Outside dimensions

Bend deduction calculator

Bend deduction is what comes off the sum of the outside dimensions to give the flat blank, and it is built out of two terms: BD = 2 × setback − bend allowance. This page prints all three separately, in inches and millimeters, free and with no signup, handles up to six bends off one set of tooling, and ends in a deduction card by angle you can print and leave at the brake. It is the same bend the allowance page works on, approached from the other face of the metal.

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Up to 6 bends
Setback shown
Printable die card

The tooling, and the legs as the drawing gives them

Outside dimensions, measured to the corner the two outside faces would make if the bend were sharp. One deduction comes off per bend, and a part with n bends has n + 1 legs.

Material thickness

It enters twice — inside the setback and inside the arc — so measure it.

Inside bend radius

R/t = 1.24. Setback is built on R + t, so both matter here.

Angle bent through, degrees

At exactly 90 the setback collapses to R + t, which is why so many shop rules quote that as if it were the formula.

Number of bends

All at the angle and radius above. A part whose bends differ has to be worked in groups.

K-factor

Prefilled at 0.4469. Implied by the traditional bend-allowance formula BA = (0.017453 × R + 0.0078 × t) × angle, printed in Machinery's Handbook and in shop layout tables for decades: 0.0078 ÷ (π/180) = 0.4469. This is one formula's built-in assumption, not a measurement of your material. It sits at the top of the realistic range and suits generous radii in mild steel; tight bends run well below it.

Outside leg dimensions

Leg 1

Leg 2

Leg 3

3 legs summing to 7.0000 in before the deduction comes off.

Deduction per bend, inches

0.1373

Deduction per bend, mm

3.487

Setback, allowance and deduction, and the flat blank they produce
Term	Inches	mm
Setback, per side of the bendtan(angle / 2) × (R + t) — outside corner back to where the bend starts	0.1680	4.267
Bend allowanceangle in radians × (R + K × t) — the arc that has to be in the blank	0.1987	5.048
Bend deduction2 × setback − allowance — what the two setbacks cost minus what the arc gives back	0.1373	3.487
Total taken off, 2 bendsone deduction per bend, regardless of how many legs there are	0.2745	6.973
Sum of the outside legsstraight off the drawing, before anything is removed	7.0000	177.800
Flat blank lengthsum of the legs − total deduction	6.7255	170.827

Two of the three terms above are geometry you can check with a protractor and the third is a guess. Setback and the outside legs are fixed by the shape of the part; only the allowance carries K, so a deduction is only as trustworthy as the K inside it — and rearranging the same identity the other way, BA = 2 × SB − BD, is how a deduction somebody hands you turns back into a K you can inspect.

Deduction card for this material and this radius

0.0750 in material, 0.0930 in inside radius, K 0.4469. Print it and tape it to the brake — the angle is the only thing that changes from job to job on one tooling setup.

Setback, bend allowance and bend deduction by bend angle for one tooling setup
Bent through	Setback, in	Allowance, in	Deduction, in	Deduction, mm
15°	0.0221	0.0331	0.0111	0.282
30°	0.0450	0.0662	0.0238	0.604
45°	0.0696	0.0994	0.0398	1.011
60°	0.0970	0.1325	0.0615	1.562
75°	0.1289	0.1656	0.0922	2.342
90°	0.1680	0.1987	0.1373	3.487
105°	0.2189	0.2319	0.2060	5.233
120°	0.2910	0.2650	0.3170	8.052
135°	0.4056	0.2981	0.5131	13.032
150°	0.6270	0.3312	0.9227	23.438
165°	1.2761	0.3643	2.1878	55.571

Watch the bottom of the setback column. Because setback carries tan(angle / 2), it runs away as the bend approaches flat: at 165° it is more than seven times R + t, and the deduction with it. That is not an error in the arithmetic — the two outside mold lines really are that far out on a nearly closed bend — but it does mean the outside method stops being a useful way to dimension a hem, which is laid out from its own flat-back allowance instead.

How to lay out a flat pattern from an outside-dimensioned drawing

Outside dimensions are what a caliper reads and what most drawings carry. Three steps turn them into a blank.

