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The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s−2.[66] The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s−2. A newton is thus equal to 100,000 dyne.
The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of 9.80665 m·s−2.[66] The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force.[66]
An alternative unit of force in a different foot-pound-second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one pound mass at a rate of one foot per second squared.[66] The units of slug and poundal are designed to avoid a constant of proportionality in Newton's second law.
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass.[66] The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass which accelerates at 1 m·s−2 when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated; however it still sees use for some purposes as expressing jet thrust, bicycle spoke tension, torque wrench settings and engine output torque. Other arcane units of force include the sthène which is equivalent to 1000 N and the kip which is equivalent to 1000 lbf.
| 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. | |||||
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