# Fulcrum Calculator

Table of contents

What is the fulcrum of a lever?Law of the lever and calculating mechanical leverageTypes of leversFulcrum equationHow do you find the fulcrum point?How to use this lever fulcrum calculatorFAQsThis **fulcrum calculator** with 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!

You've come to the right place if you were wondering how one chooses a lever's fulcrum position on one's lever. In this article, let's discuss the fundamental laws that calculate a lever fulcrum and answer these basic questions:

- What is the fulcrum of a lever?
- How do you calculate
**mechanical leverage**? - What is the
**fulcrum equation**for the three classes of levers? - How to find the
**fulcrum point**?

If you're exclusively interested in calculating lever forces, use our lever calculator.

## 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) of your lever, there are three main components you need to know:

**Fulcrum**is the pivot point around which a lever rotates.**Resistance**is the load we want to lift or apply force through our lever.**Effort**is the force we shall apply to the lever to move it.

## 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 to obtain:

where:

- $F_r$ -
**Resisting force**(or**load**); - $d_r$ -
**Distance**of the**resistance**from the fulcrum (or the "**load arm**"); - $F_e$ -
**Effort force**that we apply to*lift*(or*counterbalance*) the resistance; and - $d_e$ -
**Distance**of the**effort**from the fulcrum (or the "**effort arm**").

We use this lever equation for calculating lever forces. To understand the moments in a lever, we recommend you read further in our torque calculator.

A lever's **mechanical leverage** or the **mechanical advantage** is the **ratio** of the **resisting force** to the **effort force**. By combining with the lever equation we introduced above, we can calculate **mechanical leverage** as:

Here $MA$ is the mechanical advantage.

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.*"

If you wish to learn more about this, use our mechanical advantage calculator.

## Types of levers

Before we proceed to the lever fulcrum calculation, we must learn the class of the lever. Based on the location of its three components, we can classify levers as follows:

**Class I lever**has the**fulcrum**between the**load**and the**effort**. A see-saw is the first image that should come to mind.**Class II lever**has the**resistance**between the**fulcrum**and the**effort**. Wheelbarrows are an excellent example of this kind.**Class III lever**has the**effort**between the**fulcrum**and the**load**. A pair of tongs and tweezers are great examples to visualize this class.

## Fulcrum equation

Say $L$ is the **length of the lever** at hand, and you need to calculate the **fulcrum** of the lever.

First, consult the previous section to decide which class of lever you have because it determines the type of the fulcrum equation we must use.

- For
**Class I lever**, the length of the lever is:

Substituting this in the lever equation, we get:

We can use this fulcrum formula for calculating lever distances for all class I levers.

- For
**Class II lever**, the length of the lever is:

In other words, the fulcrum and the effort are on the opposite ends of the lever. Substituting this in the lever equation, we get:

Using this fulcrum equation, we can calculate lever distances for all class II levers.

- For
**Class III levers**, the length of the lever is:

In other words, the fulcrum and the load are at the opposite ends of the lever. Substituting this in the lever equation, we get:

This fulcrum equation can calculate all lever distances for all class III levers.

Let's summarize everything we've learned so far in the next section.

## How do you find the fulcrum point?

To calculate the **fulcrum location** of a lever of length *L*, follow these steps:

**Determine**the**class**of the lever based on the location of the**fulcrum**, the**load***F*, and the_{r}**effort***F*._{e}**Calculate**the**mechanical advantage***MA*using the equation*MA = F*._{r}/F_{e}-
- For a
**class I lever**,**calculate**the**distance***d*of the_{r}**fulcrum**from the**load**using*d*._{r}= L / (MA + 1) - For a
**class II lever**,**determine**the**distance***d*of the_{r}**fulcrum**from the**load**using*d*._{r}= L / MA - For a
**class III lever**, the**distance***d*of the_{r}**fulcrum**from the**load**is equal to the**length**of the lever,*d*._{r}= L

- For a

## How to use this lever fulcrum calculator

This fulcrum calculator will help you pinpoint the ideal fulcrum location for your lever, no matter the lever class. It is pretty simple to use:

**Select**the appropriate**lever class**from the`Lever class`

list.-
**Enter**the correct values for the`Load`

,`Effort`

, and the`Length of the lever`

fields. This calculator will show you the ideal**fulcrum**position relative to the**load**and**effort**and the**mechanical advantage**you will achieve.- Alternatively,
**give**the correct values for the`Length of the lever`

and`Mechanical advantage`

you want to achieve. You will get the best**fulcrum**position relative to the**load**and**effort**.

### Which fulcrum position on a 1m lever can give twice the mechanical advantage?

**1/3 m** away from the **load** and **2/3 m** away from the **effort**.

To calculate the fulcrum position that gives a mechanical advantage of *MA = 2* with a class I lever of length *L = 1 m*, follow these simple steps:

**Calculate**the**distance***d*from the_{r}**load**to the**fulcrum**using*d*._{r}= L/( MA + 1) = 1/3**Determine**the**distance***d*from the_{e}**fulcrum**to the**effort**using*d*._{e}= L - d_{r}= 1 - 1/3 = 2/3- Verify your results using our fulcrum calculator.

### What type of lever is the human elbow joint?

The human elbow joint is an example of a **Class III lever**. When we lift loads in our fists, the elbow joint acts as a fulcrum and the bicep muscle exerts the needed force a small distance from the elbow.

### How do you calculate the length of the effort arm?

To calculate the **length** of the **effort arm** *d _{e}* of a lever to lift a

**load**

*F*with an

_{r}**effort**

*F*, follow these simple steps:

_{e}**Determine**the mechanical advantage*MA*using*MA = F*._{r}/F_{e}**Measure**the**length**of the**load arm***d*as the distance between the fulcrum and the load._{r}**Multiply***MA*with*d*to get the_{r}**effort arm**as*d*._{e}= MA × d_{r}