Wheel and Axle Calculator
Enter the load, wheel radius and axle radius to compute the effort and mechanical advantage. W=100N, R=0.5m, r=0.1m → MA=5, F=20N.
Input Data
Results
At a glance:The wheel and axle is a simple machine of a large wheel (radius R) and a small axle (radius r) on the same axis. Effort is applied at the wheel rim, the load hangs on the axle. Torque balance: F·R=W·r, so the mechanical advantage MA=W/F=R/r. When R>r, MA>1: it reduces the force but increases the distance moved (the wheel and axle each turn once, but the rim travels further). Energy conservation: F·2πR=W·2πr (ideal, frictionless). Applications: (1) steering wheel (large wheel, small axle); (2) winch (anchor lifting); (3) faucets and doorknobs; (4) bicycle pedal (wheel) and sprocket (axle); (5) screwdriver (thick handle = wheel, thin shaft = axle).
Formula
Torque balance: F·R = W·r
Mechanical advantage: MA = R/r = W/F
Effort: F = W·r/R = W/MA
Energy conservation: F·2πR = W·2πr
$$F\cdot R = W\cdot r, \quad MA = \frac{R}{r} = \frac{W}{F}$$How to Use
- Enter the load W (N).
- Enter the wheel radius R (m) and axle radius r (m).
- The tool computes the effort F and mechanical advantage MA.
Case Studies
Steering a vehicle
A large steering wheel (R=0.2) on a small column (r=0.02) gives MA=10.
A 10 N hand force produces 100 N of torque at the column.
This is why a big wheel makes steering easy.
Winch lifting
Crank radius R=0.5, drum radius r=0.1 → MA=5.
To lift a 100 N load, effort F=W/MA=20 N.
You trade five times the cranking distance for one-fifth the force.
FAQ
What is the wheel and axle?
A simple machine: a large wheel and a small axle sharing an axis. Effort at the wheel rim and load on the axle balance by torque F·R=W·r, giving MA=R/r.
Why does it reduce force?
Because R>r, so MA=R/r>1 and F=W·r/R < W. The trade-off is distance: you turn the wheel farther than the load moves.
Is it like a lever?
Yes — it is a continuous lever rotating about the axle. The same torque-balance idea applies; the radii act as the lever arms.
What are common examples?
Steering wheels, winches, faucets, doorknobs, bicycle pedals/sprockets and screwdrivers (handle = wheel, shaft = axle).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.