How this instrument works
Levers multiply force by trading distance for it. Turning moment about a pivot is force times perpendicular arm, so a load sitting 0.4 m from its fulcrum and an effort applied 2 m out balance when effort runs one fifth of load. Archimedes set this down around 250 BCE in On the Equilibrium of Planes, deriving it from symmetry axioms rather than measurement — and Pappus of Alexandria later credited him with that boast about shifting Earth, given somewhere to stand.
Engineers sort levers into three classes by which part sits in between. Fulcrum between load and effort gives you crowbars, claw hammers, scissors. Load in between gives you wheelbarrows and nutcrackers. Effort in between gives you tweezers, fishing rods, and your own forearm — one class that multiplies force by less than unity, deliberately. Your biceps inserts roughly 50 mm past your elbow while your palm sits near 300 mm out, so gripping 5 kg of dumbbell costs that tendon around 300 N of tension.
Two assumptions prop this arithmetic up. First, it is statics: an equilibrium condition, not a motion, silent on how fast anything travels. Second, each arm must be measured perpendicular to its force line — shove at 30° to your bar and only half that push counts, because moment arm is d·sinθ. Real bars also flex, weigh something, and grind at their pivot, each costing some few percent. Energy is never manufactured: whatever factor you win in force, you repay in travel.
- Enter Load force — weight or resistance you need to shift — in newtons, kilonewtons, or pounds-force.
- Set Load distance from fulcrum: pivot to load, measured square to that force, not along a tilted bar.
- Set Effort distance from fulcrum on your side of that pivot. Longer arm, lighter work.
- Read Effort force needed. Divide it into Load force to get mechanical advantage.
- Nudge either arm to see how quickly advantage scales — it is linear in both.
Worked example — prying up a 51 kg paving slab
A concrete slab bears down with 500 N, near enough 51 kg. You slide a steel bar beneath one edge, wedge a brick as fulcrum 0.4 m back from that edge, and grip your bar 2 m beyond that brick. Load force 500 N, Load distance from fulcrum 0.4 m, Effort distance from fulcrum 2 m gives 500 × 0.4 ⁄ 2 = 100 N. Effort force needed: 100 N, roughly 10 kgf — a one-handed lean.
Two consequences deserve attention. Your hands travel five times as far as that slab rises, so lifting an edge 20 mm means pressing 100 mm down. And your brick carries both forces at once: 500 N of concrete plus 100 N of you, 600 N crushing through one contact patch about coin-sized. Fulcrums crumble far more often than bars bend.
Questions
Why is a moment measured in newton metres and not joules?
Because torque is not energy, though both reduce to kg·m²/s². Moments multiply force by an arm at right angles to it; work multiplies force by distance along it. NIST SP 811 asks that joules stay reserved for energy and heat, so moments stay newton metres. Your 500 N load at 0.4 m exerts 200 N·m about its pivot while nothing has moved at all.
Does a lever create extra energy?
No. Force multiplied is distance divided, exactly. Five-to-one levers cut effort to one fifth and make your hand sweep five times further, so work in equals work out. Friction at that pivot and flex along its bar make real levers give back slightly less than you feed them. Nothing gives back more.
Where exactly do I measure arm lengths from?
From your fulcrum, along a line perpendicular to each force — never load-to-hand, and never simply along a tilted bar. This is where most lever arithmetic quietly goes wrong. Should your push meet a bar at angle θ rather than square on, effective arm becomes d·sinθ, so a 30° shove contributes only half what its raw length suggests.
What if my effort arm is shorter than my load arm?
Mechanical advantage then drops below one and you supply more force than you shift — on purpose, in a great many tools. Tweezers, chopsticks, a fishing rod, and your forearm all work this way, buying tip speed and reach in exchange for muscle. Enter such a case anyway; identical arithmetic applies, and Effort force needed simply exceeds Load force.
How much force does a fulcrum itself take?
On a class-one lever, with load and effort straddling opposite sides, that pivot carries their sum: 500 N plus 100 N makes 600 N. Anyone sizing a pin or blade edge for load alone has undersized it. On a class-two lever such as a wheelbarrow, effort and load act in opposing senses at that axle, so reaction becomes a difference instead.
Can I use this for a seesaw or a torque wrench?
Yes — both balance on that same moment equation. For a seesaw, enter one child's weight as Load force with their seat distance, then read what a partner must weigh at whatever distance they choose. For a wrench, treat bolt axis as pivot and handle length as Effort distance from fulcrum; grip closer in and your knuckles pay for it.