Enter the tooling before the part
Thickness, inside radius and bend angle decide the deduction between them, and the legs do not affect it at all — a deduction is a property of the bend, not of the part it sits in. Get those three settled first and the rest of the page is addition. If several jobs run on the same setup, the card at the bottom of the page is the whole answer for all of them, because only the angle changes.
Read the legs to the outside corner, not to where the metal curves away
An outside dimension runs to the point where the two outside faces would cross if the corner were sharp. On a 90° flange that is exactly what a caliper across the finished part reads, which is why outside dimensioning became shop practice in the first place. On an acute or obtuse bend it is not: the crossing point moves away from the metal as the angle opens, and a dimension scaled off the part instead of taken from the drawing will be short.
Take one deduction per bend, then check the shortest flange
A part with n bends has n + 1 legs and loses n deductions, whatever order they are in. The one thing to check afterwards is the shortest flange against the setback: if a leg is not longer than the setback there is no flat left on it, and the page says so rather than returning a blank length for a part that cannot be made. That is a geometry problem, and the die opening will impose a longer minimum on top of it.

Technical specifications

Identity evaluated	BD = 2 × SB − BA, where SB = tan(θ/2) × (R + t) and BA = θ in radians × (R + K × t). Rearranged, BA = 2 × SB − BD, which turns somebody else's deduction back into a K you can inspect.
Setback at 90°	Collapses to R + t exactly, because tan(45°) is 1. That special case is quoted in shops as though it were the general formula, and it is wrong at every other angle.
Worked example	0.075 in material, 0.093 in inside radius, 90°, K 0.4469: setback 0.1680 in, allowance 0.1987 in, deduction 0.1373 in (3.487 mm). Two bends off legs of 1.5, 4 and 1.5 in leaves a 6.7255 in blank.
Parts supported	One to six bends, two to seven legs, all sharing one angle and one radius. A part whose bends differ is worked in groups and the deductions added.
K-factor default	0.4469, prefilled and editable. It is not a measurement — it is the constant hidden inside the old layout formula BA = (0.017453 × R + 0.0078 × t) × θ, recovered as 0.0078 ÷ 0.017453.
Deduction card	Eleven angles from 15° to 165° for the tooling entered, printable with the chrome dropped and the header row repeated on every sheet.
The tail on that card	Setback carries tan(θ/2), so it runs away near flat: on the worked tooling the 165° deduction is 2.1878 in against 0.1373 in at 90°, a factor of sixteen. Hems are laid out another way for that reason.
Where it runs	In this browser tab. The tooling and part dimensions you type are never uploaded, logged or kept.

Frequently asked questions

My brake control wants a bend deduction and my CAD exports a bend allowance. Which do I give it?

Whichever the control asks for by name, and never one in the other's field — they are different numbers for the same bend and on the worked example above they differ by 0.06 in. Allowance is added to the flat legs; deduction is subtracted from the outside legs. The two are related by BD = 2 × SB − BA, so if a control gives you one and your CAD gives the other, you can convert rather than guess, and if the two disagree after converting, the discrepancy is a difference in assumed K or in assumed radius and is worth finding before the first part is cut. Some controls also label the field simply BA or BD with no units shown, in which case a test bend settles it faster than the manual.

Is bend deduction just another name for setback?

No, and the confusion costs a whole setback per bend. Setback is a one-sided measurement: the distance from the outside corner back to the point where the bend begins, on one leg. Deduction is what is left after both setbacks are removed and the arc is given back, which is what the 2 in the formula and the minus sign are doing. On the worked tooling the setback is 0.1680 in and the deduction is 0.1373 in, so treating them as interchangeable makes each bend 0.03 in wrong — small enough to look like a machine problem and large enough to fail a fit-up on a part with six bends.

Can a bend deduction come out negative?

Not for any bend a brake can make, and the reason is a property of the tangent rather than a rule of thumb. The setback term is 2 tan(θ/2) × (R + t) and the allowance is θ × (R + K × t), with θ in radians. Since tan x is always at least x, the first bracket is always at least the second, and because K is always below 1 the (R + t) factor beats (R + K × t) as well. So the deduction is positive at every angle from a sliver to a fold, which means a flat blank is always shorter than the sum of the outside dimensions. If you have calculated a negative deduction, the angle was entered as the included angle rather than as the movement.

