Understanding Foot-pounds to Ergs Conversion
A foot-pound (ft-lbf) measures work in the imperial system as one pound-force acting over one foot. An erg is the energy unit of the centimetre-gram-second (CGS) system, equal to the work done by a force of one dyne over one centimetre, or exactly 10⁻⁷ joules. Converting foot-pounds to ergs is common when reconciling imperial mechanics with older CGS-based physics literature, where ergs remain standard for small energies.
Conversion Formula
To convert Foot-pounds to Ergs, multiply by this factor:
Step-by-Step Example
Convert 25 Foot-pounds to Ergs.
How to Convert Foot-pounds to Ergs
Move an imperial foot-pound value into the CGS erg with one multiplication.
- Record the value: Write down the energy in foot-pounds (ft-lbf).
- Multiply by the factor: Multiply by 13,558,180, the ergs in one foot-pound.
- Use scientific notation: The large result is clearest as a power of ten.
- Worked result: For 25 ft-lbf, 25 × 13,558,180 = 3.38955 × 10⁸ erg.
Foot-pounds to Ergs conversion table
| Foot-pounds (ft-lbf) | Ergs (erg) |
|---|---|
| 0 | 0 |
| 1 | 13558180 |
| 2 | 27116360 |
| 3 | 40674540 |
| 4 | 54232720 |
| 5 | 67790900 |
| 6 | 81349080 |
| 7 | 94907260 |
| 8 | 108465400 |
| 9 | 122023600 |
| 10 | 135581800 |
| 15 | 203372700 |
| 20 | 271163600 |
| 25 | 338954500 |
| 30 | 406745400 |
| 40 | 542327200 |
| 50 | 677909000 |
| 60 | 813490800 |
| 70 | 949072600 |
| 80 | 1084654000 |
| 90 | 1220236000 |
| 100 | 1355818000 |
| 150 | 2033727000 |
| 200 | 2711636000 |
| 250 | 3389545000 |
| 300 | 4067454000 |
| 400 | 5423272000 |
| 500 | 6779090000 |
| 600 | 8134908000 |
| 700 | 9490726000 |
| 800 | 10846540000 |
| 900 | 12202360000 |
| 1000 | 13558180000 |
| 2000 | 27116360000 |
| 3000 | 40674540000 |
| 4000 | 54232720000 |
| 5000 | 67790900000 |
| 10000 | 135581800000 |
| 25000 | 338954500000 |
| 50000 | 677909000000 |
| 100000 | 1355818000000 |
| 250000 | 3389545000000 |
| 500000 | 6779090000000 |
| 1000000 | 13558180000000 |
What is the Foot-pound?
The foot-pound (foot-pound-force) is a unit of energy or work in the imperial and US customary systems, representing mechanical work done against gravity or by a force.
Definition
One foot-pound is the work done when a force of one pound-force moves an object one foot in the direction of the force:
Precisely, 1 ft·lbf = 1.3558179483314004 J, derived from the standard pound-force (4.4482216152605 N) times the international foot (0.3048 m). It should not be confused with the pound-foot, the identical-magnitude unit conventionally reserved for torque.
Origin and History
The unit grew directly out of imperial mechanics, combining the foot and the pound-force, the everyday units of length and weight in Britain and America. It became a standard measure of work in engineering and firearms ballistics long before metric energy units gained ground in the English-speaking world.
Law and Notable Facts
The foot-pound remains widely used in the United States, especially for muzzle energy of firearms and for engine and tool work ratings. Multiplying foot-pounds per unit time gives power; 550 ft·lbf per second defines one mechanical horsepower.
Real-World Examples and Conversions
- 1 foot-pound is about 1.356 joules.
- A .22 Long Rifle bullet typically leaves the muzzle with roughly 100 to 140 ft·lbf of energy.
- Lifting a 50-pound weight by 4 feet requires 200 ft·lbf, or about 271 joules of work.
What is the Erg?
The erg is a unit of energy in the centimetre-gram-second (CGS) system, historically common in physics, astronomy, and mechanics before the SI joule became standard.
Definition
One erg is the work done by a force of one dyne acting over a distance of one centimetre:
This equals exactly one ten-millionth of a joule (10⁻⁷ J), or equivalently 1 g·cm²/s². The erg is a small unit, reflecting the small base units of the CGS system.
Origin and History
The name comes from the Greek ergon, meaning "work." The unit was formally adopted by the British Association for the Advancement of Science in 1873 as part of the CGS system and remained the dominant energy unit in physics literature well into the 20th century.
Law and Notable Facts
The erg has been largely superseded by the joule and is deprecated in the modern SI framework, but it persists in astrophysics, where luminosities and energies are still frequently quoted in ergs and erg per second.
Real-World Examples and Conversions
- 1 joule equals 10 million ergs.
- A mosquito in flight expends energy on the order of a few ergs per wingbeat.
- The Sun radiates about 3.8 × 10³³ ergs every second, equivalent to 3.8 × 10²⁶ watts.
Frequently Asked Questions
How many ergs are in a foot-pound?
One foot-pound equals about 13,558,180 ergs, or 1.355818 × 10⁷ ergs. The large number reflects that an erg is a very small unit of energy.
What is an erg?
An erg is the CGS unit of energy, equal to 10⁻⁷ joules, defined as one dyne of force acting through one centimetre. It is convenient for the tiny energies common in classical and atomic physics.
How do I convert foot-pounds to ergs?
Multiply the foot-pound figure by 13,558,180. For example, 3 ft-lbf equals about 4.06745 × 10⁷ erg.
When are ergs still used?
Ergs persist in astrophysics, plasma physics, and older scientific texts that follow the CGS convention. Converting foot-pounds into ergs helps compare imperial-engineering data with those sources.
How do I convert ergs back to foot-pounds?
Multiply ergs by 7.375621 × 10⁻⁸. So 10⁸ erg equals about 7.376 ft-lbf.
People also convert
Complete Foot-pounds conversion table
| Unit | Result |
|---|---|
| Watt-seconds (Ws) | 1.355818 Ws |
| Watt-minutes (Wm) | 0.02259697 Wm |
| Watt-hours (Wh) | 0.0003766161 Wh |
| Milliwatt-hours (mWh) | 0.3766161 mWh |
| Kilowatt-hours (kWh) | 3.766161e-7 kWh |
| Megawatt-hours (MWh) | 3.766161e-10 MWh |
| Gigawatt-hours (GWh) | 3.766161e-13 GWh |
| Joules (J) | 1.355818 J |
| Kilojoules (kJ) | 0.001355818 kJ |
| Megajoules (MJ) | 0.000001355818 MJ |
| Gigajoules (GJ) | 1.355818e-9 GJ |
| British Thermal Units (IT) (BTU) | 0.001285067 BTU |
| US Therms (thm) | 1.285374e-8 thm |
| Electronvolts (eV) | 8462350000000000000 eV |
| Ergs (erg) | 13558180 erg |
| Tonnes of TNT (t-tnt) | 3.240483e-10 t-tnt |
| calories (cal) | 0.3240483 cal |
| Kilocalories (kcal) | 0.0003240483 kcal |