The gravitational metric system (original French term ) is a non-standard system of units, which does not comply with the

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

(SI). It is built on the three base quantities

length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...

and

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

with

base units A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a ''base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in term ...

metre The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...

second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...

and

kilopond The kilogram-force (kgf or kgF), or kilopond (kp, from la, pondus, lit=weight), is a non-standard gravitational metric unit of force. It does not comply with the International System of Units (SI) and is deprecated for most uses. The kilogram-f ...

respectively. Internationally used abbreviations of the system are MKpS, MKfS or MKS (from French or ). However, the abbreviation MKS is also used for the

MKS system of units The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second (MKS) as base units. It forms the base of the International System of Units (SI), though SI has since been redefined by different fundamental co ...

, which, like the SI, uses

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...

as a base unit.

Disadvantages

Nowadays, the mass as a property of an object and its weight, which depends on the gravity of the earth at its position are strictly distinguished. However historically, the kilopond was also called kilogram, and only later the kilogram-mass (today's kilogram) was separated from the kilogram-force (today's kilopond). A kilopond originally referred to the weight of a mass of one kilogram. Since the gravitational acceleration on the surface of the earth can differ, one gets different values for the unit kilopond and its derived units at different locations. To avoid this, the kilopond was first defined at sea level and a

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

of 45 degrees, since 1902 via the

standard gravity The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...

of . Further disadvantages are inconsistencies in the definition of derived units such as

horsepower Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are the ...

(1 PS = 75 kp⋅m/s) and the missing link to electric, magnetic or thermodynamic units. In Germany, the kilopond lost its legal status as a unit of force on 1 January 1978, when for legal purposes the SI unit system was adopted. A kilopond can be converted to the SI unit

newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton ( ...

by multiplication with the standard acceleration ''g''_n: :1 kp = ''g''_n ⋅ 1 kg = =

Units

Force

In English contexts the unit of force is usually formed by simply appending the suffix "force" to the name of the unit of mass, thus ''gram-force'' (gf) or ''

kilogram-force The kilogram-force (kgf or kgF), or kilopond (kp, from la, pondus, lit=weight), is a non-standard gravitational metric unit of force. It does not comply with the International System of Units (SI) and is deprecated for most uses. The kilogram-f ...

'' (kgf), which follows the tradition of

pound-force The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with pound-ma ...

(lbf). In other, international, contexts the special name ''pond'' (p) or ''kilopond'' (kp) respectively is more frequent. ; 1 p = 1 gf := 1 g ⋅ ''g''_n = 9.80665 g⋅m/s² = 980.665 g⋅cm/s² = 980.665 dyn ; 1 kp = 1 kgf := 1 kg ⋅ ''g''_n = 9.80665 kg⋅m/s² = 980665 g⋅cm/s²

Mass

The hyl, metric

slug Slug, or land slug, is a common name for any apparently shell-less terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced shell, or only a smal ...

(mug), or TME (german: technische Masseneinheit, lit=technical mass unit), is the mass that accelerates at 1 m/s² under a force of 1 kgf. The unit, long obsolete, has also been used as the unit of mass in a metre–gram-force–second (mgfs) system.metre–kilogram-force–second systems of units
/ref> ; 1 TME := 1 kp / 1 m/s² = 1 kp⋅s²/m = ; 1 hyl := 1 kp⋅s²/m = ''or'' ; 1 hyl (alternate definition – mgfs) := 1 p⋅s²/m =

Pressure

The gravitational unit of pressure is the

technical atmosphere Technical may refer to: * Technical (vehicle), an improvised fighting vehicle * Technical analysis, a discipline for forecasting the future direction of prices through the study of past market data * Technical drawing, showing how something is co ...

(at). It is the gravitational force of one kilogram, i.e. 1 kgf, exerted on an area of one square centimetre. ; 1 at := 1 kp/cm² = 10 000 × ''g''_n kg/m² = 98 066.5 kg/(m⋅s²) = 98.066 5

kPa KPA may refer to: * Keele Postgraduate Association, Keele University, UK, formerly Keele Research Association (KRA) * Kensington (Olympia) station, London, England, National Rail station code * Kenya Ports Authority * ''Kiln phosphoric acid'', a d ...

Energy

There is no dedicated name for the unit of energy, "metre" is simply appended to "

", but usually the symbol of the kilopond-metre is written without the middle dot. ; 1 kpm := 1 kp⋅m = ''g''_n kg⋅m = 9.806 65 kg⋅m²/s² = 9.806 65 J

Power

In 19th-century France there was as a unit of power, the

poncelet The poncelet (symbol p) is an obsolete unit of power, once used in France and replaced by (ch, metric horsepower). The unit was named after Jean-Victor Poncelet.François Cardarelli, ''Encyclopaedia of Scientific Units, Weights and Measures: The ...

, which was defined as the power required to raise a mass of 1

quintal The quintal or centner is a historical unit of mass in many countries which is usually defined as 100 base units, such as pounds or kilograms. It is a traditional unit of weight in France, Portugal, and Spain and their former colonies. It is com ...

(1 q = 100 kg) at a velocity of 1 m/s. The German or metric

(PS, ''Pferdestärke'') is arbitrarily selected to be three quarters thereof. ; 1 p_q := 1 q_f⋅m/s = 100 kp⋅m/s = 100 × ''g''_n kg⋅m/s = 980.665 kg⋅m²/s³ = 0.980 665 kW ; 1 PS := p_q = 75 kp⋅m/s = 75 × ''g''_n kg⋅m/s = 735.498 75 kg⋅m²/s³ = 0.735 498 75 kW

References

{{systems of measurement Systems of units Gravitational metric system