Lever Calculator
Give me a place to stand, said Archimedes, and I shall move the Earth — the price list for that boast is this page. Enter the load and the two arm lengths, and the calculator returns the effort the lever demands and the mechanical advantage it grants.
Torque Balance: The Whole Law
A lever in balance is two torques in a tie: the load's weight times its distance from the fulcrum equals the effort times its distance — effort = load × load arm ÷ effort arm — and everything else is commentary. The mechanical advantage is the same ratio read backwards (effort arm ÷ load arm), and the note names the conservation law hiding under the bargain: what the lever returns in force it collects in distance, so the work in equals the work out (minus friction's toll), which is why no arrangement of sticks and stones will ever lift the Earth for free — Archimedes' hypothetical lever trades an unreachable force for an unusable travel distance, and this calculator prices both sides of that trade for any real stick you own.
Worked Example: Two Hundred Newtons, a Child's Push
The defaults rig a garden problem: a 200 N load (a heavy stone, a loaded barrow's handles) sitting 0.5 m from the fulcrum, with 2 m of bar on your side. Effort = 200 × 0.5 ÷ 2 = 50.0 N — the push of a firm hand — at a mechanical advantage of 4.00. The distance clause collects its fee immediately: to raise the stone 10 cm your end of the bar sweeps 40 cm, and a long lift becomes a pumping exercise of repeated short strokes, exactly as anyone who has levered a stump with a crowbar knows in their shoulders. Move the fulcrum to 0.25 m and the effort halves to 25 N while the sweep doubles — the calculator's two arms are the only variables, and the fulcrum's position is the entire art.
The Three Classes, One Equation
Levers sort by which element sits in the middle. Class 1 (fulcrum central — seesaw, crowbar, this page's picture) can multiply force or distance depending on the arms. Class 2 (load central — wheelbarrow, nutcracker) always multiplies force, because the effort arm is necessarily the longer. Class 3 (effort central — tweezers, the human forearm) always divides force, buying speed and range: your biceps pulls at a few centimetres from the elbow while the hand sweeps at thirty, an MA near 0.15 that the calculator would call a terrible lever and evolution calls a throwing arm. The equation never changes — only the arm assignment does — and the classes are a filing system for a single torque balance wearing three costumes.
The Steelyard: A Lever That Weighs
For two thousand years commerce ran on this equation in its steelyard costume: a beam with the load hung close to the fulcrum and a single known counterpoise slid along the long arm until torques tie — the poise's position is the weight, read off a graduated beam, no set of standard weights required. Roman merchants, Chinese traders and every scrapyard into the industrial age weighed with a sliding lever, because one accurate rider beats a bag of iron discs for portability. The calculator is the steelyard's algebra with the beam removed: whatever pair of arms you enter, the balance condition answers — and the antique's continued use in places without batteries is a working review of the principle's durability.
Tongue Weight and the Trailer Hitch
A trailer hitched to a car is this page on wheels: the coupler sits behind the rear axle, so the tongue weight acts on a short load arm while the car's wheelbase is the effort arm that the front axle's grip must answer — too much tongue load and the lever lifts the steering axle's share toward uselessness, too little and the trailer's own pendulum takes charge. Weight-distribution hitches are deliberate lever surgery, spring bars prying load forward onto the front axle by exactly the torque bookkeeping the calculator performs. It is the same audit as the crowbar's — arms, a fulcrum, a balance of torques — conducted at motorway speed, which is why the numbers deserve to be run before the journey rather than discovered during it.
The Crowbar's Working Day
Site folklore says the crowbar is the oldest tool still in daily professional use, and its working geometry is the worked example with worse footing: the bar's curve exists to place the fulcrum (the bar's own belly, or a block slipped beneath) within centimetres of the nail or the slab's edge, buying mechanical advantages of twenty or more in a tool that fits one hand. Every demolition crew member has an intuitive PhD in the calculator's trade — when the load arm cannot shrink further, they lengthen the effort arm with a pipe slipped over the bar ('cheater bar' is the trade's honest name) and feel the torque balance relent in exact proportion. The page dignifies the folklore with its numbers: arms in metres, loads in newtons, advantage as a quotient — the site hut's arithmetic, formalised.
Related Tools
More from the Physics Calculators hub: the Force Calculator for the newtons themselves, and the Friction Calculator — the toll every real fulcrum quietly collects.
Frequently Asked Questions
What did Archimedes actually need to move the Earth?
Run his boast through this page: Earth's weight is about 5.9 × 10²⁵ N; a strong human pushes with perhaps 600 N, so the required mechanical advantage is near 10²³ — an effort arm 10²³ times the load arm. Keep the load arm at 1 m and the effort arm stretches some ten million light-years; push your end at a metre per second and the Earth moves one metre in about 3 trillion years. The calculator's arithmetic, extrapolated, is the honest footnote to the most famous sentence in mechanics: the lever law has no force limit, only a distance invoice, and the invoice is where boasts go to be audited.
Where should the fulcrum go for maximum advantage?
As close to the load as the geometry allows — the load arm is the divisor's partner, and halving it doubles the advantage — subject to three practical taxes: the bar must not bend or snap under the concentrated torque (strength sets a floor under useful closeness), the load needs room to actually rise (a fulcrum touching the load leaves no travel), and the effort end needs ground clearance for its long sweep. Real levering is the negotiation among those taxes; the calculator gives the ideal each negotiation departs from, which is the correct division of labour between arithmetic and mud.
Does the lever's own weight matter?
Yes, and increasingly as the bar lengthens toward Archimedean absurdity: a uniform bar's weight acts at its centre, adding its own torque to the ledger — helping when the long end is yours and the bar's mass leans your way, hindering when you must first lift the bar itself. Precision work (balances, steelyards) accounts for it explicitly; garden work folds it into the fudge. The calculator computes the massless ideal; treat heavy bars as a second load located at their midpoint and add the two torque demands — the same equation, one more term, as physics always permits.
How is a lever different from a pulley or a ramp?
It isn't, in the ledger that matters: all simple machines trade force against distance under the same conservation law, differing only in geometry. The ramp spreads the lift along a slope (advantage = slope length ÷ height), the pulley redirects and (in gun-tackle arrangements) multiplies by rope count, the screw is a ramp wrapped on a cylinder, the wheel-and-axle is a lever that never runs out of arm. Learn the lever's torque balance cold — this page's whole content — and the family resemblance becomes unmistakable: one equation, several costumes, no free lunches anywhere in the wardrobe.
What is the mechanical advantage of the human arm?
About 0.1–0.15 for loads in the hand: the biceps inserts roughly 4–5 cm from the elbow joint while the hand rides at 30–35 cm, so the muscle must pull with seven to ten times the load's weight — which is why holding a 10 kg bag at arm's length (about 100 N of load) demands on the order of 700 to 1,000 N of biceps tension and fails within the minute. Evolution paid that force tax to buy hand speed (the hand moves seven times the muscle's shortening) — the throwing, striking, tool-swinging bargain of a Class 3 lever, priced by exactly this calculator's ratio with the arms assigned by anatomy.
Can a lever multiply energy or power?
Never energy — the distance clause forbids it — and power only in the accountant's sense of rate redirection: a lever can deliver a brief high force from a slow accumulation (the catapult's arm, storing work over a long wind and releasing it in a snap), which feels like power multiplication and is really time-shifting. The calculator's statics cannot see time; the note's distance bookkeeping is where the energy audit lives. Any machine, ancient or modern, that appears to break the tie between the two sides of this page's equation is hiding an energy store or a fuel line — look for those first, as investigators of perpetual motion have learned to do.