Fulcrum Calculator — Find the Ideal Lever Pivot Point | Class I, II & III

This fulcrum calculator will help you find the ideal fulcrum point on your lever so that you can lift a load or apply a force with the mechanical advantage you desire. Below we discuss the fundamental laws that govern a lever fulcrum and answer the most common questions about levers.

What is the fulcrum of a lever?

A lever is a simple machine made up of a beam or a bar that pivots around a point on itself. This pivot point is called its fulcrum (or pivot point), and it usually connects the lever to the ground.

Aside from the beam (or bar), there are three main components you need to know:

• Fulcrum — the pivot point around which a lever rotates.
• Resistance (load) — the load we want to lift or the resistance to overcome.
• Effort — the force we apply to the lever to move it.

A length of bar pivoted at a fulcrum can be used to multiply the effort force (F_e) to easily lift loads or move a resistance (F_r).

Law of the lever and calculating mechanical leverage

The law of the lever states that the forces applied farther away from the fulcrum must be less than the forces applied closer to it. We can summarize this with a balance of moments:

F_r × d_r = F_e × d_e

where:

• F_r — resisting force (the load);
• d_r — distance of the resistance from the fulcrum (the "load arm");
• F_e — effort force we apply to lift or counterbalance the resistance; and
• d_e — distance of the effort from the fulcrum (the "effort arm").

A lever's mechanical leverage — the mechanical advantage (MA) — is the ratio of the resisting force to the effort force:

MA = F_r / F_e = d_e / d_r

This relation shows that we can lift heavy loads with little effort if the effort arm is longer than the load arm. To quote Archimedes: "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."

Types of levers

Based on the location of its three components, we can classify levers as follows:

• Class I lever — the fulcrum is between the load and the effort. A see-saw is the first image that comes to mind.
• Class II lever — the resistance is between the fulcrum and the effort. A wheelbarrow is an excellent example.
• Class III lever — the effort is between the fulcrum and the load. Tongs and tweezers are great examples.

Fulcrum equation

Let L be the length of the lever. The class of lever determines which fulcrum equation we use.

Class I lever: the length of the lever is L = d_r + d_e. Substituting into the lever equation gives:

d_r = F_e × L / (F_e + F_r)   and   d_e = F_r × L / (F_e + F_r)

Class II lever: the effort acts at the very end, so the effort arm equals the full lever length (d_e = L) and the load arm is d_r = F_e × L / F_r. Because the load sits between fulcrum and effort, the effort force must be smaller than the load.

Class III lever: the load acts at the very end, so the load arm equals the full lever length (d_r = L) and the effort arm is d_e = F_r × L / F_e. Because the effort sits between fulcrum and load, the effort force must be greater than the load.

How do you find the fulcrum point?

Choose the lever class, enter the total lever length L, the load (resistance) force F_r, and the effort force F_e. The calculator solves the moment-balance equation to give you the load arm d_r and effort arm d_e — i.e., exactly where the fulcrum should sit relative to the load and the effort — together with the resulting mechanical advantage.

How to use this lever fulcrum calculator

1. Pick the lever class (I, II, or III).
2. Select the unit system — metric (cm, N) or US/imperial (in, lbf).
3. Enter the lever length, the load force, and the effort force.
4. Read off the load arm, effort arm, fulcrum position, and mechanical advantage.

If you're exclusively interested in calculating lever forces, use our lever calculator; to learn about the mechanical advantage of every simple machine, see our mechanical advantage calculator.

FAQs

What units does the fulcrum point have?

The load arm and effort arm are given in the same length unit you entered for the lever length (cm or inches). Mechanical advantage is a dimensionless ratio.

Why does the mechanical advantage equal F_r / F_e?

From the moment balance F_r × d_r = F_e × d_e, dividing both sides gives F_r / F_e = d_e / d_r. The longer the effort arm relative to the load arm, the greater the mechanical advantage.

Can the mechanical advantage be less than 1?

Yes. A Class III lever (like tweezers) always has MA < 1: it trades force for speed and range of motion, so you must apply more effort than the load.

Why did I get an error for a Class II or Class III lever?

A Class II lever can only multiply force, so the effort must be less than the load. A Class III lever can only reduce force, so the effort must be greater than the load. Adjust the forces or switch to a Class I lever, which works for any combination.