Two ideal pitch circles linked by no-slip contact or an ideal belt have equal tangential speed. Their angular-speed magnitudes vary inversely with effective pitch radius.
Variable Speed Gear Interactive Calculator
Enter input speed and two effective pitch radii. Results are an ideal lossless ratio comparison—not a gear-tooth design, variable-pitch mechanism, belt selection or machine rating.
Equation Used
- R1 and R2 are positive effective pitch radii.
- Tangential speed is equal at the ideal contact or belt pitch line.
- Input speed is steady and output speed is reported as a magnitude.
- The reciprocal torque factor assumes lossless equal-power transmission.
- Gear teeth, belt length, center distance, wrap, tension, slip, efficiency, load, stress, wear, guarding and safety are omitted.
Ideal Two-Radius Speed Relation
The U.S. Department of Energy's Microhydropower Handbook uses pitch diameter for belt-drive speed ratio, while NASA gear references use pitch circles for ideal rolling relations. This calculator evaluates only the common no-slip radius arithmetic and does not design either implementation.
What This Calculator Represents
The tool divides entered driver pitch radius by driven pitch radius, applies that ratio to input speed, reports the percentage difference from 1:1 and gives the reciprocal ideal torque factor.
Ideal Radius-ratio Calculation
Nout=Nin q
speed change=(q-1)100%
ideal torque factor=R2/R1
The factor assumes lossless equal-power transmission; it is not a torque rating.
Worked Idealized Example
At 1750 rpm with R1=50 mm and R2=25 mm, the ideal ratio is 2:1, output-speed magnitude is 3500 rpm, speed change is +100% and the reciprocal ideal torque factor is 0.50.
Model Boundary
- Calculated: ideal radius ratio, output-speed magnitude, percentage change and reciprocal equal-power factor.
- Illustrated: two effective pitch circles linked by an ideal open belt.
- Not calculated: gear teeth, variable pitch geometry, belt length, center distance, wrap, tension, slip, efficiency, actual torque, stress, wear, guarding, capacity or safety.
Frequently Asked Questions
Does this design gears?
No.
Does it design a variable-speed sheave?
No.
Is torque factor actual output torque?
No; it is only the ideal reciprocal ratio.
Are losses or slip included?
No.
Are belt length and center distance calculated?
No.
Can it establish a safe drive rating?
No.
References
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
