Rebar Bend Deduction Calculator: True Cut Lengths for Bent Bars

A rebar bend deduction calculator answers the question that separates people who read cut sheets from people who write them: why does a bar with an 18-inch leg and a 24-inch leg get cut at 40.53 inches instead of 42? The answer is that every bend replaces a sharp corner with an arc, and the arc is always shorter than the corner it replaces. Fabricators call the difference the bend deduction, they carry it in charts tabulated by angle and bar size, and they guard it jealously — because a shop that ignores deduction ships bars that are too long by half a bar diameter per bend, and a crew that double-deducts ships bars that do not close. This page owns the arithmetic: a live calculator up top, the geometry underneath it, chart values and hook rules, and two fully worked bars including one with a seismic hook.

Worked Example: One #4 L-Bar, Two Legs, One 90-Degree Bend

Set the calculator to its defaults — #4 bar (d = 0.5 in), a 90-degree bend, a 2-inch inside radius, legs of 18 in and 24 in measured to the outside corner — and follow the chain from layout to shear. Every number below is reproduced live by the tool above.

What Bend Deduction Is (and Why 18 + 24 Does Not Equal 42)

Every bar detail is drawn as if steel had corners. The 18-inch and 24-inch legs of the L-bar meet at a crisp point on the drawing, and anyone checking the bar with a tape naturally measures to that point — the intersection of the two outside faces. But a bending pin cannot make a sharp inside corner in a 0.5-inch bar, and nobody wants one: a true knife-edge would locally cold-work the steel, crack the bar, and crush the concrete against it. So the bend is made as an arc of some finite inside radius R, and the outside of the bar sweeps through the theoretical corner as a smooth curve.

Here is the consequence that deduction quantifies. The theoretical outside corner is a point that the steel never actually reaches — the outside face arcs inside of it, cutting the corner short. Walk the finished bar with a tape: up the first leg the steel follows the layout perfectly, then at the bend it departs from the corner and swings around the pin, rejoins the second leg, and the second leg again matches its dimension. The only place the bar comes up short of the layout is the corner itself, and the shortfall is exactly the difference between the two straight tangent legs the layout assumed and the one arc the steel actually took. That difference is the bend deduction: deduction = (sum of outside legs) − (centerline path through the bend). For the default bar it is 5.00 − 3.53 = 1.47 in of steel that the layout imagined and the bar does not contain.

Cut First, Bend Second — in That Order

Every bent bar on a site was a straight stick on a shear table first. The cut length written on the cut sheet is the one number the shear operator sets, and it must already contain every deduction — no bending machine can recover steel that was never there. A bar cut at the naive leg sum bends up long at every corner; the error compounds linearly with bend count, which is why a six-corner closed tie cut without deductions can run nearly 3 bar diameters over.

The Geometry: Where the Bend Deduction Formula Comes From

The deduction formula is three lines of trigonometry, and each term has a physical meaning you can point at on the bending table. Call d the bar diameter, R the inside bend radius, and θ the bend angle in radians.

One counterintuitive result falls straight out of term ④: under the standard outside-face measuring convention, a larger inside radius R produces a larger deduction. Collect the coefficient on R — 2tan(θ/2) − θ — and it is positive at every angle: 0.0123 in per inch of R at 30°, 0.0430 at 45°, 0.1075 at 60°, and 0.4292 at 90°. So opening a 90-degree bend from a 1-inch to a 3-inch inside radius adds roughly 2 × 0.4292 = 0.86 in of deduction, because the longer arc eats proportionally more of the corner the tape assumed. (Conventions measured to the inside face behave differently — which is precisely why mixing conventions is dangerous, as the warning card below says.) This radius sensitivity is why fabricators standardize tooling: bending pins come in fixed sizes, stirrup benders hold a set radius per bar diameter, and the shop's deduction chart is only guaranteed against those pins. Ask for a special radius and the chart values stop applying — the calculator above is what handles that case.

Fabricator Quick-Reference: Deduction by Bend Angle

Shop charts compress the formula into d-multipliers per angle. The values below pair each rule of thumb with the exact answer for the default geometry — a #4 bar bent with a 2-inch inside radius — so you can see where the chart is tight and where the radius widens the gap.

Read the two hook rows as a boundary, not as values: 135-degree and 180-degree bends are not processed as deductions at all, because fabricators dimension hooks by their extension past the bend instead. And remember what the chart values assume — standard tooling radii and the outside-face convention. The exact numbers shift with R (that 0.4292 in-per-inch coefficient at 90° again), which is exactly what the calculator at the top of this page is for when your pin is not the chart's pin.

Hooks Are Measured, Not Deducted

The moment a bend becomes a hook — 90-degree standard hooks, 135-degree seismic ties, 180-degree J-bars — the industry switches conventions. Hooks are dimensioned by their extension beyond the bend, the length of bar sticking out past the tangent point, and that extension is added to the cut length as a measured quantity rather than processed through the deduction formula. The standard extensions are short and memorable:

Two boundaries keep this page honest about its scope. The radii that those hooks bend around — and the minimums that keep them from cracking — belong to our rebar bend radius guide, which owns minimum bend radii and standard hook dimensions; this page owns the cut-length arithmetic that turns radii and legs into a shear setting. And when the bar is a closed stirrup with two hooks and four corners, the fastest route is our rebar stirrups calculator, which builds cut lengths from the perimeter plus hook extensions the way fabricator charts do.

Full Cut-Sheet Logic: Straight Segments Minus Every Deduction

A real bar rarely has one bend. The general cut-sheet rule handles any shape: cut length = Σ straight legs (each measured to its outside corner) − Σ bend deductions (+ hook extensions measured as such). Every corner contributes its own deduction at its own angle and radius, and nothing else changes the arithmetic.

Work the canonical case: a #4 U-bar with legs of 18, 24, and 18 inches and two 90-degree bends at R = 2 in. The legs sum to 60 in. Each 90-degree bend deducts 1.47 in — the same number as the L-bar, because deduction depends on the bend, not on which end of the bar it sits on. Two bends deduct 2 × 1.466 = 2.93 in, so the cut is 60 − 2.93 = 57.07 in. Cut a 60-inch stick and the finished U-bar oversails its legs by nearly 3 inches — enough to force the whole cage out of square when the stirrup will not seat.

The Cut Sheet Is a Contract

A fabrication cut sheet lists, per bar mark: size, quantity, cut length, bend angles, and bend radii. The cut length column already contains every deduction — that is what makes it a contract between the detailer and the shop. When a field crew re-cuts bent bars to "fix" a length, they are charged twice: once for the steel and once for the realization that the deduction math was skipped the first time.

Worked Example: #4 L-Bar With a 135-Degree Seismic Hook

Now combine both conventions on one bar — a deduction on one end, a measured hook extension on the other. The bar is the familiar L-bar (18-in and 24-in legs, 90-degree bend at R = 2, #4) with a 135-degree seismic hook added to the 18-in end. This is the shape of a boundary tie in a seismic detail, and it exercises every rule on this page.

Bend deduction is one piece of the ordering puzzle. Before any steel is called in, cross-check the straight-run quantities and weights with the free rebar calculator on the homepage, and when the job involves a different member — footings, slabs, stirrups, piers — the hub of specialized rebar calculators keeps every variant of the arithmetic one click away, each with its own worked examples and code minimums.