The lever calculator above balances the two turning effects acting on a rigid bar about its fulcrum and solves for whichever quantity you are missing — the effort force, the load it can move, or either arm length. It also reports two figures that most lever calculators leave out: the force pressing on the fulcrum itself, which is what actually breaks pivots in practice, and the distance the effort end has to travel to move the load the distance you specified.
Arb Digital builds free calculators that each own one job. This page owns the lever specifically. The site's torque calculator computes a single turning moment from a force, a distance and an angle; this page sets two opposing moments equal to each other and rearranges. The mechanical advantage calculator compares the force ratio across machine types generally, while this page stays with the bar and the pivot and adds the reaction force that only a lever has.
What This Lever Calculator Does
A lever is in balance when the load's moment about the fulcrum equals the effort's moment about the same point. That single statement, Fe × de = Fl × dl, contains four quantities, so knowing any three gives you the fourth. The solve-for selector picks which one is the unknown, and the hero label always names it so there is no ambiguity about what you are reading.
The class selector does not change the equation. It changes the geometry, and through the geometry it changes the fulcrum reaction and what mechanical advantages are achievable. A first class lever has the fulcrum between the effort and the load, so both forces push the same way and the pivot carries their sum. A second class lever puts the load between, so the fulcrum carries the difference. A third class lever puts the effort between, which forces the effort arm to be shorter than the load arm and guarantees a mechanical advantage below one.
The tool checks the geometry against the class you chose. Ask for a second class lever with an effort arm shorter than the load arm and it will say so, because that arrangement is physically a third class lever wearing the wrong label. This is a common slip when someone measures a real mechanism and assigns a class from memory rather than from where the pivot actually sits.
How to Use It
- Locate the fulcrum first. Both arm lengths are measured from it, and the class follows from whether the effort or the load lies between the fulcrum and the other point.
- Enter the load in whatever force unit you have. Newtons, kilograms-force and pounds-force are all accepted; a mass in kilograms becomes a load in kilograms-force directly.
- Enter both arm lengths in one unit. Only their ratio matters to the force answer, but the absolute lengths are needed for the travel figure.
- Pick what you are solving for. Solving for an arm length is the design question: how long a bar do I need to move this with the force I have?
- Check the fulcrum figure before you build anything. On a first class lever with a large mechanical advantage the pivot carries slightly more than the load itself, and pivots fail more often than bars do.
The Formula: How a Lever Is Calculated
The governing condition is that the net torque about the fulcrum is zero. OpenStax University Physics Volume 1, section 12.2 on examples of static equilibrium, works exactly this problem for a loaded meter stick and states the second equilibrium condition as the sum of all the torques about the pivot equalling zero. Written for two opposing forces on a bar, that becomes Fede = Fldl.
Mechanical advantage is the ratio of the two forces, which by rearrangement is also the ratio of the two arms: MA = Fl/Fe = de/dl. OpenStax College Physics 2e, section 9.5 on simple machines, defines mechanical advantage as the ratio of output to input force magnitudes for any simple machine and gives the lever's value as the input lever arm divided by the output lever arm.
Work the default values. A 500 N load sits 0.4 m from the fulcrum and you push 1.6 m out on the other side. The mechanical advantage is 1.6 ÷ 0.4 = 4, so the effort needed is 500 ÷ 4 = 125 N. Both forces press downward on their own sides of a first class fulcrum, so the pivot carries 500 + 125 = 625 N. To raise the load 0.1 m, the effort end must travel 0.1 × 4 = 0.4 m.
The Fulcrum Carries More Than You Think
This is the number that gets left out of textbook lever problems and then causes failures in real ones. On a first class lever the effort and the load both press toward the fulcrum from opposite sides, so the pivot reaction is their sum. Crowbar a 2 kN load with a mechanical advantage of 10 and you apply 200 N, but the pivot point is carrying 2.2 kN — and it is carrying it through whatever small contact patch the bar happens to be resting on.
A second class lever is gentler on its pivot. The load sits between the fulcrum and the effort, and the effort lifts while the load presses down, so the fulcrum takes the difference rather than the sum. A wheelbarrow with a 600 N load and a 200 N lift puts 400 N through the wheel axle. That is one of the reasons the arrangement is so common in hand tools: the pivot is the part you least want to over-stress.
A third class lever reverses the sign. The effort is between the fulcrum and the load and exceeds the load in magnitude, so the fulcrum is pulled rather than pushed. Your elbow is the clearest example — the biceps attaches close to the joint, lifts a load held far out at the hand, and the joint itself is loaded in tension by the difference. The tool states the direction in words rather than leaving you to interpret a minus sign.
