Pulley Calculator

Mechanical advantage, belt length, RPM, acceleration, and force for fixed, movable, and compound pulley systems.

Mechanical Advantage (MA) = Load / Effort. For ideal systems (no friction), MA = number of rope segments supporting the load.

N

Belt Length (open) ≈ 2C + π(D+d)/2 + (D-d)²/(4C)

Speed Ratio = RPM₁/RPM₂ = D₂/D₁

mm

Acceleration for ideal Atwood machine: a = (m₂ - m₁)g / (m₁ + m₂)

Positive means m₂ accelerates downward.

kg
kg
m/s²
m/s²

RPM = (Belt Speed) / (π × Diameter) [Belt speed in compatible units]

rev/min
m/s
Fixed pulley (100 N) Movable pulley (200 N) Belt: 150→300 mm Accel: 2 vs 8 kg RPM: 250 mm @15 m/s
Computing...

Understanding Pulley Systems

A pulley (or sheave) is a wheel on an axle designed to support movement and change direction of a taut cable or belt, or transfer power between the shaft and cable . Pulley systems are fundamental in mechanical engineering for lifting loads and transmitting power.

Fixed Pulley

Attached to a support; changes direction of force but offers no mechanical advantage (MA = 1). Ideal for lifting where pulling down is easier .

Movable Pulley

Attached to the load; provides MA = 2 (ignoring friction). The load is shared between two rope segments .

Compound / Block & Tackle

Combines fixed and movable pulleys. MA equals the number of rope segments supporting the load. For example, a three-pulley block and tackle gives MA = 3 or 4 depending on configuration .

Belt Drive

Transmits power between shafts. Speed ratio is inversely proportional to diameter. Belt length must accommodate center distance .

Formulas & Mechanical Advantage

Configuration Ideal MA Effort for 100 N Load
Fixed pulley 1 100 N
Movable pulley 2 50 N
Two-pulley compound 3 or 4 33.3 N or 25 N
Block & tackle (3 sheaves) 6 16.7 N

Velocity Ratio (VR) = distance moved by effort / distance moved by load. For ideal frictionless systems, MA = VR. Real systems include efficiency η, so actual MA = ideal MA × η/100 .

Belt Drive Equations

For two pulleys with diameters D₁ (driver) and D₂ (driven), center distance C, the approximate open belt length is :

L ≈ 2C + (π/2)(D₁ + D₂) + (D₁ - D₂)²/(4C)

Speed ratio: RPM₁ / RPM₂ = D₂ / D₁ (ignoring slip).

Acceleration in Pulley Systems

For a simple Atwood machine (two masses over frictionless pulley), acceleration is given by :

a = (m₂ - m₁)g / (m₁ + m₂)

Tension T = (2 m₁ m₂ g) / (m₁ + m₂). If pulley has mass or friction, effective acceleration reduces.

RPM and Belt Speed

Given belt speed v (m/s) and pulley diameter D (m), RPM = v / (π D) . Conversely, belt speed v = π D × RPM / 60.

Applications

  • Cranes & Hoists: Block and tackle systems multiply force to lift heavy loads.
  • Conveyor Systems: Belt drives transfer power over distances.
  • Engines: Serpentine belts drive alternators, water pumps.
  • Exercise Equipment: Cable pulley systems in gyms.

Frequently Asked Questions

Friction in bearings and rope bending reduces output. Efficiency η (0-100%) multiplies ideal mechanical advantage. For example, a 4:1 block with 90% efficiency gives actual MA = 3.6:1.

Mechanical Advantage (MA) = Load/Effort. Velocity Ratio (VR) = distance moved by effort / distance moved by load. In ideal systems, MA = VR. In real systems, MA = VR × efficiency.

For crossed belt, use L = 2C + (π/2)(D₁ + D₂) + (D₁ + D₂)²/(4C). This calculator uses open belt formula; crossed belt is similar but with + sign inside the squared term.

Yes, the belt length formula is a good approximation for V-belts. For precise length, refer to manufacturer standards as V-belts have pitch length and require specific pulley groove dimensions.