My part is a box with four bends. Does one blank length cover it?

No — a box has two independent chains and each needs its own. Bends across the width form one chain of legs and bends along the length form another, and the blank is a rectangle whose two sides come from the two chains separately. Run this page twice, once with the legs across and once with the legs along, and the two answers are the two dimensions to cut. The corners are a third question the arithmetic does not touch: they need a relief notch, and how much depends on the radius and the tooling rather than on the deduction.

Why does a 30° bend take off so much less than a 90° in the same tooling?

Because setback is not proportional to the angle — it carries tan(θ/2), which is nearly linear at small angles and accelerates hard as the bend closes. On the worked tooling a 30° bend deducts 0.0238 in and a 90° deducts 0.1373 in, which is nearly six times as much for three times the angle. The practical consequence is that you cannot scale a known deduction to a new angle. A shop that measures its 90° deduction once and then divides it by two for a 45° will be out by 0.03 in per bend, and the card at the bottom of this page exists so nobody has to.

Our supplier's deduction chart disagrees with this page. Who is wrong?

Probably neither — you are almost certainly working from different K values or different radii, and the identity lets you find out which. Take their deduction and your setback, rearrange to BA = 2 × SB − BD, and back out the K their chart assumed. If it comes back near 0.33 they were charting a tight bend in soft material; near 0.45 they were using the handbook constant. If it comes back above 0.5 the disagreement is not K at all and the radius or the thickness in one of the two charts is not what you think. Their number is likely to be better than any table for their own material and tooling, and worse than a coupon bent on your machine.

Do I measure the outside legs on the drawing or on a sample part?

On the drawing, and treat a sample only as a check. On a 90° bend the two agree, because the outside corner is a real place a caliper can reach. At any other angle they do not: the point where the two outside faces would intersect sits off the metal, further away the closer the bend gets to flat, and a dimension scaled off a physical part is measuring to the corner of the material instead. If all you have is a sample, measure the flange from the tangent line where the flat begins, and add the setback this page reports to get back to the outside dimension.

About setback, and why shops dimension from the outside

Outside dimensioning won because it is what you can measure. Put a caliper on a finished bracket and the jaws land on two outside faces; there is no way to reach an inside mold line, which is a construction rather than a place, and a tangent line is invisible on a formed part until somebody scribes it. So drawings carry outside dimensions, inspectors check outside dimensions, and layout works from them — which means the number a shop actually needs is the one that comes off the sum of those dimensions to leave a blank. That is bend deduction, and it exists because the setback that separates an outside corner from the start of a bend is counted twice in the sum of the legs while the arc between the two tangent points is not counted at all.

Setback is the term worth spending a minute on, because it is the one nobody has handy and the one that misbehaves. It is tan(θ/2) × (R + t): at 90° the tangent is 1 and it collapses to the radius plus the thickness, which is the version most shop rules quote, and away from 90° that version stops being true in both directions. At 30° the setback is a quarter of its 90° value; at 150° it is nearly four times; approaching a fold it heads for infinity, because the two outside faces are becoming parallel and their intersection is running off to meet them somewhere past the end of the bench. That is why the deduction card on this page runs to 165° and then stops, and why a hem is laid out from a flat-back allowance instead of from this geometry at all.

The mistake worth naming is not arithmetic but vocabulary: three different quantities on this page get called the deduction by somebody. The setback gets called it, which loses a setback per bend; the allowance gets called it, which changes the sign of the correction; and a machine control that says BD when its manual means BA will produce a part wrong by the two together. This page prints all three side by side so it is obvious which is which, and the identity that connects them runs both ways — the bend allowance calculator does the same bend from inside dimensions and lands on the same blank, and any deduction handed to you can be turned back into the K it assumed. That K is the only soft number in the chain, and the K-factor calculator replaces it with a measured one. The other two inputs come from outside this page: the thickness begins as a gauge number in a named standard, and the radius is set by the vee the job runs in, which the press brake tonnage calculator picks along with the force. Once the channel is formed, its stiffness is a different question again — the moment of inertia calculator takes the finished section and returns what it will carry.

Where the part dimensions go

Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.

The deduction card is generated in the page from the tooling you typed rather than fetched from a server, so printing it involves no request and leaves no record of the job it was printed for.