Free Pulley Calculator

Analyzing a belt drive system that connects two pulleys requires handling multiple parameters: the rotational speed of each pulley, the belt length, tension, torque, and more. This online belt drive calculator (also functioning as a pulley RPM calculator and belt length calculator) streamlines those calculations by providing instant results for any two-pulley setup joined by a belt.

Understanding the Pulley System

A typical pulley arrangement includes a driver pulley (where power is applied) and a driven pulley (which receives motion via the belt). The two pulleys often have different diameters. The key parameters for each pulley are its diameter (twice the radius) and its angular velocity, usually expressed in revolutions per minute (RPM). The relationship between these quantities forms the foundation of the belt drive analysis.

Core Formulas Used by the Calculator

The tool implements several fundamental relationships:

Pulley Diameter and RPM Relation

For a system of two pulleys connected by a belt, the product of diameter and RPM is constant across both pulleys:

$$d_1 n_1 = d_2 n_2$$

Where $d_1$ and $n_1$ are the diameter and RPM of the driver pulley, and $d_2$, $n_2$ correspond to the driven pulley. This equation allows you to solve for any missing value when the other three are known.

Belt Speed (Velocity)

The linear speed of the belt can be derived from the driver pulley’s rotation:

$$v = \frac{\pi d_1 n_1}{60}$$

The factor 60 converts RPM (revolutions per minute) to revolutions per second so that velocity is expressed in meters per second when diameter is in meters.

Belt Length

The total belt length depends on both pulley diameters and the center distance $D$ between the two pulleys:

$$L = \frac{d_1 \pi}{2} + \frac{d_2 \pi}{2} + 2D + \frac{(d_1 - d_2)^2}{4D}$$

This formula assumes the belt is taut and follows the pulleys without slipping. The calculator can also work in reverse: given a known belt length, it can compute the required center distance.

Belt Tension

The tension in the belt is determined by the transmitted power $P$ and the belt speed:

$$F = \frac{P}{v}$$

Thus, if you know the power and the belt velocity, the calculator returns the tension force in newtons (or other units, depending on input).

Drive Torque and Driven Torque

Torque at each pulley is a function of power and its rotational speed:

$$T = \frac{P}{2\pi n / 60}$$

The driver torque $T_1$ uses $n_1$, and the driven torque $T_2$ uses $n_2$. Both are expressed in newton‑meters.

Worked Example: Step‑by‑Step Computation

Suppose you have a driver pulley with diameter $d_1 = 0.4\,\text{m}$ turning at $n_1 = 1000\,\text{RPM}$, a driven pulley with diameter $d_2 = 0.1\,\text{m}$, a center distance $D = 1\,\text{m}$, and transmitted power $P = 1500\,\text{W}$. The calculator follows these steps:

1. Driven pulley RPM
   Using $d_1 n_1 = d_2 n_2$:

   $$n_2 = \frac{d_1 n_1}{d_2} = \frac{0.4 \times 1000}{0.1} = 4000\,\text{RPM}$$

2. Belt speed

   $$v = \frac{\pi \times 0.4 \times 1000}{60} \approx 20.944\,\text{m/s}$$

3. Belt length

   $$L = \frac{\pi \times 0.4}{2} + \frac{\pi \times 0.1}{2} + 2 \times 1 + \frac{(0.4-0.1)^2}{4 \times 1} \approx 2.808\,\text{m}$$

4. Belt tension

   $$F = \frac{1500}{20.944} \approx 71.62\,\text{N}$$

5. Torque on driver pulley

   $$T_1 = \frac{1500}{2\pi \times 1000 / 60} \approx 14.324\,\text{N·m}$$

6. Torque on driven pulley

   $$T_2 = \frac{1500}{2\pi \times 4000 / 60} \approx 3.581\,\text{N·m}$$

These results illustrate how the pulley speed calculator, belt tension calculator, and drive torque calculator work together within the same tool.

Why This Calculator Matters

By automating these repetitive and error‑prone manual calculations, this online belt drive system analysis tool saves time and reduces mistakes. Whether you are designing a new transmission system or troubleshooting an existing one, having a reliable pulley belt tension calculator at hand ensures you can quickly evaluate different configurations.