Lever Calculator
Enter the lever class, the forces and arm lengths you know, and this calculator finds the missing value instantly. Choose which quantity you want to solve for, pick metric or imperial units, and see the full step-by-step working alongside a diagram of your lever.
Formula
Worked example
A Class 1 crowbar with an effort arm of 1.2 m and a load arm of 0.3 m gives MA = 1.2 / 0.3 = 4. To lift a 200 N rock you only need 200 / 4 = 50 N of effort. The moments balance: 50 N x 1.2 m = 200 N x 0.3 m = 60 N·m.
What is a lever?
A lever is one of the six classical simple machines. It consists of a rigid bar or beam that pivots around a fixed point called the fulcrum. By applying a force (the effort) at one point on the bar, you can move a larger or smaller force (the load) at another point. The key principle is the law of the lever, first stated by Archimedes: the product of the effort force and its distance from the fulcrum equals the product of the load force and its distance from the fulcrum. Written as an equation: effort x effort arm = load x load arm. This moment balance is why a small effort applied far from the fulcrum can lift a large load close to it.
The three lever classes
Levers are classified by where the fulcrum sits relative to the effort and the load. A Class 1 lever has the fulcrum between effort and load, like a seesaw, crowbar, or scissors. The mechanical advantage can be less than, equal to, or greater than 1 depending on the arm lengths. A Class 2 lever has the load between the fulcrum and the effort, like a wheelbarrow or nutcracker. The effort arm is always longer than the load arm, so MA is always greater than 1: you always gain a force advantage at the cost of travel distance. A Class 3 lever has the effort between the fulcrum and the load, like tweezers or the human forearm. The effort arm is always shorter than the load arm, so MA is always less than 1: you apply more force than you need, but the load moves faster and farther than the effort point.
Mechanical advantage explained
Mechanical advantage (MA) is the ratio of load force to effort force. An MA of 5 means the lever magnifies your applied force five times: a 20 N effort lifts a 100 N load. Equivalently, MA equals the ratio of effort arm to load arm. For example, if the effort arm is 2 m and the load arm is 0.5 m, then MA = 2 / 0.5 = 4. Note that levers obey the law of conservation of energy: although you apply less force with a high-MA lever, you must push the effort end through a proportionally longer distance. The energy (force times displacement) on both sides remains equal for an ideal, frictionless lever.
Real-world applications
Levers appear throughout everyday life and engineering. Crowbars and pry bars are Class 1 levers used to multiply force when opening crates or removing nails. Wheelbarrows and nutcrackers are Class 2 levers that let you lift heavy loads or crack hard shells with modest effort. The human forearm is a Class 3 lever - the bicep muscle applies effort close to the elbow fulcrum to move the hand farther away, trading force for speed. In vehicles, the brake pedal is a Class 2 lever that amplifies foot pressure into hydraulic braking force. Engineers design levers with specific MA values to match the force and speed requirements of each task.
Lever classes and their properties
| Class | Fulcrum position | MA range | Common examples |
|---|---|---|---|
| Class 1 | Between effort and load | Any (< 1, = 1, or > 1) | Seesaw, scissors, crowbar, pliers |
| Class 2 | Load between fulcrum and effort | Always > 1 | Wheelbarrow, nutcracker, bottle opener |
| Class 3 | Effort between fulcrum and load | Always < 1 | Tweezers, forearm, fishing rod, tongs |
Summary of the three lever classes with everyday examples and mechanical advantage range.
Frequently asked questions
What is mechanical advantage and how is it calculated?
Mechanical advantage (MA) is the factor by which a lever multiplies your applied force. It equals the load force divided by the effort force: MA = load / effort. You can also calculate it from the arm lengths alone: MA = effort arm / load arm. An MA of 3 means you only need to apply one third of the load force to move the load - but you must push the effort end three times farther than the load moves.
What is the difference between the three lever classes?
The three classes differ in where the fulcrum is positioned. Class 1: fulcrum between effort and load (crowbar, scissors). MA can be above or below 1. Class 2: load between fulcrum and effort (wheelbarrow). MA is always greater than 1, meaning the lever always multiplies your force. Class 3: effort between fulcrum and load (tweezers, forearm). MA is always less than 1, meaning you apply more force than the load, but gain speed.
How do I find the effort force needed to lift a load?
Use the law of the lever: effort = load x load arm / effort arm, or equivalently effort = load / MA. For example, to lift a 300 N load with an effort arm of 1.5 m and a load arm of 0.5 m, the effort needed is 300 x 0.5 / 1.5 = 100 N. Select "Solve for: Effort force" in this calculator and enter the load force and the two arm lengths.
What happens to mechanical advantage if I move the fulcrum?
Moving the fulcrum changes both arm lengths simultaneously. For a Class 1 lever, sliding the fulcrum toward the load shortens the load arm and lengthens the effort arm, increasing the mechanical advantage and making it easier to lift. Moving the fulcrum toward the effort does the opposite, reducing MA. The same principle applies to positioning the load on a Class 2 lever or the effort on a Class 3 lever.
Does a lever with a high mechanical advantage violate conservation of energy?
No. While a high-MA lever reduces the effort force needed, the effort must travel a proportionally longer arc. Work equals force multiplied by displacement, and for an ideal frictionless lever the work input always equals the work output. A lever is a force multiplier, not a free energy source. In practice, friction and the weight of the lever itself mean the actual mechanical advantage is always slightly less than the ideal (geometric) value.
What is a moment or torque in the context of a lever?
A moment (also called torque) is the turning effect produced by a force about the fulcrum. It equals the force multiplied by its perpendicular distance from the pivot: moment = force x arm length. For a lever in equilibrium, the clockwise moment equals the anticlockwise moment: effort x effort arm = load x load arm. This is the law of the lever and the equation behind all the calculations in this tool.