Pulley Calculator
Choose between two modes: Belt Drive calculates the output RPM, belt speed, belt length, torque, and power for a two-pulley system; Pulley Block finds the mechanical advantage, effort force, and rope length needed to lift a load. Results update as you type.
What is a pulley?
A pulley is a wheel on an axle designed to carry a belt, rope, or cable. Pulleys appear in two fundamentally different roles in engineering. In a belt drive, two or more pulleys transmit rotational motion and torque between shafts; the ratio of their diameters determines whether the output shaft spins faster or slower than the input. In a block and tackle (pulley block), one or more rope-and-sheave assemblies multiply the force available to lift a load, trading distance for force. Both applications rely on the same core physics: power equals force times velocity, and that product is conserved (minus friction losses).
Belt drive: speed ratio, torque, and belt length
For a two-pulley belt drive the speed relationship is simple: driver diameter times driver RPM equals driven diameter times driven RPM (d1 x n1 = d2 x n2). A smaller driven pulley spins faster (speed increase); a larger one spins slower (speed reduction). Torque behaves in the opposite direction: doubling the speed halves the torque, and vice versa, because power stays constant in an ideal system. Belt speed is the tangential velocity at the rim (pi x d1 x n1 / 60 in m/s). Belt length for an open drive follows L = pi(d1+d2)/2 + 2C + (d1-d2)^2 / 4C, where C is the center distance. Crossed belts use a slightly different formula. When ordering, add 1-2% to allow for tensioning. Belt speed should stay within the manufacturer rating, typically 25-30 m/s for standard V-belts and up to 50 m/s for high-speed flat belts.
Block and tackle: mechanical advantage and efficiency
A block and tackle multiplies force by routing a rope through multiple sheaves. The ideal mechanical advantage (MA) equals the number of rope segments pulling upward on the lower (moving) block. With four segments the effort needed is one quarter of the load - in theory. In practice, each sheave introduces friction, so real efficiency is always below 100%. A useful approximation is to multiply the ideal MA by the overall system efficiency (e.g. 90% for well-lubricated metal sheaves). Efficiency per sheave is typically 96-98% for ball-bearing blocks; compound efficiencies drop the overall figure noticeably as segment count grows. The trade-off for easier lifting is that you must pull more rope: rope length pulled = load travel x number of segments.
Choosing the right pulley configuration
For a belt drive, choose the diameter ratio to match the desired output RPM, then verify that the resulting belt speed is within ratings and that the center distance is practical. V-belt drives are preferred for most power transmission because the wedging action increases grip; flat belts suit higher speeds and cleaner environments. For a block and tackle, more rope segments means less effort but more rope to pull and lower overall efficiency per sheave. For rescue or recovery applications a 4:1 or 6:1 rig is common; industrial crane blocks often use 8:1 to 12:1. Always select components rated to a minimum 5:1 safety factor above the working load limit.
Typical pulley block configurations
| Rope segments | Sheaves (total) | Ideal MA | Typical efficiency | Common use |
|---|---|---|---|---|
| 1 | 1 | 1 | 95-98% | Direction change only |
| 2 | 2 | 2 | 90-95% | Light lifting, halyard |
| 3 | 3 | 3 | 85-92% | Small boats, rigging |
| 4 | 4 | 4 | 80-90% | Rescue, off-road recovery |
| 5 | 5 | 5 | 75-88% | Construction, cranes |
| 6 | 6 | 6 | 70-85% | Heavy industrial |
Rope segments, sheave count, ideal mechanical advantage and typical efficiency for standard block and tackle rigs.
Frequently asked questions
How do I calculate pulley RPM from diameter?
Use the basic ratio: output RPM = input RPM x (driver diameter / driven diameter). For example, a 150 mm driver at 1450 RPM turning a 300 mm driven pulley gives 1450 x (150/300) = 725 RPM. Enter your values in the Belt Drive mode above for an instant result.
What is belt speed and why does it matter?
Belt speed is the linear velocity of the belt at the pulley rim (pi x diameter x RPM / 60 in m/s). Exceeding the belt rating causes rapid wear, heat buildup, and can cause the belt to slip or fail. Standard V-belts are rated to about 25-30 m/s; high-performance flat belts can reach 50 m/s. If your calculated belt speed is too high, increase the pulley diameters or reduce RPM.
How do I find the belt length I need to buy?
Enter both pulley diameters and the center-to-center distance in Belt Drive mode. The calculator uses the standard open-belt formula L = pi(d1+d2)/2 + 2C + (d1-d2)^2 / 4C. When ordering, round up and add 1-2% for initial tension and settling.
What is the mechanical advantage of a block and tackle?
The ideal mechanical advantage equals the number of rope segments supporting the lower (moving) block. A four-segment rig gives an ideal MA of 4, meaning you need only one quarter of the load force to lift it. In practice, friction reduces this. Enter your segment count and efficiency percentage in Pulley Block mode to get the actual effort required.
How does pulley efficiency affect my calculations?
Every sheave in a block and tackle has friction, typically reducing efficiency by 2-5% per sheave depending on bearing type and lubrication. The overall efficiency is approximately the per-sheave efficiency raised to the power of the number of sheaves. For a 6-segment rig with 96% per-sheave efficiency, overall efficiency is about 0.96^6 = 0.78 or 78%. The Pulley Block mode uses a single overall efficiency figure for simplicity.
Can I use a pulley system to increase speed instead of force?
Yes. In a belt drive, putting a smaller pulley on the output shaft increases output speed and decreases torque. For a block and tackle the arrangement is reversed: to increase speed at the output you reduce mechanical advantage, meaning you need to apply more force than the load. This is sometimes called a gun tackle in reverse and is used in some sailing applications.