Lever Mechanical Advantage Calculator

Effort arm	2 m
Load arm	0.5 m
Load force	100 N

Effort arm

2 m

Load arm

0.5 m

Load force

100 N

Mechanical advantage	0
$\begin{aligned} MA &= \dfrac{d_E}{d_L} \\ &= \dfrac{2\,\text{m}}{0.5\,\text{m}} \\ &= 0 \end{aligned}$

Mechanical advantage

\begin{aligned} MA &= \dfrac{d_E}{d_L} \\ &= \dfrac{2\,\text{m}}{0.5\,\text{m}} \\ &= 0 \end{aligned}

Last updated: 2026-07-01

Definition

A lever is a rigid bar that turns about a fixed pivot called the fulcrum. Applying an effort at one point produces a turning effect that balances a load at another point. The mechanical advantage of the lever measures how much it multiplies the input force: it is the effort arm divided by the load arm, and equivalently the load force divided by the effort force.

The formula

At balance, the torque produced by the effort equals the torque produced by the load about the fulcrum:

F_L \, d_L = F_E \, d_E

where F_L is the load force on the load arm d_L, and F_E is the effort force on the effort arm d_E. Rearranging gives the two quantities this calculator reports:

MA = \frac{d_E}{d_L} = \frac{F_L}{F_E} \qquad F_E = \frac{F_L \, d_L}{d_E}

The arm lengths are measured from the fulcrum. When the effort arm is longer than the load arm the mechanical advantage exceeds 1, so a small effort balances a large load. When it is shorter, the mechanical advantage is below 1 and you trade force for a greater range or speed of motion.

Worked example

A crowbar pivots on a fulcrum. The load — a rock pressing down with 100 N — sits on a 0.5 m load arm, and you push on a 2 m effort arm.

Mechanical advantage: 2 ÷ 0.5 = 4

Required effort force: 100 × 0.5 ÷ 2 = 50 ÷ 2 = 25 N

The lever multiplies your push four-fold, so 25 N of effort holds a 100 N load in balance. To actually lift the rock you apply a little more than 25 N; friction and the bar's own weight mean the real effort is slightly higher.

The three classes of levers

Every lever falls into one of three classes, set by the order of the fulcrum, load and effort along the bar. The relationship MA = d_E ÷ d_L holds for all three.

Class	Arrangement	Everyday example	Mechanical advantage
First	Fulcrum between effort and load	Seesaw, scissors, pliers	Greater or less than 1
Second	Load between fulcrum and effort	Wheelbarrow, bottle opener, nutcracker	Always greater than 1
Third	Effort between fulcrum and load	Tweezers, fishing rod, human forearm	Always less than 1

In a first-class lever the fulcrum sits in the middle, so moving it changes which arm is longer and the advantage can go either way. In a second-class lever the effort arm always extends past the load, so the advantage is always above 1 — these levers are built to multiply force. In a third-class lever the effort acts on the shorter arm, so the advantage is below 1; you give up force to gain speed and reach, which is why the forearm can flick the hand quickly even though the biceps pulls close to the elbow.

Ideal versus actual mechanical advantage

The value above is the ideal mechanical advantage: it assumes a rigid, weightless bar turning on a frictionless fulcrum, so it depends only on the arm lengths. The actual mechanical advantage is the real load divided by the real effort you must supply, and it is always somewhat smaller because friction at the pivot and the weight of the bar consume part of the input. Treat the ideal figure as the best case and expect to push a little harder in practice.

Notes

The two arms and the two forces must be measured consistently, but they do not need matching units between the pair — the arm ratio is dimensionless, and the effort force comes out in the same unit as the load force. Both arm lengths must be greater than zero for the ratio to be defined.

Frequently Asked Questions (FAQ)

What is the mechanical advantage of a lever?

The mechanical advantage (MA) is how much a lever multiplies the input force. For an ideal lever it equals the effort arm divided by the load arm, MA = d_E ÷ d_L, which also equals the load force divided by the effort force. An MA greater than 1 means a small effort balances a large load — the classic reason to use a lever. An MA less than 1 trades force for extra range of motion or speed instead.

How do I find the effort force needed to lift a load?

Set the torques about the fulcrum equal: F_L × d_L = F_E × d_E. Solving for the effort gives F_E = F_L × d_L ÷ d_E. For example, a 100 N load on a 0.5 m load arm balanced by a 2 m effort arm needs 100 × 0.5 ÷ 2 = 25 N of effort. The longer the effort arm relative to the load arm, the less force you need.

What are the three classes of levers?

Levers are grouped by where the fulcrum, load and effort sit. In a first-class lever the fulcrum is between the effort and the load (a seesaw or a pair of scissors); the mechanical advantage can be greater or less than 1. In a second-class lever the load sits between the fulcrum and the effort (a wheelbarrow or a bottle opener), so the effort arm is always longer and MA is always greater than 1.

In a third-class lever the effort is between the fulcrum and the load (tweezers or the human forearm), so MA is always less than 1 — you sacrifice force to gain speed and range. The formula MA = d_E ÷ d_L applies to all three.

What is the difference between ideal and actual mechanical advantage?

The ideal mechanical advantage assumes a rigid, weightless bar and a frictionless fulcrum, so it depends only on the arm lengths: MA = d_E ÷ d_L.

The actual mechanical advantage is the real load force divided by the real effort force you have to supply, and it is always a bit smaller because friction at the pivot and the weight of the bar absorb part of your effort. This calculator reports the ideal value; expect to push slightly harder in practice.

Lever Mechanical Advantage Calculator

Inputs

Results

Lever Mechanical Advantage Calculator

Details

Embed this calculator

Share this calculation

Recommended Next

Torque Calculator

Inclined Plane Calculator

Newton's Second Law Calculator

Was this calculator helpful?

No