Pulley Calculator
Calculate driven pulley RPM, belt velocity, belt length, belt tension, and torque for a two-pulley belt drive system. Free online physics calculator with charts and breakdowns.
About This Calculator
The Pulley Calculator analyzes a belt drive system consisting of two pulleys (a driver and a driven pulley) connected by a belt. It is designed for mechanical engineers, technicians, students, and hobbyists who need to quickly compute key parameters of a belt-driven power transmission system. Whether you are designing a new machine, troubleshooting an existing drive, or studying physics, this calculator provides instant, accurate results for all essential pulley system metrics.
The calculator uses standard belt drive formulas derived from the fundamental relationship d₁ × n₁ = d₂ × n₂, where the product of pulley diameter and rotational speed is constant for both pulleys. Belt velocity is computed from the driver pulley dimensions, and belt length is calculated using the complete wrap-angle formula that accounts for pulley diameters and center distance. When transmitting power is provided, belt tension and torque values are also computed. The speed ratio indicates whether the system is speed-increasing or speed-reducing.
Regional Notes
Worldwide: This calculator uses metric engineering units (mm, RPM, W, m/s, N, N·m) which are standard across all regions for mechanical engineering applications. The belt drive formulas are universal and apply regardless of geographic location. For imperial unit users, note that 1 inch = 25.4 mm, 1 hp = 745.7 W, and 1 lb-ft = 1.3558 N·m.
Frequently Asked Questions
How does a belt drive pulley system work?
A belt drive pulley system consists of two pulleys (driver and driven) connected by a belt. The driver pulley transmits rotational power through the belt to the driven pulley. The RPM relationship follows d₁ × n₁ = d₂ × n₂, where d is diameter and n is RPM. A larger driver pulley spinning at a given speed will make a smaller driven pulley spin faster, and vice versa.
How do you calculate driven pulley RPM?
Driven pulley RPM is calculated using the formula n₂ = d₁ × n₁ / d₂, where d₁ is the driver pulley diameter, n₁ is the driver pulley RPM, and d₂ is the driven pulley diameter. For example, a 400 mm driver pulley at 1000 RPM connected to a 100 mm driven pulley produces a driven RPM of 4000 RPM.
What is the belt length formula for two pulleys?
The belt length formula for two pulleys is L = (d₁ × π / 2) + (d₂ × π / 2) + 2D + ((d₁ − d₂)² / (4 × D)), where d₁ is the driver pulley diameter, d₂ is the driven pulley diameter, and D is the center distance between the two pulleys. This formula accounts for the belt wrap around each pulley and the straight sections between them.
How is belt tension calculated in a pulley system?
Belt tension in a pulley system is calculated using F = P / v, where P is the transmitting power in watts and v is the belt velocity in meters per second. Belt velocity is determined by v = π × d₁ × n₁ / 60 (with d₁ in meters) or v = π × d₁ × n₁ / 60000 (with d₁ in mm). Higher power transmission and lower belt speed result in greater belt tension.
Is this pulley calculator free to use?
Yes, this pulley calculator is completely free to use with no registration or login required. You can calculate driven RPM, belt velocity, belt length, belt tension, and torque for any two-pulley belt drive system.
Can I share my pulley calculation results?
Yes, the calculator saves all your input values in the URL so you can copy the page URL and share it with others. When someone opens the link, the calculator will automatically populate the same values and show the results.
What units does this pulley calculator use?
This calculator uses millimeters for pulley diameters and center distance, RPM for rotational speed, watts for power, meters per second for belt velocity, meters for belt length, newtons for belt tension, and newton-meters for torque. All common engineering units for belt drive analysis.
What is the speed ratio of a pulley system?
The speed ratio of a pulley system is the ratio of the driver pulley RPM to the driven pulley RPM, which is also equal to the inverse ratio of their diameters: speed ratio = n₁ / n₂ = d₂ / d₁. A speed ratio greater than 1 means the driven pulley rotates faster (speed increasing), while less than 1 means it rotates slower (speed reducing).