A rigid wheel and coaxial axle turn through the same angle. Their radii set the ideal force ratio and the two circumferential travel distances per revolution.
Wheel and Axle Interactive Calculator
Enter wheel and axle radii. The calculator reports ideal geometry only; friction, rope thickness, deformation, strength and efficiency are not included.
Equation Used
- Wheel and axle rotate together without slip.
- Input and output forces act tangentially at the entered radii.
- Rope or belt thickness is negligible.
- Friction, inertia, deformation and efficiency are omitted.
- Strength, bearing load and safety are not evaluated.
Ideal Wheel-and-Axle Geometry
The NASA simple-machines guide describes the wheel and axle as a simple machine in which a larger wheel turns a smaller axle.
What This Calculator Represents
It compares two coaxial radii that share one angular displacement.
Radius and Distance Ratios
s_w=2piR
s_a=2pir
100s_a/s_w=100r/R
Worked Scenario
For R=30 mm and r=6 mm, ideal mechanical advantage is 5:1. One turn moves the wheel rim about 188.5 mm and the axle surface about 37.7 mm, or 20% as far.
Assumptions and Limits
- Calculated: radius ratio and circumferences.
- Illustrated: shared rotation and wound-line displacement.
- Not calculated: friction, efficiency, strength, rope buildup, inertia or bearing loads.
Frequently Asked Questions
Is mechanical advantage actual?
No; it is ideal.
Does rope thickness matter?
Yes in real systems, but it is omitted.
Do both parts turn equally?
They share the same angle.
Why is axle travel smaller?
Its circumference is smaller.
Are losses included?
No.
Can this rate a hoist?
No.
References
Building or designing a mechanism like this?
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