Pulley Calculator — Honest Leverage
A block and tackle multiplies your pull by the number of rope segments holding the moving block — minus what friction steals. Enter the load, the segments and the system’s efficiency, and this calculator returns the effort required and the rope you will have to haul.
The Lever, Roped
The pulley is the hub's lever page translated into rope: each segment supporting the moving block carries the same tension, so n segments lift with n times the pull you apply — mechanical advantage n in the frictionless ideal, effort = W ÷ (n × efficiency) in the world. The conservation law collects its fee in distance: the load rises one metre for every n metres hauled, work in equals work out (plus friction's percentage), and no arrangement of sheaves cheats it. What the tackle buys is the shape of the effort — a tonne's weight becomes a person's pull, at walking pace, with control — which is why the machine, known to Archimedes and drawn by Leonardo, still rigs every boatyard, theatre and rescue litter. The calculator's four inputs are the rigger's whole arithmetic; the note's segment-counting rule is the one place beginners err, and it is printed where the error would occur.
Worked Example: A Tonne's Tenth, Nearly
The defaults rig a four-segment tackle (two double blocks) under a 1,000 N load at 90% system efficiency: effort = 1,000 ÷ (4 × 0.9) = 277.8 N — a firm two-handed pull of about 28 kg-force — and the load's 2 m lift costs 8 m of rope through the hands. The efficiency's role deserves the stare: at a frictionless 100% the effort would be 250 N, so friction's 10% tax here is 27.8 N — and with six sheaves of indifferent quality the tax compounds per sheave until elaborate tackles underperform simple ones, the paradox that caps practical rigs near six or eight segments. The calculator models system efficiency as one number because riggers carry it as one number (per-sheave figures multiply into it), and the note spends its sentence on the segment count, where the real mistakes live.
Gun Tackles, Luff Tackles and the Naming of Rigs
Sailors named the configurations like chess openings: a single fixed pulley (MA 1, direction change only — the flag halyard), a gun tackle (one double, one single: 3 segments, MA 3), a luff tackle (double + single with the pull from the moving block: 4), and the double tackle's six. The names encode the count the calculator asks for, because the count is the machine. Modern heirs — the climber's hauling system, the rescuer's 4:1 with progress-capture pulleys, the theatre's counterweight assist — run the same segment arithmetic with better bearings, which is to say a higher efficiency input. Plus ça change: the rope still must be hauled n metres per metre of rise, and a rigger who promises otherwise is selling the perpetual motion this page exists to price honestly.
The Theatre's Counterweights
Above every proscenium stage, scenery flies on this arithmetic inverted: the battens' loads hang from lines over loft blocks to a counterweight arbor, where stagehands stack iron until the system balances — the "pulley" here multiplies nothing, but its segments and friction decide how honestly the balance reads, and a flown wall that drifts betrays an efficiency or a count gone wrong somewhere in the rigging loft. Modern motorised hoists keep the same segment bookkeeping in their load cells. The calculator's four fields are, in this reading, a flyman's checklist: the load, the parts of line, the losses, and the travel — the last being the height of the grid, which no theatre has ever found sufficient. Behind the checklist stands the oldest bargain in mechanics, unchanged since the first rope was rove through the first block: strength is bought with distance, and the exchange rate is printed on the machine itself, in the count of its ropes.
The Well Sweep and the Ship's Windlass
Before engines, civilisation's heavy lifts ran on this page: the well sweep's counterweight is a lever-pulley hybrid, the ship's windlass multiplies sailors' push by drum radius against lever arms (segments' rotational cousin), and cathedral builders raised stones with treadwheel cranes whose rope reeving was a tackle in all but name — the masons' accounts record the parts of line as carefully as any modern load chart. The calculator's inputs were old when cathedrals were new; what has changed is the bearings (efficiency's climb from perhaps 70% in hemp-and-iron to the 90s in ball bearings) — two centuries of metallurgy expressed as a single percentage field.
