Pounds-force facts for kids

Kids Encyclopedia Facts

"lbf" redirects here. For the airport in North Platte, Nebraska, assigned the IATA code LBF, see North Platte Regional Airport.

For the unit of mass, see Pound (mass). For the basis weight of paper, see Paper density. For the monetary unit, see Pound (currency).

Quick facts for kids Pound-force
Unit system	English Engineering units, British Gravitational System
Symbol	lbf
Conversions
1 lbf in ...	... is equal to ...

SI units	4.448222 N
CGS units	444,822.2 dyn
Absolute English System	32.17405 pdl

The pound-force (symbol: lbf) is a unit used to measure force. Force is a push or a pull that can make an object move, stop, or change direction. The pound-force is part of some older measurement systems, like the English Engineering units.

It's important not to confuse pound-force with other similar terms:

Pound-mass (lb) is a unit of mass, which measures how much "stuff" is in an object.
Foot-pound (ft⋅lbf) is a unit of energy, which is the ability to do work.
Pound-foot (lbf⋅ft) is a unit of torque, which is a twisting force.

What is Pound-Force?
- How is Pound-Force Calculated?
Pound-Force in Different Systems
Pound of Thrust
See also
Definitions
- Product of avoirdupois pound and standard gravity
Conversion to other units
Foot–pound–second (FPS) systems of units
Pound of thrust
See also

What is Pound-Force?

The pound-force (lbf) is defined based on gravity. Imagine you have an object that weighs one pound (specifically, an avoirdupois pound). The pound-force is the amount of gravitational pull that the Earth has on that one-pound object.

For a long time, people used this unit for measurements where small changes in Earth's gravity didn't matter much. Earth's gravity actually changes slightly depending on where you are, like at the equator versus the poles.

However, as science and engineering became more precise in the 20th century, a more exact definition was needed. This led to using a standard value for how fast objects fall due to gravity.

How is Pound-Force Calculated?

The pound-force is calculated by multiplying one avoirdupois pound (which is exactly 0.45359237 kilograms) by the standard acceleration due to gravity. This standard acceleration is about 9.80665 meters per second squared (or about 32.174049 feet per second squared).

So, 1 pound-force is equal to:

1 pound (mass) × 9.80665 meters/second²
This works out to be exactly 4.4482216152605 Newtons. The Newton is the standard unit of force in the SI system.

Another way to think about it involves a unit of mass called the slug. A slug is a much larger unit of mass, equal to about 32.174049 pounds. One pound-force is the amount of force needed to make a slug accelerate at a rate of 1 foot per second squared.

Pound-Force in Different Systems

In some measurement systems, like the "engineering" systems, the weight of one pound-mass on Earth is roughly equal to one pound-force. This can be handy because it means a one-pound object exerts about one pound of force due to gravity.

However, in these systems, you need an extra factor (called g_c) when using Newton's second law (Force = mass × acceleration). This is because the force unit isn't simply the mass unit times the acceleration unit.

"Absolute" systems, like the SI system (which uses kilograms and meters), are simpler. They don't need this extra factor because their units are designed to work together directly with Newton's laws.

Pound of Thrust

The term pound of thrust is another name for pound-force, often used when talking about jet engines and rockets. You might see this term in older US documents about space travel or aircraft. For example, the powerful engines of the Space Shuttle's Solid Rocket Boosters produced millions of pounds of thrust!

Definitions

The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (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 0.45359237 kg) and the standard acceleration due to gravity, 9.80665 m/s² (32.174049 ft/s²).

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 4.4482216152605 N.

\begin{align} 1\,\text{lbf} &= 1\,\text{lb} \times g_\text{n} \\ &= 1\,\text{lb} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2} / 0.3048\,\tfrac{\text{m}}{\text{ft}}\\ &\approx 1\,\text{lb} \times 32.174049\,\mathrm{\tfrac{ft}{s^2}}\\ &\approx 32.174049\,\mathrm{\tfrac{ft {\cdot} lb}{s^2}} \\ 1\,\text{lbf} &= 1\,\text{lb} \times 0.45359237\,\tfrac{\text{kg}}{\text{lb}} \times g_\text{n} \\ &= 0.45359237\,\text{kg} \times 9.80665\,\tfrac{\text{m}}{\text{s}^2}\\ &= 4.4482216152605\,\text{N} \end{align}

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 1 ft/s², so:

\begin{align} 1\,\text{lbf} &= 1\,\text{slug} \times 1\,\tfrac{\text{ft}}{\text{s}^2} \\ &= 1\,\tfrac{\text{slug} \cdot \text{ft}}{\text{s}^2} \end{align}

Conversion to other units

Units of force
	newton	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	≡ g_n × 1 kg	≈ 2.2046 lbf	≈ 70.932 pdl
1 lbf	≈ 4.448222 N	≈ 444822 dyn	≈ 0.45359 kp	≡ g_n × 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 g_n as used in the official definition of the kilogram-force (9.80665 m/s²) is used here for all gravitational 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⋅s²/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.

Three approaches to units of mass and force or weight
Base	Force		Weight		Mass
2nd law of motion	$m = F / a$		$F = W \cdot a / g$		$F = m \cdot a$
System	BG	GM	EE	M	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	pound-mass	kilogram	pound	gram	tonne	kilogram
Force (F), weight (W)	pound	kilopond	pound-force	kilopond	poundal	dyne	sthène	newton
Pressure (p)	pound per square inch	technical atmosphere	pound-force per square inch	standard atmosphere	poundal per square foot	barye	pieze	pascal

In the "engineering" systems (middle column), the weight 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, F = m ⋅ a, requires another factor, g_c, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s²). "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's two Solid Rocket Boosters was 3,300,000 pounds-force (14.7 MN), together 6,600,000 pounds-force (29.4 MN).