A belt transmission connects rotating shafts through a flexible loop. This calculator shows an open flat-belt arrangement: both pulleys turn in the same direction, and their ideal speed ratio follows their effective pitch diameters.
Belt Transmission Interactive Calculator
Change driver speed and both pulley diameters. The tangent belt path, pulley proportions, rotation ratio and calculated driven speed update together.
Equation Used
- An open belt preserves rotation direction.
- Both pulley rim speeds equal belt speed in the ideal model.
- Illustrative animation speed is reduced; its speed ratio is retained.
- No torque, tension, power rating or service life is calculated.
Construction reference: Henry T. Brown, movement 1, open belt and pulleys.
How the belt connects the pulleys
The driving pulley moves the belt, which turns the driven pulley. In an open arrangement both turn in the same direction. The straight spans meet the circular pulley surfaces tangentially. When the diameters differ, the contact points are not directly at the top and bottom of both circles.
This illustration uses common tangent spans and continuous wrap arcs. Its pitch circles share one scale. Bearings and supports show where the shafts are held, while moving belt marks and pulley spokes show the speed relationship. For a real friction drive, belt tension and traction must also be established; the speed equation does not size those.
Where belt drives are used
Belt drives transfer motion between separated shafts in fans, workshop machinery and other equipment. Flat, V-section and toothed belts use different pulley surfaces and design procedures. This flat-belt schematic explains the ideal speed relationship; it does not represent a specific product or installation.
Pitch diameter and speed
A pulley advances one circumference of belt per revolution in the ideal no-slip model. Equating the two rim speeds gives πD₁N₁ = πD₂N₂, and therefore N₂ = N₁D₁/D₂. The output/input speed ratio is D₁/D₂; the reduction ratio displayed here is D₂/D₁.
With D₁ in inches, dividing by 12 converts it to feet. Belt speed is then π(D₁/12)N₁ feet per minute. A result below 1:1 in the reduction field means the driven pulley turns faster. These equations do not establish power capacity, minimum diameter, tension, alignment tolerance or expected life.
Worked speed example
A 4-inch pitch-diameter driver at 1750 rpm drives an 8-inch pulley at 875 rpm, assuming no slip. The reduction is 2:1 and belt speed is approximately 1833 ft/min. Replacing the driven pulley with a 10-inch one gives 700 rpm; a 5-inch one gives 1400 rpm. Each option needs a separate check against the selected belt and equipment specifications.
What this comparison tells you
Pulley diameter provides a simple way to change shaft speed. The belt also permits separation between the shafts. In a friction drive, slip and elastic effects can change actual speed under load. A synchronous toothed drive uses compatible tooth profiles and counts to maintain its ratio, but still requires proper installation and load selection.
The speed ratio describes motion. Efficiency, service life and maintenance intervals depend on the selected belt system and operating conditions; they are not calculated here.
Belt-transmission questions
Why does a larger driven pulley turn more slowly?
Each of its revolutions requires a greater length of belt. At the same belt speed it completes fewer revolutions per minute.
Which diameter should I enter?
The effective pitch diameter used by the selected drive system, not an assumed outside diameter. Check the belt and pulley documentation.
Does the animation predict belt slip or required tension?
No. It shows an ideal no-slip speed ratio. Tension, traction, ratings and service requirements need separate manufacturer data.
Construction reference
Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 1, illustrates the open belt and same-direction pulley rotation. The calculator equations follow equality of the two ideal rim speeds.
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