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Levers can be used to exert a large force over a small distance at one end by exerting only a small force over a greater distance at the other.

In physics, a lever (from French lever, meaning "to raise") is a rigid object that is used with an appropriate fulcrum (pivot point) to multiply the mechanical force that can be applied to another object. The lever allows less effort to be expended to move an object through a distance. This enhancement is also termed mechanical advantage. There are three classes of levers that we come across in our everyday lives. A pry bar and a seesaw are examples of the first class; a door and a wrench are examples of the second class; and a pair of tweezers and a human arm are examples of the third kind.



Levers have been used since prehistoric times for cultivation, excavation, and moving large objects. Such implements as hoes, slings, and oars were conceived and constructed to enhance human effort.

As early as 5000 B.C.E., a simple balance scale employing a lever was used to weigh gold and other items. A Greek device called a steelyard improved on these simple scales by adding a sliding weight to enhance precision. Around 1500 B.C.E., the shaduf, a forerunner of the crane, made its appearance in Egypt and India as a device for lifting containers of water.[1]

The earliest extant writings regarding levers date from the third century B.C.E. and were provided by Archimedes—behind his famous remark Give me the place to stand, and I shall move the earth stands a correct mathematical principle of levers (quoted by Pappus of Alexandria) and of the various methods possibly used by builders.

Theory of Operation

The principle of the lever tells us that the above is in static equilibrium, with all forces balancing, if F1D1 = F2D2.

Levers are one class of simple machines. Their operation depends on the relative positions of (a) the load; (b) the pivot, called a fulcrum; and (c) the applied effort. To maximize the applied effort, the most effective placement of the fulcrum was found to be close to the load.

The principle of leverage can be derived using Newton's laws of motion, and modern statics. It is important to note that the amount of work done is given by force times distance.

To use a lever to lift a certain unit of weight with an effort of half a unit, the distance from the fulcrum of the spot where force is applied must be twice the distance between the weight and the fulcrum. For example, to halve the effort of lifting a weight resting one meter from the fulcrum, we would need to apply force two meters from the other side of the fulcrum. The amount of work done is always the same and independent of the dimensions of the lever (in an ideal lever). The lever only allows one to trade effort for distance.[2]

Three classes of levers

There are three classes of levers, representing variations in the location of the fulcrum and the input and output forces.

First-class levers

First class lever

A first-class lever is one in which the fulcrum is located between the input force and the output force. In operation, a force is applied (by pulling or pushing) to a section of the bar, which causes the lever to swing about the fulcrum, overcoming the resistance force on the opposite side. The fulcrum is the center of the lever on which the bar (as in a seesaw) lays upon. This supports the effort arm and the load.


  1. Seesaw (also known as a teeter-totter)
  2. Crowbar (can also be used as a second-class lever)
  3. Spud bar (moving heavy objects)
  4. Pliers (double lever)
  5. Scissors (double lever)
  6. Wheel and axle because the wheel's motions follows the fulcrum, load arm, and effort arm principle
  7. Trebuchet, an upside down example of the above picture
  8. Oars, when used for moving or splashing water
  9. Can opener and bottle opener
  10. Bicycle hand brakes
  11. Hand trucks are L-shaped but works on the same principle on the wheel as a fulcrum
  12. Hammer, when pulling a nail with the hammer's claw
  13. Tweezers that are shaped like scissors work as double levers
  14. Shoehorn
  15. Beam engine although here the aim is just to change the direction in which the applied force acts, since the fulcrum is normally in the center of the beam (that is, D1 = D2).

Second-class levers

Second class lever

In a second-class lever, the input is located to the far side of the bar, the output is located in the middle of the bar, and the fulcrum is located on the side of the bar opposite to the input. Examples:

  1. Nutcracker
  2. Door
  3. Crowbar (can also be used as a first-class lever)
  4. Stapler
  5. Diving Board
  6. Wrench
  7. Dental Elevator
  8. Can Opener
  9. Canoe Paddle
  10. Wheelbarrow
  11. Oars, when the boat is the resistance moving the same direction as the force and using water as the fulcrum

Third-class levers

Third class lever

It is to be noted that for this class of levers, the input effort is higher than the output load, which is different from the first-class and second-class levers. However, also notice that the input effort moves through a shorter distance than the load. Thus it still has its uses in making certain tasks easier to do. Third class lever uses the effort in the center, while the output load is on one side, raising the load on the opposite end.


  1. Human Arm
  2. Tweezers
  3. Slings, trebuchets, and fishing rods
  4. Various tools, such as a hoe or scythe
  5. The main body of a pair of nail clippers, in which the handle exerts the incoming force
  6. Shovel
  7. Broom
  8. Staple Remover
  9. Hockey Stick
  10. The Human Mandible
  11. Boat paddle
  12. Baseball bat
  13. Mousetrap
  14. Door


  • A mnemonic for remembering the three classes of levers is the word flex, where the letters f-l-e represent the fulcrum, the load, and the effort as being between the other two, in the first-class lever, the second-class lever, and the third-class lever respectively. (To relate the mnemonic to the above diagrams, note that: the "fulcrum" is represented by the triangle, the "effort" is denoted by the arrow with a hand symbol, and the "load" is the other arrow.)
  • Alternatively, the term 'Frogs lay eggs' can also be use in the similar manner. Some people remember the word 'elf', which sorts the classes from the third to first.
  • To remember what the different classes of levers look like, another mnemonic is "fre 123" In a 1st class lever the fulcrum is in the middle, 2nd class the resistance is in the middle, and 3rd class the effort is in the middle of it.

See also


  1. BookRags. 2007. Lever - World of Invention Retrieved October 9, 2007.
  2. Resistance distance is the distance from the resistance (on a lever) to the fulcrum.


  • Delta Education. 2000. Levers and Pulleys. Nashua, NH: Delta Education. ISBN 0875048110
  • Hellman, and Sweat. 1971. The Lever And Pulley. New York, NY: M. Evans and Company, Inc. ASIN B000JD0OPO
  • Seller, Mick. 1993. Wheels, Pulleys and Levers. New York, NY: Gloucester Pr. ISBN 0531174204

External links


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