Newton

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The newton (symbol: N) is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics.

## Definition

The newton is the unit of force derived in the SI system; it is equal to the amount of force required to accelerate a mass of one kilogram at a rate of one metre per second per second. Algebraically:

${\rm 1~N = 1~\frac{kg\cdot m}{s^2}}.$

## Examples

• 1 N is the force of Earth's gravity on an object with a mass of about 102 g (9.8 kg) (such as a small apple).
• On Earth's surface, a mass of 1 kg exerts a force of approximately 9.80665 N [down] (or 1 kgf). The approximation of 1 kg corresponding to 10 N is sometimes used as a rule of thumb in everyday life and in engineering.
• The force of Earth's gravity on a human being with a mass of 70 kg is approximately 687 N.
• The dot product of force and distance is mechanical work. Thus, in SI units, a force of 1 N exerted over a distance of 1 m is 1 N·m of work. The Work-Energy Theorem states that the work done on a body is equal to the change in energy of the body. 1 N·m = 1 J (joule), the SI unit of energy.
• It is common to see forces expressed in kilonewtons or kN, where 1 kN = 1 000 N.

## Common use of kilonewtons in construction

Kilonewtons are often used for stating safety holding values of fasteners, anchors and more in the building industry. They are also often used in the specifications for rock climbing equipment. The safe working loads in both tension and shear measurements can be stated in kN (kilonewtons).

1 kN equals 101.97162 kilograms of load, but multiplying the kN value by 100 is a good rule of thumb.

Units of force
newton
(SI unit)
dyne kilogram-force,
kilopond
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
System Gravitational Engineering Absolute
Force (F) F = m·a F = m·a/gc = w·a/g F = m·a
Weight (w) w = m·g w = m·g/gc ≈ m w = m·g
Units English Metric English Metric English Metric
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 m/s2
Mass (m) slug hyl pound-mass kilogram pound kilogram
Force (F) pound kilopond pound-force kilopond poundal newton

Published - July 2009