Fulcrum Calculator
This fulcrum calculator solves the lever equation in four modes: find the effort force you must apply, the load you can lift, where to position the fulcrum, or the mechanical advantage. Pick your lever class (Class 1, 2 or 3), choose what to solve for, enter the known values, and see the answer with a full worked-example panel.
What is a fulcrum and how does a lever work?
A lever is one of the six classical simple machines. It consists of a rigid beam that pivots around a fixed point called the fulcrum. By repositioning the fulcrum or changing the length of the arms on either side, you can amplify (or reduce) a force at the cost of travel distance. The governing principle is the law of the lever, first stated by Archimedes: the effort force multiplied by the effort arm equals the load force multiplied by the load arm (Fe x de = Fr x dr). When these two products, called moments, are equal, the lever is in equilibrium.
The three lever classes
Levers are grouped by where the fulcrum sits relative to the effort and load. A Class 1 lever (seesaw, crowbar, scissors) has the fulcrum between the two forces: it can provide a mechanical advantage greater than, equal to, or less than 1 depending on the arm lengths. A Class 2 lever (wheelbarrow, bottle opener, nutcracker) always places the load between the fulcrum and the effort point, so the effort arm is always longer than the load arm and MA is always greater than 1. A Class 3 lever (tweezers, fishing rod, the human forearm when lifting) places the effort between the fulcrum and the load: the effort arm is always shorter, so MA is always less than 1, but the load end moves faster and over a longer arc than the effort end.
Mechanical advantage and how to maximise it
Mechanical advantage (MA = de / dr) tells you how much force the lever multiplies. An MA of 4 means you apply one quarter of the load force to hold the system in balance. For a Class 1 or Class 2 lever, you increase MA by lengthening the effort arm or by moving the fulcrum closer to the load. There is no free lunch: every unit of MA you gain reduces the distance the load moves by the same factor, so a lever with MA = 5 moves the load one fifth as far as the effort end travels. Class 3 levers deliberately sacrifice force for range and speed, which is why tendons attach close to joints in the human body to allow rapid, wide movements.
How to use this calculator
Select the unit system (metric or imperial) and your lever class, then choose what you want to solve for. If you want the effort force, enter the load force, effort arm, and load arm. For fulcrum position, enter the total lever length plus both forces, and the calculator finds where the pivot must sit. For mechanical advantage only, you just need the two arm lengths. All modes show a step-by-step worked example and a moment verification so you can check the arithmetic.
Lever classes at a glance
| Class | Fulcrum position | MA vs 1 | Common examples |
|---|---|---|---|
| Class 1 | Between effort and load | Can be >1, =1, or <1 | Seesaw, crowbar, scissors, pliers |
| Class 2 | At one end; load between fulcrum and effort | Always >1 | Wheelbarrow, bottle opener, nutcracker |
| Class 3 | At one end; effort between fulcrum and load | Always <1 | Tweezers, fishing rod, human forearm |
MA = mechanical advantage. Class 3 levers always have MA less than 1 but provide speed and range of motion.
Frequently asked questions
What is the formula for a lever?
The fundamental lever formula is Fe x de = Fr x dr, where Fe is the effort force, de is the effort arm (distance from fulcrum to the effort point), Fr is the load force (resistance), and dr is the load arm (distance from fulcrum to the load). Rearrange this to find any one unknown when the other three are known.
What is mechanical advantage and what does an MA of 5 mean?
Mechanical advantage (MA) is the ratio of the load force to the effort force, which equals the ratio of the effort arm to the load arm (MA = de / dr). An MA of 5 means the lever multiplies your input force five times: you apply 10 lbf and lift 50 lbf. The trade-off is that the load moves only one fifth as far as your effort end.
How do I find where to place the fulcrum?
For a Class 1 lever, use dr = L x Fe / (Fe + Fr), where L is the total lever length, Fe is the effort force, and Fr is the load force. The effort arm de = L - dr. This calculator does that arithmetic automatically when you select "Fulcrum position" as the solve mode.
Which lever class gives the highest mechanical advantage?
Class 2 levers always have MA greater than 1 because the effort arm is always the full lever length. Class 1 levers can have any MA depending on where the fulcrum is placed. Class 3 levers always have MA less than 1, meaning you put in more force than the load, but the load moves faster and through a larger arc.
What are real-world examples of each lever class?
Class 1: seesaw, crowbar, scissors, pliers, balance scale. Class 2: wheelbarrow, bottle opener, nutcracker, staple remover. Class 3: tweezers, fishing rod, the human forearm when the bicep pulls the wrist up, a broom (hand at the end is the fulcrum, the grip near the top is the effort).
Does lever length affect mechanical advantage if only the arms matter?
MA depends only on the ratio de/dr, not on the absolute length. Doubling the whole lever changes neither the MA nor the forces, only the distances each end travels. Total lever length matters only when you are solving for fulcrum position given a fixed beam.