About the Lever Calculator
This lever calculator solves the law of the lever — effort × effort arm = load × load arm — for whichever of the four quantities you are missing. Pick the class of lever, enter three known values, and it returns the fourth along with the mechanical advantage, the overall beam length and a check that your arm lengths make sense for that class.
It suits physics and engineering students learning about moments and simple machines, as well as anyone working out how long a pry bar needs to be, where to put the fulcrum under a heavy stone, how hard to push a wheelbarrow, or how much force a muscle must produce to hold a weight in the hand. The table shows how the required effort changes as the effort arm gets longer.
Arm lengths are measured from the fulcrum (pivot) to where each force acts, perpendicular to the force. The calculation is for a lever in static balance and ignores the weight of the bar itself and friction at the pivot, so a real lever needs slightly more effort to start moving the load. Forces are in newtons and lengths in metres, but any consistent units work.
How to use the lever calculator
- 1Choose the lever class that matches your setup.
- 2Choose which quantity you want to find.
- 3Enter the other three values, measuring each arm from the fulcrum.
- 4Read the answer, the mechanical advantage and the class check.
- 5Use the chart to see how a longer effort arm reduces the effort needed.
Formula and method
A lever is in balance when the turning moments about the fulcrum are equal: the effort force times its distance from the fulcrum equals the load force times its distance. Rearranging gives any one of the four quantities from the other three, for example effort = load × load arm ÷ effort arm. The mechanical advantage is the ratio of the arms, d_e ÷ d_l.
The class only changes where the parts sit. In class 1 the fulcrum is between effort and load, so the beam is at least d_e + d_l long and the advantage can be above or below 1. In class 2 the load sits between, so d_l < d_e and the advantage is always above 1. In class 3 the effort sits between, so d_e < d_l and the advantage is below 1, trading force for speed. The model ignores the beam’s own weight and pivot friction.
- F_e
- Effort force applied
- F_l
- Load force (resistance)
- d_e
- Effort arm: fulcrum to where the effort acts
- d_l
- Load arm: fulcrum to where the load acts
- MA
- Mechanical advantage
Worked examples
Crowbar lifting a 500 N load
With the load 0.5 m from the fulcrum and the effort 2 m away, effort = 500 × 0.5 ÷ 2 = 125 N. The mechanical advantage is 2 ÷ 0.5 = 4, and the bar must be at least 2.5 m long.
Wheelbarrow (class 2) carrying 800 N
The load’s centre of gravity is 0.4 m from the wheel and the handles are 1.2 m from it, so lifting needs 800 × 0.4 ÷ 1.2 ≈ 266.7 N — one third of the load.
Forearm (class 3): what can the biceps hold?
The biceps attaches about 4 cm from the elbow and the hand is 35 cm away. A 600 N muscle force supports 600 × 0.04 ÷ 0.35 ≈ 68.6 N (about 7 kg) in the hand — a mechanical advantage of only 0.114.
How long an effort arm to lift 1,000 N with 250 N?
Effort arm = 1,000 × 0.3 ÷ 250 = 1.2 m. With a 0.3 m load arm the bar needs to be at least 1.5 m long.
Frequently asked questions
What is the law of the lever?+
The law of the lever, described by Archimedes, says a lever balances when effort × effort arm equals load × load arm. A small force far from the fulcrum can balance a large force close to it.
What are the three classes of levers?+
Class 1 has the fulcrum between effort and load (seesaw, crowbar). Class 2 has the load in the middle (wheelbarrow, nutcracker). Class 3 has the effort in the middle (tweezers, broom, the human forearm).
How do you calculate the mechanical advantage of a lever?+
Divide the effort arm by the load arm. A 2 m effort arm and a 0.5 m load arm give a mechanical advantage of 4, so the effort needed is one quarter of the load.
Why would anyone use a class 3 lever?+
Class 3 levers have a mechanical advantage below 1, but the load end moves farther and faster than the effort. That is useful for throwing, swinging and quick movements, which is why most limb joints work this way.
Does the weight of the lever matter?+
Yes, for heavy bars. The bar’s weight acts at its centre of gravity and adds its own moment. This calculator ignores it, so add the bar’s moment to the load side (or effort side) if it is significant.