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Ideal Lever Force, Arms & Mechanical Advantage

Balance ideal lever moments and calculate force ratio from perpendicular effort and load arms.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

An effort arm of 2 m and load arm of 0.5 m give ideal mechanical advantage 4. Balancing a 200 N load requires 50 N effort.

Effort × effort arm = load × load arm; mechanical advantage = effort arm / load arm

Worked example

Enter these known values and leave the other values blank.

Perpendicular effort arm
2 m
Perpendicular load arm
0.5 m
Load force magnitude
200 N
Effort force magnitude
50 N
Ideal mechanical advantage
4

Assumptions and limitations

  • Both forces and both arms are positive. Moment arms are perpendicular distances from the pivot to the lines of force, not necessarily distances along the lever.
  • The lever is in static rotational equilibrium, with a rigid bar and ideal pivot. Pivot friction, bar weight, deformation and inertia are omitted.
  • Mechanical advantage describes the force ratio. It does not imply energy gain; an increased force corresponds to a smaller ideal travel distance.

Common questions

Can mechanical advantage be less than one?

Yes. A shorter effort arm than load arm gives a force disadvantage while increasing load travel relative to effort travel.

Can I enter angled forces?

Use each force’s perpendicular moment arm. Entering the length along the bar without accounting for its angle can give an incorrect moment.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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