Related Tools
More from the Physics Calculators hub: the Lever Calculator — the same trade of force for distance in rigid form — and the Spring Rate Calculator, for the elastic machine sharing this wave.
Frequently Asked Questions
How do I count the segments correctly?
Count the rope parts attached to or passing around the moving block — equivalently, the parts that shorten as the load rises. If the hauling part itself comes off the moving block (you pull upward, standing below the load's travel), it counts too; if it comes off the fixed anchor block after a final redirect, it does not add a segment, only a direction change. The test that never lies: pull one metre of rope and measure the load's rise — the reciprocal of the rise in metres is your n. The calculator trusts your count; this FAQ is how to deserve it.
Why does efficiency fall as I add sheaves?
Each sheave's bearing and each rope bend taxes the tension by a few percent, and the taxes multiply down the line of segments: the last segment of a many-sheave rig may carry barely half the first's tension, so the effective advantage saturates — an eight-sheave rig of 90%-per-sheave blocks delivers an MA nearer 5 than 8. Ball bearings, larger sheave diameters (gentler rope bending) and stiff modern rope all defend the percentage the calculator takes as its input. The rigger's optimisation is real: choose n where the marginal segment still pays, typically 4–6 for hand work.
Can a pulley system lift the person pulling?
Yes, with the geometry respected: bosun's chairs, climbing ascents and the classic self-haul (the puller sits in the moving system, adding their weight to the load side while their pull counts on the effort side, an accounting puzzle this page's formula settles if you enter the total moving weight and the true segment count). The hauling part in self-rescue rigs typically comes off the moving block, which is why the segment-counting FAQ leads with that case. The calculator's physics is neutral about who pulls; safety practice is not, and progress-capture (a ratchet or prusik that holds the load while the pull resets) is the difference between a machine and a trap.
What did Archimedes actually claim?
That with a compound pulley (the polyspastos) he could move the earth itself given a place to stand — and, in the attested demonstration, that he single-handedly launched a laden ship of Syracuse with a tackle while seated, "moving it as smoothly as if it were running through the sea," in Plutarch's telling. The claim is this page's formula with n large and confidence larger; the physics is sound (the Earth's answer would be a haul measured in ages, the distance fee again), and the calculator is the boast reduced to four fields and an efficiency discount Archimedes would have disputed and needed.
How does a crane relate?
A crane's hook block is this page industrialised: the wire rope reeved between the boom-tip sheaves and the hook block in 4, 6, 8 or more parts of line, the winch's line pull multiplied by the count into the hook's capacity — crane load charts literally rate by parts of line, and re-reeving for a heavier lift is the operator changing n. The calculator's segment model is the load chart's skeleton; add the block's own weight (a real term the chart includes) to the load input, and the arithmetic is the same one the lift director signs.
What is a Spanish Burton?
The connoisseur's rig: two tackles arranged so one hauls the other's moving block in a geometry that multiplies their advantages and adds a lateral pull into the bargain — historically used to exert enormous directional forces on ships (stepping masts, careening hulls) with hand power alone. Compound tackles generally are this page's formula staged twice, advantages multiplied and efficiencies multiplied too (0.9 × 0.9 = 0.81 before the counting starts), which is why the great rigs belong to eras rich in sailors and poor in winches. The calculator prices each stage; the burton is two runs of it, honestly compounded.
Is the mechanical advantage ever greater than the segment count?
Never in a simple tackle (efficiency only subtracts); compound systems — one tackle hauling another's hauling part — multiply their advantages (a 3:1 pulling a 4:1's rope gives 12:1 ideal), which the calculator models by multiplying the stages' (n × efficiency) products. Differential and worm-gear hoists escape the segment model entirely (their advantage is a gear ratio). The segment rule's jurisdiction is the single tackle honestly rigged, and its statement — advantage cannot exceed the count of shortening ropes — is the energy law wearing rope, unbroken since Syracuse.