Levers: First, Second and Third Class, With a Lever Calculator

Lever calculator

Drag the fulcrum, the load or the effort. Or Tab to one and use the arrow keys: 5 cm a press, 1 cm with Shift.

Class 1 examples: seesaw, crowbar, scissors, balance scale, pliers, claw hammer pulling a nail.

The fulcrum is in the middle, so this is a class 1 lever.
Load arm = 0.5 m from the fulcrum, effort arm = 1.1 m.
Load moment = 100 N × 0.5 m = 50 N m
To balance, effort × 1.1 m = 50 N m, so effort = 50 ÷ 1.1 = 45.45 N
Mechanical advantage = effort arm ÷ load arm = 1.1 ÷ 0.5 = 2.2 (the effort is smaller than the load)

Using the lever

Pick a class to set the three points in its usual order, then drag any of them. Move the load past the fulcrum and the class changes with it, because the class is only ever about which point sits in the middle. The arms can be typed too, in metres, and the beam is 2 m long.

Give the load in newtons or kilograms. For kilograms, choose g: 9.81 N/kg is the usual school value, and 9.80665 is the standard value, which is exact by definition. Leave Your effort empty and the tool finds the effort that balances. Type one in and the beam settles on its low end toward whichever moment is bigger.

The parts of a lever

A lever is a rigid bar that turns about a pivot called the fulcrum. You push or pull on it with the effort, and it moves the load, also called the resistance.

The distance from the fulcrum to the effort is the effort arm. The distance from the fulcrum to the load is the load arm. Those two lengths decide everything else.

First, second and third class levers

Class	In the middle	Mechanical advantage	Examples
First	Fulcrum	Above 1, below 1 or exactly 1, depending on the arms	Seesaw, crowbar, scissors, balance scale, pliers, claw hammer pulling a nail
Second	Load	Always above 1	Wheelbarrow, nutcracker, bottle opener, car brake pedal, bellows
Third	Effort	Always below 1	Tweezers, tongs, fishing rod, the forearm lifting with the biceps, the human jaw

Which class is it?

Find the middle point. In a seesaw the pivot sits between the two riders, so it's first class. A wheelbarrow has its wheel as the fulcrum at one end, the handles at the other, and the load in the tub between them. Second class.

Tweezers are third class. The hinge is the fulcrum, your fingers press in the middle, and the tips grip the load at the far end. Your forearm works the same way when you lift something in your hand, with the elbow as the fulcrum and the biceps pulling between the elbow and the hand.

A second-class lever always has the longer arm on the effort side, so it always multiplies the force. A third-class lever always has the shorter arm on the effort side. It needs more effort than the load, and in return the load end moves further and faster. In Example 9.4 of OpenStax College Physics, a biceps attached 4 cm from the elbow has to pull with 470 N to hold a 4 kg load in the hand, along with the forearm's own 2.5 kg.

Moments and the law of the lever

A force's turning effect about the fulcrum is its moment, the force times its distance from the fulcrum, measured in newton metres. A lever balances when the moments on each side are equal.

effort × effort arm = load × load arm

Say a 100 N load sits 0.5 m from the fulcrum and you push 1.1 m away on the other side. The load's moment is 100 × 0.5 = 50 N m, so the effort is 50 ÷ 1.1 = 45.45 N.

Mechanical advantage is load ÷ effort. For an ideal lever, with no bending and no friction, that's the same as effort arm ÷ load arm, here 1.1 ÷ 0.5 = 2.2. Nothing comes free. The effort end travels 2.2 times as far as the load end does.

The oldest surviving writing on levers dates from the third century BC and is credited to Archimedes. So is the boast that, given a lever and somewhere to put the fulcrum, he could move the world. The Greek usually quoted for it says nothing about a lever or a fulcrum, though.

Pulleys

Fixed pulley, MA 1. The wheel is fixed to the ceiling. It changes the direction of the pull and not its size, so 100 N still needs 100 N, pulled down instead of lifted up.

Movable pulley, MA 2. The wheel hangs on the rope with the load. Two rope segments hold it up, so each carries half, and you pull 50 N while drawing in twice as much rope.

