The pound of force or pound-force (symbol: lbf, sometimes lb
f,
) is a
unit
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in a theatrical presentation
Music
* ''Unit'' (a ...
of
force used in some
systems of measurement
A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement i ...
, including
English Engineering units
Some fields of engineering in the United States use a system of measurement of physical quantities known as the English Engineering Units. Despite its name, the system is based on United States customary units of measure; it is not used in England ...
and the
foot–pound–second system
The foot–pound–second system or FPS system is a system of units built on three fundamental units: the foot for length, the (avoirdupois) pound for either mass or force (see below), and the second for time..
Variants
Collectively, the varian ...
.
Pound-force should not be confused with
pound-mass
The pound or pound-mass is a unit of mass used in British imperial and United States customary systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally define ...
(lb), often simply called ''pound'', which is a unit of
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 eleme ...
, nor should these be confused with
foot-pound
The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a fo ...
(ft⋅lbf), a unit of energy, or
pound-foot
A pound-foot (lbf⋅ft) is a unit of torque representing one pound of force acting at a perpendicular distance of one foot from a pivot point. Conversely one pound-foot is the moment about an axis that applies one pound-force at a radius of one ...
(lbf⋅ft), a unit of torque.
Definitions
The pound-force is equal to the gravitational force exerted on a
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 eleme ...
of one
avoirdupois pound
The pound or pound-mass is a unit of mass used in British imperial and United States customary systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally defin ...
on the surface of
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in
Earth's gravity
The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).
It is a vector quanti ...
(which varies from equator to pole by up to half a percent) can safely be neglected.
The 20th century, however, brought the need for a more precise definition, requiring a standardized value for acceleration due to gravity.
Product of avoirdupois pound and standard gravity
The pound-force is the product of one
avoirdupois pound (
exactly ) and the
standard acceleration due to gravity, .
The standard values of acceleration of the standard gravitational field (''g''
n) and the
international avoirdupois pound (lb) result in a pound-force equal to
.
:
This definition can be rephrased in terms of the
slug. A slug has a mass of 32.174049 lb. A pound-force is the amount of force required to accelerate a slug at a rate of , so:
:
Conversion to other units
Foot–pound–second (FPS) systems of units
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf⋅s
2/ft. In other contexts, the unit "pound" refers to a
unit of mass. The international standard symbol for the pound as a unit of mass is lb.
In the "engineering" systems (middle column), the
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit—the use of
Newton's second law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in moti ...
, , requires another factor,
''gc'', usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s
2).
"Absolute" systems are ''coherent'' systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The
SI is an "absolute" metric system with kilogram and meter as base units.
Pound of thrust
The term pound of thrust is an alternative name for pound-force in specific contexts. It is frequently seen in US sources on jet engines and rocketry, some of which continue to use the FPS notation. For example, the thrust produced by each of the
Space Shuttle
The Space Shuttle is a retired, partially reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. Its official program ...
's two
Solid Rocket Boosters
A solid rocket booster (SRB) is a large solid propellant motor used to provide thrust in spacecraft launches from initial launch through the first ascent. Many launch vehicles, including the Atlas V, SLS and space shuttle, have used SRBs to giv ...
was , together .
See also
*
Foot-pound (energy)
The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a fo ...
*
Ton-force A ton-force is one of various units of force defined as the weight of one ton due to standard gravity.All calculations on this page assume the following definition of standard gravity, ''g''0.
:''g''0 = The precise definition depends on the def ...
*
Kip (unit)
A kip is a US customary unit of force. It equals 1000 pounds-force, and is used primarily by structural engineers to indicate forces where the value represented in pound-force is inefficient. Although uncommon, it is occasionally also considere ...
*
Mass in general relativity
The concept of mass in general relativity (GR) is more subtle to define than the concept of mass in special relativity. In fact, general relativity does not offer a single definition of the term mass, but offers several different definitions th ...
*
Mass in special relativity
The word "mass" has two meanings in special relativity: '' invariant mass'' (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity o ...
*
Mass versus weight
In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Nevertheless, one object will always weigh more than a second object, if the first object has greater mass, and t ...
for the difference between the two physical properties
*
Newton
*
Poundal
The poundal (symbol: pdl) is a unit of force, introduced in 1877, that is part of the Absolute English system of units, which itself is a coherent subsystem of the foot–pound–second system.
:1\,\text = 1\,\text\text/\text^2
The poundal is de ...
*
Pounds per square inch, a unit of
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
Notes and references
General sources
* Obert, Edward F. (1948). ''Thermodynamics''. New York: D. J. Leggett Book Company. Chapter I "Survey of Dimensions and Units", pp. 1-24.
{{United States Customary Units
Customary units of measurement in the United States
Imperial units
Units of force