Pulley System Calculator

Mechanical advantage, effort force, velocity ratio, and efficiency for fixed, movable, block-and-tackle, and compound pulleys.

Block and Tackle — MA = n (rope segments)

Load Weight W (N)

51.0 kg · 112.4 lbf

Supporting Rope Segments n

IMA = n (number of rope segments supporting the load)

Rope/Pulley Efficiency η (%)

Ideal MA (IMA)4.00

Actual MA (AMA = IMA × η)3.600

Effort Force F_e = W / AMA138.89 N (14.16 kg)

Velocity Ratio (rope / load distance)4.0 : 1

Work input (per unit load motion)555.56 N·m

Work output500.00 N·m

Power loss to friction10.0%

What This Calculator Does

A pulley system trades distance for force. This calculator computes the ideal mechanical advantage (IMA), actual mechanical advantage (AMA) accounting for friction losses, the required effort force to lift a given load, and the velocity ratio (how much rope must be pulled per unit of load travel). Supports fixed pulleys (MA=1, direction change only), movable pulleys (MA=2), block and tackle (MA=n rope segments), and compound multi-stage systems.

It combines Load Weight, Supporting Rope Segments (n), Efficiency η (%) to estimate Ideal MA (IMA), Actual MA (AMA), Effort Force.

Formula & Method

Ideal mechanical advantage:

IMA = n

(number of supporting rope segments). Actual mechanical advantage:

AMA = IMA \times \eta

where

\eta

is efficiency. Effort force:

F_e = W / AMA

. Velocity ratio:

VR = IMA

(rope pulled / load distance). Work input

W_{in} = F_e \times d_{rope}

, work output

W_{out} = W \times d_{load}

, efficiency

\eta = W_{out} / W_{in}

Notation used in the formulas: $R$ = Ideal MA (IMA); $x_{1}$ = Load Weight; $x_{2}$ = Supporting Rope Segments (n); $x_{3}$ = Efficiency η (\%).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

Block and tackle — 4 rope segments, 600 N load, 90% efficiency

IMA = 4, η = 0.90 AMA = 4 × 0.90 = 3.6 Effort force = 600 / 3.6 = 166.7 N To lift load 1 m, you pull 4 m of rope. Power loss = (1 − 0.90) × 600 = 60 N·m per metre of lift.

Reference Book

Engineering Mechanics: Statics & Dynamics

Russell C. Hibbeler · Pearson

A standard mechanics reference for torque, pulleys, equilibrium, load balance, and rigid-body reasoning.

View Book

Inputs Used

Load Weight: Used directly in the calculation.
Supporting Rope Segments (n): Used directly in the calculation.
Efficiency η (%): Used directly in the calculation.

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