Block and tackle, MA 4. Fixed and movable pulleys together. Here four segments hold the moving block, so the ideal effort is a quarter of the load and you pull four times as far.

Counting the rope segments

The ideal mechanical advantage of any pulley system is the number of rope segments that hold up the moving block. Count the segments running up from the load's pulley, and leave out the end you pull on if it runs downward from a fixed wheel.

Real pulleys have friction, so the actual effort is a little more than the ideal one. Each extra wheel adds friction too, and past a point another wheel costs more than it saves.

Printable levers worksheet

Levers

Name:

1. Label the parts. Write the word for each letter: fulcrum · effort · load · effort arm · load arm.

2. F is the fulcrum, E the effort and L the load. Write the class (1, 2 or 3) of each lever.

aClass ____

bClass ____

cClass ____

dClass ____

eClass ____

fClass ____

3. Which class of lever is each of these?

Balance scale Class ____
Bellows Class ____
Pliers Class ____
Tweezers Class ____

4. Use effort × effort arm = load × load arm. Show your working.

A crowbar lifts a 160 N load 0.4 m from the fulcrum. You push down 1.6 m from the fulcrum on the other side. What effort balances the load?
A wheelbarrow carries a 40 N load. Lifting the handles 0.4 m from the wheel takes 20 N. How far from the wheel is the load?
On a seesaw a 24 kg child sits 1 m from the pivot. How far from the pivot on the other side must a 20 kg child sit to balance?
A spanner is turned with a 80 N force 0.25 m from the nut. What is the moment of the force?
A lever has an effort arm of 2.4 m and a load arm of 0.3 m. What is its mechanical advantage?

Levers: answer key

1. A effort, B load, C load arm, D effort arm, E fulcrum

2. a class 3, b class 1, c class 3, d class 2, e class 1, f class 2

3. a balance scale: class 1, b bellows: class 2, c pliers: class 1, d tweezers: class 3

E × 1.6 = 160 × 0.4 = 64, so E = 64 ÷ 1.6 = 40 N
40 × d = 20 × 0.4 = 8, so d = 8 ÷ 40 = 0.2 m
24 × 1 = 20 × d (g is on both sides and cancels), so d = 24 ÷ 20 = 1.2 m
moment = force × distance = 80 × 0.25 = 20 N m
MA = effort arm ÷ load arm = 2.4 ÷ 0.3 = 8

The worksheet

Four parts on one page. Label a lever's five parts, name the class of six drawn levers and four everyday ones, then work five moment problems: a crowbar, a wheelbarrow, a seesaw in kilograms, a spanner and a mechanical advantage.

Each sheet number gives its own questions, and the second page is the answer key with the working. Print it on A4 or US Letter.

Questions

What are the three types of levers?

First class has the fulcrum in the middle (a seesaw). Second class has the load in the middle (a wheelbarrow). Third class has the effort in the middle (tweezers).

How do you calculate the effort on a lever?

Multiply the load by the load arm, then divide by the effort arm. A 100 N load 0.5 m from the fulcrum, with the effort 1.1 m away, needs 100 × 0.5 ÷ 1.1 = 45.45 N.

What is the mechanical advantage of a lever?

Load divided by effort. For an ideal lever it's the effort arm divided by the load arm, so a 1.2 m effort arm and a 0.3 m load arm give 4.

Is a bottle opener a second-class lever?

Yes. It's on Wikipedia's list of second-class levers with the wheelbarrow and the nutcracker. The cap is the load, between the fulcrum and your hand on the handle.

Why is the forearm a third-class lever?

The elbow is the fulcrum and the weight is in the hand, while the biceps pulls on the forearm between them. The effort is in the middle.

Why use a third-class lever if it needs more effort?

Speed and reach. A small movement near the fulcrum becomes a big, fast movement at the far end, as with a fishing rod.

What is the mechanical advantage of a pulley?

The number of rope segments holding up the moving block, ignoring friction. A fixed pulley alone has an MA of 1, a movable pulley 2.

Sources

Written, edited and reviewed by Rory Hansen.

Added and reviewed 15 October 2026. What's new