Wheel & Axle Calculator
Work out the mechanical advantage, load force, and torque of a wheel-and-axle machine from the effort force and the two radii.
Wheel & axle result
The physics behind the wheel and axle
A wheel and axle is really a lever bent into a circle: the wheel and the axle rotate together about the same center, so a force applied at the wheel's rim produces a torque equal to that force times the wheel's radius. Because the axle turns with the same torque but a smaller radius, the force available at the axle must be correspondingly larger.
The trade-off is the same as any simple machine: the point on the wheel's rim travels a much larger circular distance for each turn than the point on the axle, so you move your hand farther and faster than the load moves, in exchange for needing less force to move it.
Frequently Asked Questions
What counts as a wheel-and-axle machine?
Any device with a wider wheel and a narrower shaft turning together on the same axis — a screwdriver (handle = wheel, shaft = axle), a doorknob, a steering wheel, a windlass, or a bicycle's pedal-and-crank. Turning the wide wheel with modest force produces a much larger force at the narrow axle.
How is the mechanical advantage calculated?
It's simply the wheel's radius divided by the axle's radius. A 15cm-radius wheel turning a 3cm-radius axle has a mechanical advantage of 5 — the force delivered at the axle is 5 times the force you apply at the wheel's rim (ignoring friction).
Why does turning a large steering wheel feel easier than a small one?
A larger wheel radius increases the mechanical advantage for the same axle, so the same turning effort at the rim produces more torque at the axle (or, conversely, the same output torque needs less effort). This is exactly why oversized steering wheels were common before power steering, and why a large screwdriver handle is easier to turn than a thin one.
What does the torque figure mean?
Torque is the turning force multiplied by the radius at which it acts (effort force × wheel radius here). In an ideal, frictionless wheel-and-axle, torque is the same whether you measure it at the wheel or the axle — only the force and the radius trade off, not the torque itself.
Educational estimate only, based on ideal (frictionless) mechanics. Verify load-bearing or safety-critical figures with a qualified engineer.