# Newton

The newton (symbol: N) is the SI derived unit of force, named after Sir 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 give a mass of one kilogram an acceleration of one meter per second squared . Algebraically:

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

## Examples

• 1 N is the force of earth's gravity on an object with a mass of about 102 g (​19.8 kg) (such as a small apple).
• On Earth's surface, a mass of 1 kg exerts a force of approximately 9.81 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 decanewton (daN) = 10 N is increasingly used when specifying load bearing capacity of items such as ropes and anti-vibration mounts, being approximately equivalent to the more familiar non-SI unit of force, the kgf.
• The force of Earth's gravity on a human being with a mass of 70 kg is approximately 687 N.
• The scalar product of force and distance is energy. Thus, in SI units, a force of 1 N exerted over a distance of 1 m is 1 N·m = 1 joule, the SI unit of energy.
• Because a newton is a small force, it is common to see forces expressed in kilonewtons or kN, where 1 kN = 1 000 N.
• A metric tonne (1 000 kg) exerts a force of 9.8 kN (or 1 000 kgf) under standard gravity conditions on Earth.

## Notes

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.

## References

• Halliday, Resnick and Walker Fundamentals of Physics, John Wiley & Sons ISBN 0471470619