Wedge Calculator

Calculate the volume and surface area of a triangular wedge (right triangular prism).

Results

Volume

96.00

Total Surface Area

132.84

Visual Comparison

Wedge Calculator

PropertyValue
Volume96.0000
Lateral Surface Area100.8444
Total Surface Area132.8444
Slant Edge7.2111

About the Wedge

What Is a Wedge?

A wedge is a triangular prism shaped like a doorstop. It has a rectangular base, a vertical back face, two triangular side faces, and a sloping front face. The wedge is one of the six classical simple machines, converting linear force into lateral force.

Volume

The volume of a right triangular wedge is V = (1/2) x base_length x base_width x height. This is equivalent to half the volume of a rectangular box with the same dimensions.

Surface Area

The total surface area includes the rectangular base, vertical back, sloping front, and two triangular sides. The slant edge (sloping height) is calculated using the Pythagorean theorem from the base length and height.

Applications

Wedges are fundamental in mechanics and engineering. They are used as simple machines (axes, knives, chisels), in doorstops, shim plates for alignment, and split wedges for splitting materials. Understanding wedge geometry is essential for mechanical design.

Practical Example

Wedge with L=8, W=4, H=6

Step 1: Volume = (1/2)(8)(4)(6) = 96

Step 2: Slant = sqrt(4² + 6²) = sqrt(52) = 7.21

Step 3: Base area = 8 x 4 = 32

Step 4: Back = 4 x 6 = 24, Slope = 4 x 7.21 = 28.84, Sides = 2 x 24 = 48

Step 5: TSA = 32 + 24 + 28.84 + 48 = 132.84

Perguntas Frequentes

Is a wedge a simple machine?

Yes, the wedge is one of the six classical simple machines. It converts a force applied to its blunt end into forces perpendicular to its inclined surfaces.

How does a wedge differ from an inclined plane?

An inclined plane is stationary, while a wedge is a movable inclined plane. A wedge is essentially two inclined planes joined back to back.

What is the mechanical advantage?

The ideal mechanical advantage of a wedge equals its length divided by its thickness. A longer, thinner wedge provides greater force multiplication.

How is the slant edge calculated?

The slant edge uses the Pythagorean theorem: slant = sqrt((base_length/2)² + height²). This gives the length of the sloping surface.

Can the height be greater than the base?

Yes. The height, base length, and base width can be any positive values. A taller wedge has a steeper angle and greater mechanical advantage.

Disclaimer: This calculator uses standard geometric formulas. Results are for informational purposes only.

References

  1. Wikipedia. "Ellipsoid." en.wikipedia.org
  2. NIST. "SI Units." nist.gov

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