An open belt carries continuous rotation between two parallel shafts. Both shafts turn in the same direction. Their speeds are inversely proportional to their effective pulley diameters when the belt does not slip.
Continuous Rotary Motion Interactive Calculator
Set motor speed and the two effective pulley diameters. Compare shaft speed, ratio and ideal torque multiplication while the supported pulleys and open belt turn together.
Equation Used
- Parallel fixed shafts with an open, uncrossed belt. Both shafts rotate in the same direction.
- Effective pulley diameters and no slip or elastic creep.
- Ideal torque multiplier assumes no power loss; it is not a rated load.
- Centre spacing, belt width, support structure and motor dimensions are illustrative. No tension, wrap-dependent capacity, bearing load or motor sizing is calculated.
Effective diameter is the diameter relevant to belt travel, not necessarily the measured outside diameter. Ratios below 1:1 give a speed increase. The drawing preserves diameter proportions, including very small pulleys.
Two supported shafts and an open belt
The motor turns the driver pulley. The belt follows the two common external tangents and the contact arcs around the pulleys. Because the belt is not crossed, the driven pulley rotates in the same direction.
The animation uses one physical diameter scale and one belt-travel coordinate. Both spoke angles follow that travel divided by their respective radii, so the belt and pulley rims cannot drift apart. Bearings, a motor housing and a common support frame show what holds the rotating parts.
Compare reduction and speed increase
A larger driven pulley reduces speed and increases the ideal torque multiplier. A smaller driven pulley increases speed and reduces that multiplier. Equal diameters give a 1:1 drive.
Use these results to compare ratios before selecting a belt and motor. Real drive selection also depends on required power, belt type, wrap, tension, service conditions and manufacturer limits; those are outside this three-input calculator.
The speed and torque relations
With effective diameters D₁ and D₂ and shaft speeds N₁ and N₂, equal rim speed gives πD₁N₁=πD₂N₂. Therefore N₂=N₁D₁/D₂ and the reduction ratio is D₂/D₁.
For an ideal lossless drive, input and output power are equal. Thus T₂/T₁=N₁/N₂=D₂/D₁. This is a relative torque multiplier; no actual torque is calculated without an input torque or power.
The displayed percentage is 100(1−N₂/N₁). A negative value is valid and means the output is faster than the motor. Effective pitch diameter should be used rather than assuming that an outside measurement is always appropriate.
Example with the initial settings
A motor speed of 1,750 rpm, a 50 mm driver and a 250 mm driven pulley give a 5:1 reduction. Output speed is 350 rpm, the ideal torque multiplier is 5× and the speed drop is 80%.
Changing the driven diameter to 25 mm gives a 0.5:1 ratio and 3,500 rpm output. The ideal torque multiplier becomes 0.5× and the speed-drop result is −100%, meaning a 100% increase.
What this model does and does not establish
The calculated speed relation assumes no slip. The torque multiplier additionally assumes no power loss. Real belts can slip, creep and dissipate power; the ideal ratio does not establish a permissible force, efficiency, lifetime or operating speed.
Animation is slowed by a fixed factor of 400 while retaining the entered speed relationship. Pulley diameters remain proportional, but centre spacing, motor size and supports are schematic. The belt is exposed to explain its motion, rather than to depict a complete guarded machine.
Questions about this calculator
Why do both pulleys turn the same way?
The belt is open rather than crossed. Its path makes both contact rims travel in the same rotational sense.
Does a negative speed drop indicate an error?
No. It indicates a speed increase. For example −100% means output speed is twice input speed.
Is the torque multiplier a torque rating?
No. It is the ideal output-to-input torque ratio with no losses. The calculator does not size a motor, belt or shaft.
Which diameter should I enter?
Use the effective diameter for the selected belt and pulley system. Depending on its geometry, the measured outside diameter can differ.
Why can one pulley look very small?
Both diameters use the same scale. Enlarging a small pulley independently would misrepresent the selected ratio.
References
Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 1, illustrates an open belt producing same-direction rotation.
Gates Heavy Duty V-Belt Drive Design Manual, technical data D15–17, covers speed/diameter relationships, efficiency and effective versus datum diameters.
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