By Zencalcy Editorial TeamLast reviewed About us
A wheel and axle multiplies force by the ratio of the wheel radius to the axle radius. Turning the large wheel through a small angle winds the rope on the small axle, so a modest effort on the rim lifts a much heavier load.
Force multiplication from wheel and axle radii.
F_load = F_effort × (R / r)
R is the wheel radius where the effort is applied, r is the axle radius where the load is wound, both measured from the shared centre. Friction is ignored.
| Symbol | Meaning |
|---|---|
| F_load | Load force, in newtons. |
| F_effort | Effort applied at the wheel rim, in newtons. |
| R | Wheel radius, in metres. |
| r | Axle radius, in metres. |
The radius ratio is 5, so 100 N on the wheel rim lifts a 500 N load. The effort must travel five times farther than the load rises.
Continue with the Gear Ratio Calculator, Lever Calculator, or the Mechanical Advantage Calculator — or browse more simple machines tools and all physics calculators.
Steering wheels, winches, doorknobs and screwdrivers all use the same principle: a large-radius input driving a small-radius output.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026