 m = 333 joules (110 kcal).

Commonly seen as kilonewtons[edit]

A newton is not much force, so it is common to see forces expressed in kilonewtons, or kN, where 1 kN = 1000 N. For example, the tractive effort of a Class Y steam train and the thrust of a an F100 fighter jet are both around 130 kN.

Where units are commonly in kilonewtons, a common rule of thumb is to multiply the kilonewton value by a factor of 100 to get the kilograms. One kilonewton, 1 kN, is 102.0 kgf, or about 100 kg of load.

1 kN = 102 kg × 9.81 m/s2    (102 kg ≅ 100 kg)

So for example, a platform 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[edit]

Units of force
(SI unit)
dyne kilogram-force,
pound-force poundal
1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbF ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g⋅cm/s2 ≈ 1.0197 × 10−6 kp ≈ 2.2481 × 10−6 lbF ≈ 7.2330 × 10−5 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 lb⋅ft/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 mass and force units[4][5]
Base force, length, time weight, length, time mass, length, time
Force (F) F = ma = wa/g F = ma/gc = wa/g F = ma = wa/g
Weight (w) w = mg w = mg/gcm w = mg
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 Gal m/s2 m/s2
Mass (m) slug hyl lbm kg lb g t kg
Force (F) lb kp lbF kp pdl dyn sn N
Pressure (p) lb/in2 at PSI atm pdl/ft2 Ba pz Pa
Standard prefixes for the SI 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
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 100 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24

See also[edit]

Notes and references[edit]

  1. ^ 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. 
  2. ^ "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. 
  3. ^ Whitbread BSc (Hons) MSc DipION, Daisy. "What weighs 100g?". Retrieved 28 August 2015. 
  4. ^ Michael R. Lindeburg (2011). Civil Engineering Reference Manual for the Pe Exam. Professional Publications. ISBN 1591263417. 
  5. ^ Wurbs, Ralph A, Fort Hood Review Sessions for Professional Engineering Exam (PDF), retrieved October 26, 2011