# Foot-pound (energy)

The foot-pound (symbol ft·lbf, also written ft·lb) is a unit of energy and work in the British imperial and United States customary systems, defined as the work done when a force of one pound-force moves an object through a distance of one foot in the direction of the force. In *Theory of Heat*, James Clerk Maxwell states the definition in everyday terms: raising a one-pound weight through a height of one foot against gravity performs an amount of work that engineers call a foot-pound.<sup>[1](https://en.wikisource.org/wiki/Theory_of_Heat_(Maxwell,_4th_edition)/Chapter_4)</sup> In SI units, one foot pound-force equals 1.355818 joules.<sup>[2](https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf)</sup>

| Key fact | Detail |
|---|---|
| Definition | Work done by a one-pound-force acting through one foot; equivalently, lifting one pound one foot against gravity<sup>[1](https://en.wikisource.org/wiki/Theory_of_Heat_(Maxwell,_4th_edition)/Chapter_4)</sup> |
| SI equivalent | 1 foot pound-force (ft·lbf) = 1.355818 joule<sup>[2](https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf)</sup> |
| Related unit | The foot-poundal, an absolute FPS-system unit, equals 4.214011 × 10⁻² joule<sup>[3](https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook102.pdf)</sup> |
| Force basis | One pound-force is the weight of a one avoirdupois pound mass at standard gravity, equal to 4.448 newtons<sup>[4](https://www.nist.gov/glossary-term/29611)</sup> |
| Torque namesake | The term foot-pound is also used for a unit of torque, sometimes called the pound-foot to distinguish it from the energy unit<sup>[5](https://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/foot-pound)</sup> |
| Ballistics use | Projectile kinetic energy and firearm recoil energy are conventionally expressed in foot-pounds<sup>[6](https://saami.org/glossary/kinetic-energy-formula/)</sup><sup> • </sup><sup>[7](https://saami.org/faqs/)</sup> |

## Definition and conversion

The unit combines two customary measures: the pound-force, defined by NIST as the weight of a one avoirdupois pound mass at standard gravity and equal to 4.448 newtons, and the foot.<sup>[4](https://www.nist.gov/glossary-term/29611)</sup> Multiplying force by distance gives the energy unit, and NIST's conversion tables give the exact relationship to SI: one foot pound-force equals 1.355818 joule.<sup>[2](https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf)</sup> The related foot-poundal, from the absolute foot-pound-second system in which force is based on the poundal rather than the pound-force, equals 0.04214011 joule, about 32 times less.<sup>[3](https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook102.pdf)</sup>

A worked example from an engineering textbook illustrates the magnitude: slowly lifting a 10 pound sack of sugar upward 1 foot requires 10 foot-pounds of work.<sup>[8](https://catalogimages.wiley.com/images/db/pdf/9781119800255.excerpt.pdf)</sup> In the British system of units, with force in pounds and distance in feet, work comes out in pound-feet, more commonly written foot-pounds (ft·lb).<sup>[8](https://catalogimages.wiley.com/images/db/pdf/9781119800255.excerpt.pdf)</sup>

## Foot-pounds and pound-feet: energy versus torque

Torque, the turning effect of a force, has the same dimensions as energy, since both are a force multiplied by a length. To keep the two quantities apart in speech, the torque unit is often called the pound-foot while the energy unit is called the foot-pound.<sup>[5](https://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/foot-pound)</sup> According to NIST's SI guidance, torque and energy share the same dimension, yet the joule may not be used to express torque, whose SI unit is instead the newton meter.<sup>[9](https://convertcalc.org/guides/force-vs-torque-explained/)</sup>

## Role in the mechanical equivalent of heat

The foot-pound served as the work unit in the nineteenth-century experiments that established the conservation of energy. James Prescott Joule of Manchester measured the heat produced by the friction of liquids with a paddle-wheel driven by descending weights, and found the same equivalence with water, mercury, and sperm oil.<sup>[10](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Heat)</sup> His 1850 paper gave a value of J = 772 foot-pounds, which continued to be accepted for almost thirty years.<sup>[11](https://tile.loc.gov/storage-services/public/gdcmassbookdig/notesonmechanics00cros/notesonmechanics00cros.pdf)</sup> The 1853–60 *Encyclopædia Britannica* records Joule's conclusion that one unit of heat could raise 772 pounds one foot in height, the figure known as "Joule's equivalent."<sup>[12](https://jimclifford.ca/britannica-articles-4/a/EB.16/193469393/592.html)</sup> The 1911 edition gives his later determination as 772.692 foot-pounds in the latitude of Manchester for the heat required to raise one pound of water through one degree [Fahrenheit](https://www.edgepedia.org/fahrenheit) from the freezing point, and lists 777 foot-pounds (at latitude 45°) as equivalent to one [British thermal unit](https://www.edgepedia.org/british-thermal-unit).<sup>[13](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Energy)</sup><sup> • </sup><sup>[10](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Heat)</sup> Tyndall's *Heat* likewise states that 772 foot-pounds constitute the mechanical equivalent of heat, taking as standard the heat needed to raise a pound of water one degree Fahrenheit.<sup>[14](https://darwin-online.org.uk/converted/pdf/1868_Tyndall_Heat_mode_motion_A6175.pdf)</sup>

