Why the bar is always shorter than it looks
Nothing leaves a forging except scale. Whatever section you take away from one part of the bar reappears somewhere else as length, and the arithmetic that connects the two is volume, not length and not weight. So the question "how long a piece do I cut" is really "what is the volume of the finished thing, divided by the cross-section of the bar I am cutting it from".
The part that trips people up is the shape of a taper. A taper is not a wedge unless the width is held. Draw a square bar down to a point on all four sides and the solid you have made is a pyramid: its volume is one third of the square prism it sits inside, not one half. Do the same on a round bar and you have a cone, which is also one third. Only a flat drawn on two faces with the width unchanged is a genuine wedge, and a wedge is one half.
That difference is not academic. On half inch square bar, six inches of taper to a point is 0.5 cubic inches of steel, which is two inches of bar. Average the two ends instead — the intuitive move, since one end is 0.25 square inches and the other is zero — and you get 0.75 cubic inches and cut three inches. Fifty percent more bar than the job needs, every time, on every taper.
The three volumes this page uses
| Shape | Volume | Bar it eats, per unit of finished length |
|---|---|---|
| Square or round taper (frustum) | h/3 × (A1 + A2 + √(A1·A2)) | One third when it runs to a point |
| Flat taper, width held (wedge) | w × h × (t1 + t2)/2 | One half when it runs to an edge |
| Drawn-down parallel section (prism) | A2 × h | The section ratio A2/A1 |
The last row is the one that explains why drawing takes so long. Halve the thickness of a square bar and the section falls to a quarter, so the length goes up by four. Halve the thickness of a flat while holding the width and the section falls to a half, so the length only doubles. The same hammer work buys you very different amounts of length depending on which way the steel is allowed to spread, and that is the whole reason a smith turns the bar ninety degrees between blows.
Scale, and why it is a field rather than a number
Every time the bar comes out of the fire it has a skin of oxide on it, and that skin is steel that is no longer part of the piece. How much you lose over a job is not a property of the steel — it is a property of how you run the fire and how many heats you take. A piece finished in three heats in a slightly reducing fire loses a fraction of what the same piece loses in twelve heats in a hard oxidising one.
The honest way to get your own figure is to weigh a bar, forge something you have made before, weigh the finished piece and the cut-offs, and take the difference. That number belongs to your fire and your habits, which is why it sits in a box on this page instead of being baked in.
What this does not cover
Upsetting is the inverse operation and the arithmetic still holds — the volume is the same, the bar just gets shorter instead of longer. What the arithmetic cannot tell you is the limit: hot bar pushed on its end will fold sideways rather than swell if too much of it is hot and unsupported, and how much is too much depends on the heat length, the support and how square the end is. That is a judgement at the anvil, not a formula.
Nor does it say anything about how many heats or how long the job takes. Those depend on your hammer, your fire and your arm, and the only useful version of that number is one you have timed yourself.
Questions people ask
Why is my taper eating less bar than I expected?
Because a taper to a point is a cone or a pyramid, and both hold exactly one third of the volume of the parallel bar that would occupy the same length. The intuition that fails is averaging the two end sections, which treats the taper as though it were a wedge and asks for half instead of a third. On any taper that runs to a point, that shortcut asks for fifty percent more steel than the job needs.
Does it matter whether the bar is square or round?
It changes the volume but not the ratio. A round bar has a section of about 78.5 percent of the square that encloses it, so the cubic inches come out lower — but the bar length consumed per inch of finished taper is identical, because that length is the ratio of two areas of the same shape and the shape factor cancels. Square and round tapers with the same proportions draw at exactly the same rate.
What scale loss percentage should I put in?
Your own, measured. Weigh the bar you start with, forge a piece you have made before, then weigh the piece together with every cut-off. What is missing left as scale. The figure depends far more on how many heats the job takes and how hard the fire is running than on what the steel is, which is why this page has no default worth trusting and asks instead.
How does drawing a flat differ from drawing a square?
By where the steel is allowed to go. Draw a square bar and both cross dimensions shrink together, so halving the thickness quarters the section and quadruples the length. Draw a flat over the edge of the anvil with the width held and only one dimension shrinks, so halving the thickness halves the section and only doubles the length. Same reduction in thickness, twice the length out of the square.
Can I use this for upsetting instead of drawing?
The volume arithmetic works in both directions, so yes — set the finished section larger than the bar and the length multiplier comes out below one, meaning the bar gets shorter. What the page cannot give you is the limit. A length of hot bar struck on its end folds over sideways instead of swelling once too much of it is hot and unsupported, and where that point sits depends on the heat length and the support, not on arithmetic.