Kilogram-force

A kilogram-force (kgf or kg_F), or kilopond (kp, from latin pondus meaning weight), is a gravitational metric unit of force. It is equal to the magnitude of the force exerted by one kilogram of mass in a 9.80665 m/s² gravitational field (standard gravity, a conventional value approximating the average magnitude of gravity on Earth).^[1] Therefore one kilogram-force is by definition equal to 9.80665 N.^[2][3] Similarly, a gram-force is 9.80665 mN, and a milligram-force is 9.80665 µN.

History

The gram-force and kilogram-force were never well-defined units until the CGPM adopted a standard acceleration of gravity of 980.665 cm/s² for this purpose in 1901, though they had been used in low-precision measurements of force before that time. The kilogram-force has never been a part of the International System of Units (SI), which was introduced in 1960. The SI unit of force is the newton.

Prior to this, the unit was widely used in much of the world and it is still in use for some purposes. The thrust of a rocket engine, for example, was measured in kilograms-force in 1940s Germany, in the Soviet Union (where it remained the primary unit for thrust in the Russian space program until at least the late 1980s), and it is still used today in China and sometimes by the European Space Agency.

It is also used for tension of bicycle spokes, for torque measured in "meter-kilograms", for informal references to pressure in kilograms per square centimeter (1 kp/cm² = 1 at ≈ 1 bar ≈ 1 atm), for the draw weight of bows in archery, and to define the "metric horsepower" (PS) as 75 metre-kiloponds per second^[2] or the technical atmosphere (at) as 1 kilopond per square centimetre.

Three approaches to mass and force units^[4] v · d · e

Base	force, length, time		weight, length, time		mass, length, time
Designations	gravitational, technical		colloquial, pre-newtonian		absolute, scientific
Type	coherent		incoherent		coherent
Force (F)	$F = m\cdot {a} = w\cdot\tfrac{a}{g}$		$F = m\cdot\tfrac{a}{g_c} = w\cdot\tfrac{a}{g}$		$F = m\cdot {a} = w\cdot\tfrac{a}{g}$
Weight (w)	$w = m\cdot g$		$w = m\cdot\tfrac{g}{g_c} \approx m$		$w = m\cdot g$
System	BG	GM	EE	EM	AE	CGS	MTS	SI
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 (PSI)	at	lbF/in2 (PSI)	atm	pdl/in2	Ba	pz	Pa

Related units

A tonne-force, metric ton-force, megagram-force, or megapond (Mp) are 1000 kilograms-force.

The decanewton or dekanewton (daN) is used in some fields as an approximation to the kilogram-force, being exactly rather than approximately 10 newtons.

Units of force

v · d · e	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.

See also

• Metrology
• Avoirdupois

References

1. ^ The international system of units (SI) – United States Department of Commerce, NIST Special Publication 330, 2008, p. 52
2. ^ ^{a b} NIST Guide for the Use of the International System of Units (SI) Special Publication 811, (1995) page 51
3. ^ BIPM SI brochure, chapter 2.2.2.
4. ^ Lindeburg, Michael, Civil Engineering Reference Manual for the PE Exam