A wedge is a moving inclined plane, commonly represented as two inclined faces back-to-back. In an ideal symmetric geometry, greater axial travel is exchanged for a smaller lateral separation and a corresponding force ratio; real behavior depends strongly on friction, deformation and the materials in contact.
The Wedge Interactive Calculator
Enter centerline penetration length L and total heel thickness t for an ideal symmetric wedge. The calculator reports geometry and a frictionless per-face force ratio only; it does not predict cutting, splitting, holding or anchor capacity.
Equation Used
- L is axial penetration distance and t is total separation across both symmetric faces at the heel.
- The wedge and surrounding bodies are rigid, frictionless and quasi-static, with symmetric face reactions.
- Material properties, fracture, cutting edge, friction, wear, impact, misalignment, buckling, retention and safety factors are omitted.
Ideal Wedge Geometry
NOAA describes a wedge as a portable inclined plane, and U.S. Navy training material describes the common double-inclined-plane form used for cutting or splitting. Axial motion of the wedge produces lateral separation at its faces.
For the symmetric diagram here, L is centerline penetration and t is the total face-to-face thickness at the heel. The included angle follows beta = 2 atan[t/(2L)].
What This Calculator Illustrates
OpenStax defines ideal mechanical advantage through force and displacement ratios under conservation of work. Applying that idealization to this symmetric wedge gives the dimensionless displacement ratio L/t.
The result is an explanatory geometry comparison. It does not establish the performance of an axe, chisel, taper, shim, anchor, cutting tool or splitting wedge.
Frictionless Symmetric Relation
beta = 2 atan[t/(2L)]
Flateral, each face = FaxialL/t
Because each face moves laterally by half the total separation, the two equal face reactions satisfy ideal work balance. The calculator normalizes axial input to 1 kN for the third output.
Worked Ideal Geometry
For L = 100 mm and t = 25 mm, R = 4 and beta ≈ 14.25 degrees. Under the stated frictionless symmetric assumptions, a 1 kN axial input corresponds to 4 kN lateral force on each face.
This is an ideal static relation, not a prediction of fracture, penetration, retention or safe capacity.
Model Boundary
- Calculated: L/t, included angle and frictionless lateral force per symmetric face for a normalized axial input.
- Geometry: rigid symmetric two-face wedge with centerline penetration L and total thickness t.
- Not calculated: friction, self-locking, edge radius, contact pressure, fracture, cutting, plastic deformation, impact energy, rebound, wear, hardness, lubrication, taper retention, anchor capacity, structural strength or safety.
Frequently Asked Questions
Is L the sloping face length?
No. In this calculator L is centerline axial penetration distance.
Is t the half-thickness?
No. It is total heel thickness across both faces.
Why is the per-face force ratio L/t?
In the ideal symmetric work balance, each face moves half the total separation while two equal face forces act.
Does the result include friction?
No. Friction and deformation can materially change the required input and reactions.
Does the angle determine whether a real wedge self-locks?
Not by itself. Real retention depends on friction, elasticity, surface condition and geometry.
Can this size a wedge anchor or cutting tool?
No. Use product-specific standards, ratings and engineering data.
References
- NOAA Ocean Exploration, Simple Machines: wedge as a portable inclined plane and mechanical advantage as a force ratio.
- U.S. Navy training manual, Basic Machines: wedge as two inclined planes and theoretical length-to-thickness advantage.
- OpenStax Physics, Simple Machines: ideal mechanical advantage from force and displacement ratios under work conservation.
- Georgia State University HyperPhysics, The Wedge: ideal penetration-to-separation relation and friction limitation.
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