Why Third Class Levers Exist At All
A third class lever always has a mechanical advantage below one, meaning you must apply more force than the load. That sounds like a bad trade until you look at the other half of the bargain: the load moves further and faster than the effort by the same ratio. Muscles are strong but they contract slowly and over a short distance, so the body deliberately trades force for reach and speed almost everywhere.
The forearm preset makes this concrete. A biceps attached about 50 mm from the elbow lifting a load 350 mm out at the hand has a ratio of 7 against it, so holding 50 N in the hand needs about 350 N of muscle tension. In exchange, a few centimetres of muscle contraction sweeps the hand through tens of centimetres. Tweezers, fishing rods, brooms and shovels all make the same trade for the same reason.
This is also why the mechanical advantage figure alone is a poor way to judge a mechanism. It tells you the force ratio and nothing about whether force was even the quantity you wanted to optimise. The mechanical advantage calculator covers the ratio across machine types; the useful question is usually which of force, speed or travel the design is actually buying.
What the Ideal Calculation Leaves Out
Everything here is an ideal rigid lever with a frictionless pivot and a weightless bar. Three things move a real result away from it. Pivot friction consumes part of the effort, and on a rough or corroded pivot it can be a significant fraction. The weight of the bar itself adds its own moment about the fulcrum, which helps a second class lever and hinders a first class one with a long effort arm. And a bar that flexes stores energy and changes the effective arm lengths as it bends.
The force directions also matter. The equation as used here assumes both forces act perpendicular to the bar. Push at an angle and only the perpendicular component contributes to the moment, so the effective arm shortens by the cosine of the departure from perpendicular. The torque calculator handles that angle term explicitly if your force is not square to the bar, and the net force calculator will resolve a set of forces into components first.
Finally, this is a statics calculation. It tells you the force needed to hold the system in balance, not to accelerate it. Lifting a load quickly needs more than the balance force, by whatever the inertia of the load demands, and a lever swung at speed also has to accelerate its own mass. Treat the result as the threshold below which nothing moves at all.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Measuring an arm from the wrong point — both arms run from the fulcrum, not from the load to the effort or from the end of the bar.
- Forgetting the fulcrum reaction — on a first class lever the pivot carries the sum of both forces, which is more than the load it is helping you move.
- Assigning a class from memory — the class is fixed by which of the three points lies in the middle, and a second class lever cannot have the shorter effort arm.
- Pushing at an angle and using the full arm length — only the component perpendicular to the bar creates a moment, so an angled push has a shorter effective arm.
- Expecting free force — the effort always travels further than the load by exactly the mechanical advantage, so nothing is gained in energy terms.
Related Free Tools From Arb Digital
For a single turning moment rather than a balance, use the torque calculator, and for bolted joints the bolt torque calculator. Compare the lever against other simple machines with the mechanical advantage calculator, the pulley calculator and the inclined plane calculator. Resolve angled forces first with the net force calculator, convert units with the force converter, and see the surface reaction side of a contact problem on the normal force calculator. Everything is indexed on the free online tools hub.
Frequently Asked Questions
Look at which of the three points sits between the other two. Fulcrum in the middle is first class, load in the middle is second class, effort in the middle is third class. The equation is the same for all three; the class determines the achievable advantage and the fulcrum reaction.
Always from the fulcrum. The load arm runs from the fulcrum to the point where the load acts, and the effort arm from the fulcrum to where you apply force. Measuring from the end of the bar or between the two forces gives the wrong ratio.
Because the pivot has to carry it, and pivots fail more often than bars do. On a first class lever the reaction is the sum of the effort and the load; on a second class lever it is the difference; on a third class lever the fulcrum is pulled rather than pushed.
Because the effort acts between the fulcrum and the load, which forces the effort arm to be shorter than the load arm. The trade is deliberate: you spend extra force to gain range and speed at the load end, which is exactly what limb muscles need.
No. The effort travels further than the load by exactly the mechanical advantage, so force multiplied by distance is the same at both ends. A lever redistributes a fixed amount of work; it never adds any.
In a real lever, yes. The bar's own weight acts at its centre of mass and adds a moment about the fulcrum, helping or hindering depending on which side that centre falls. This calculator treats the bar as weightless, so long heavy bars will differ from its answer.
Then only the perpendicular component of your force creates a moment, and the effective arm is the true arm multiplied by the sine of the angle between the force and the bar. Work that component out first, or use the torque calculator, which takes the angle directly.
This tool is provided for educational and estimating use. It solves an idealised static lever with a weightless rigid bar, a frictionless pivot and perpendicular forces, so treat its output as a physics result rather than a mechanical design. Anything that will carry a person or a significant load should be checked by a qualified engineer.
