Wedge Calculator
Enter load, wedge length and thickness to get the effort, mechanical advantage MA=L/t and wedge angle θ=2·arctan(t/2L). Axe L=0.2, t=0.05 → MA=4; knife L=0.05, t=0.002 → MA=25.
Input Data
Results
At a glance:A wedge is a triangular simple machine formed by two inclined planes meeting at one edge (the blade). The applied effort acts along the wedge length L and the load is split perpendicular to the thickness t. In the ideal frictionless case the mechanical advantage is MA=L/t (slope length over thickness). The wedge angle θ=2·arctan(t/(2L)). A longer L or thinner t gives a larger MA (more force amplification, less effort) but a longer push. Energy conservation: effort×distance = load×distance, i.e. F·L=W·t, solved as F=W·t/L. Example: an axe with L=0.2 m, t=0.05 m → MA=4; to split W=500 N of wood needs F=500/4=125 N. A kitchen knife L=0.05 m, t=0.002 m → MA=25, so W=100 N needs only F=4 N, with a wedge angle ≈2.3°. History: the wedge is one of the six classical simple machines (lever, wheel, pulley, inclined plane, screw, wedge); the screw is essentially a helical wedge. Applications: (1) axes, knives, chisels (split/cut material); (2) door wedges (hold a door, self-locking by friction); (3) nails (wedge into wood, fibres spread and grip); (4) cutting tools (scissors combine two wedges, ploughs open soil); (5) the inclined plane is a wedge variant for lifting loads. Notes: (1) real wedges lose to friction, so actual F is larger than W·t/L; (2) a sharper (smaller t) wedge cuts easier but is weaker — edge design balances sharpness and strength; (3) keep L and t in the same unit.
Formula
Mechanical advantage: MA = L/t
Effort: F = W/MA = W·t/L
Wedge angle: θ = 2·arctan(t/(2L))
Energy conservation: F·L = W·t
$$MA = \frac{L}{t}, \quad F = \frac{W\cdot t}{L}, \quad \theta = 2\arctan\left(\frac{t}{2L}\right)$$How to Use
- Enter the load force W (N).
- Enter wedge length L (m) and thickness t (m).
- The tool gives effort F, mechanical advantage MA and wedge angle θ.
Case Studies
Axes and knives
Axe: L=0.2 m, t=0.05 m → MA=4; split W=500 N with F=125 N; wedge angle ~14°.
Knife: L=0.05 m, t=0.002 m → MA=25; cut W=100 N with F=4 N; edge ~2.3°.
Chisel: L=0.08 m, t=0.01 m → MA=8; woodworking with small force.
Door wedge and nails
Door wedge: L=0.1 m, t=0.03 m → MA=3.3; friction self-locks it.
Nail: L=0.05 m, t=0.005 m → MA=10; drives into wood, fibres spread and grip.
Plough: L=0.3 m, t=0.05 m → MA=6; opens the soil by wedging.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.