## Use in ballistics and engineering

In firearms measurement, the foot-pound is the conventional unit for kinetic energy. The [Sporting Arms and Ammunition Manufacturers' Institute](https://www.edgepedia.org/sporting-arms-and-ammunition-manufacturers-institute) (SAAMI), the US standards body for ammunition, gives the projectile formula

\[ E = \frac{W \cdot V^{2}}{14000 \cdot g_{\mathrm{c}}} \]

where E is the kinetic energy in foot-pounds, W the projectile weight in grains, V the velocity in feet per second, and \( g_{\mathrm{c}} \) the gravitational constant 32.174 ft/s².<sup>[6](https://saami.org/glossary/kinetic-energy-formula/)</sup> The same body notes that recoil energy, a conventional way of recording and comparing recoil, is usually expressed in foot-pounds, with firearm weight in pounds, ejecta and propellant charge in grains, and velocity in feet per second.<sup>[7](https://saami.org/faqs/)</sup> [Muzzle energy](https://www.edgepedia.org/muzzle-energy), a projectile's energy at the time it leaves the muzzle of a gun, is rated in the same unit.<sup>[15](https://saami.org/glossary/muzzle-energy/)</sup>

[Mechanical engineering](https://www.edgepedia.org/mechanical-engineering) references list the foot-pound among the customary units still used in the field, alongside the mil and the horsepower, for energy, work, or heat.<sup>[16](https://ftp.idu.ac.id/wp-content/uploads/ebook/tdg/DESIGN%20SISTEM%20DAYA%20GERAK/An%20Introduction%20to%20Mechanical%20Engineering.pdf)</sup>

## References

1. [James Clerk Maxwell, Theory of Heat, 4th edition, Chapter 4, Wikisource](https://en.wikisource.org/wiki/Theory_of_Heat_(Maxwell,_4th_edition)/Chapter_4)
2. [Guide for the Use of the International System of Units (SI), NIST Special Publication 811 (2008)](https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf)
3. [ASTM Metric Practice Guide, NBS Handbook 102](https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook102.pdf)
4. [Pound-force/lbf, NIST Glossary](https://www.nist.gov/glossary-term/29611)
5. [Foot-pound, Encyclopedia.com](https://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/foot-pound)
6. [Kinetic Energy (Formula), SAAMI Glossary](https://saami.org/glossary/kinetic-energy-formula/)
7. [FAQs, SAAMI](https://saami.org/faqs/)
8. [Excerpt, Wiley (work and energy units)](https://catalogimages.wiley.com/images/db/pdf/9781119800255.excerpt.pdf)
9. [Force vs. Torque: Newtons, Pound-Force, and Foot-Pounds Explained, ConvertCalc](https://convertcalc.org/guides/force-vs-torque-explained/)
10. [1911 Encyclopædia Britannica, Heat, Wikisource](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Heat)
11. [Notes on Mechanics (history of the mechanical equivalent), Library of Congress](https://tile.loc.gov/storage-services/public/gdcmassbookdig/notesonmechanics00cros/notesonmechanics00cros.pdf)
12. [Encyclopædia Britannica 8th ed., Steam (1853–60)](https://jimclifford.ca/britannica-articles-4/a/EB.16/193469393/592.html)
13. [1911 Encyclopædia Britannica, Energy, Wikisource](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Energy)
14. [John Tyndall, Heat: A Mode of Motion (1868)](https://darwin-online.org.uk/converted/pdf/1868_Tyndall_Heat_mode_motion_A6175.pdf)
15. [Muzzle Energy, SAAMI Glossary](https://saami.org/glossary/muzzle-energy/)
16. [An Introduction to Mechanical Engineering, 3rd ed.](https://ftp.idu.ac.id/wp-content/uploads/ebook/tdg/DESIGN%20SISTEM%20DAYA%20GERAK/An%20Introduction%20to%20Mechanical%20Engineering.pdf)

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*Topic: Encyclopedia › Physical world and mathematics › Measurement and time › Units and unit systems › Units by physical quantity › Units of energy, work, heat, and power*

*Initially written Sep 17, 2026 · Reviewed: Sep 20, 2026; Sep 30, 2026; Oct 15, 2026 · Edited: Sep 20, 2026; Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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