FORGING CALCULATORS / TAPER GEOMETRY
Calculate the stock required for square, rectangular, and wedge-shaped tapers using volume-conserving geometry.
A forged taper changes cross-sectional area along its length. As steel is drawn out, the material is redistributed. Assuming no loss, the volume of the original stock equals the volume of the finished taper.
For square or rectangular stock, multiply width by thickness:
W = starting width; H = starting thickness; A = cross-sectional area.
If width and thickness each change uniformly (linearly) from the starting dimensions to the tip dimensions, the average cross-sectional area is:
tw = tip width; th = tip thickness. Multiply average area by finished taper length to obtain volume:
Unlike a uniform bar, a taper does not have the same area everywhere along its length.
Divide the finished taper volume by the starting cross-sectional area:
Example: Forge 1" × 1" square stock into a 6" long taper ending at a ¼" × ¼" tip.
Starting area: 1 × 1 = 1 in²
Average taper area: (2 + 0.25 + 0.25 + 0.125) ÷ 6 = 0.4375 in²
Finished volume: 0.4375 × 6 = 2.625 in³
Original stock required: 2.625 ÷ 1 = 2.625"
For a four-sided square taper drawn to a point, both width and thickness reach zero at the tip:
For a wedge taper, where one dimension remains constant and the other decreases linearly to zero:
These simplified relationships apply only to the specified tip geometry.
Additional stock can be prepared for scale loss and cleanup:
P = extra allowance percentage. For the example above, with 5% allowance:
2.625" × 1.05 = 2.756" to prepare.
Important: The model assumes a straight taper with width and thickness changing linearly, uniform starting stock, and conservation of volume. Real forging can introduce uneven deformation, scale loss, and dimensional variation.
Calculate the original stock required to forge a square, rectangular, or wedge-shaped taper. All dimensions are in inches.
For a wedge, leave one tip dimension equal to its starting dimension and reduce the other.
Side View — Thickness
Top View — Width
Cross-Section View — Starting Stock and Finished Tip
Cross-sections use the same scale, showing actual relative width and thickness. A zero-sized tip appears as a line or point.
Side and top views use one proportional scale. All drawings automatically fit their available space.
Assumes width and thickness vary linearly along the taper and material volume is conserved. Results are theoretical and do not include scale loss unless added through the allowance.