Rebar Hook and Bend Calculator

Hook extension and bend gain by bar size

The extension is the straight tail the code requires past the end of the bend. The gain is the arc the bend itself consumes — the centreline length you add once per bend. Both are in inches. Bend diameters are the finished inside diameters from ANSI/CRSI IPG5.1-2026; extensions are the ACI 318-19 standard-hook geometry. The stirrup table uses the stirrup/tie bend diameter (4db for #3–#5, 6db for #6–#8); the standard table uses the standard hook diameter (6db for #3–#8).

Stirrups, ties and hoops — 90°, 135° and 180° hooks

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Standard hooks on main bars — 90° and 180°

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Standard hooks per ACI 318-19: 90° extension 12db, 180° extension 4db but not less than 2.5 in. Bend diameter from the ACI 318-19 table.

Extensions in inches: 12db (90° standard), 4db min 2.5 in (180° standard), 6db min 3 in for #3–#5 and 12db for #6–#8 (stirrup 90° and 135°). Gains are arc lengths, rounded to 0.01 in. Recompute, do not interpolate, if your drawing calls a different bend diameter.

Rebar bending chart — every angle, not just the three code angles

The chart above answers the code question: at the three angles the code names (90°, 135°, 180°), how long is the tail and how much arc does the bend consume. The rebar bending chart below answers the shop question. Ramps run at 30°, bevels at 45°, offset blocks at 60°, splayed corners at 120° — none of those are in the code tables, and every one of them still eats centreline. The geometry does not change with the angle; only two terms move:

• Gain (bend allowance) = angle in radians × centreline radius, where centreline radius = (finished bend Ø + db) ÷ 2. Add it once per bend when the legs are measured tangent-to-tangent.
• Deduction (bend deduction) = 2 × outside radius × tan(angle ÷ 2) − gain, where the outside radius is the centreline radius + db/2 — the radius to the outside face of the bar, which is what an out-to-out dimension runs to. Subtract it once per bend when the legs are measured out-to-out.

Everything on this page uses the same finished bend diameters as the chart above — the stirrup/tie diameter for hoops (from ANSI/CRSI IPG5.1-2026) and the standard hook diameter for main bars — so a number read off either chart drops straight into the same calculation. Nothing below is interpolated; every cell is the formula, rounded to 0.01 in.

The angle table — one #5 bar, seven angles

A #5 bar bent on the stirrup diameter (Ø 3.25 in) has a centreline radius of 1.94 in and an outside radius of 2.25 in. Hold the bar still and sweep the bend from a shallow ramp to a full turn, and the two numbers behave very differently: the gain grows in proportion to the angle, the deduction grows with the tangent of half the angle, so it starts smaller and finishes bigger.

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Gain is centreline arc length minus the two tangent lengths: one #5 bar, seven angles, same bend diameter throughout.

Three things a shop chart has to say out loud. The gain always leads, until it does not: at 90° the gain is 2.1× the deduction, by 120° they are nearly level (1.09×), and at 135° the deduction is the bigger number (6.30 against 4.57) — past roughly 123° an out-to-out takeoff loses more at the corner than the arc gives back. Shallow bends still need the gain (1.01 in at 30°, 1.52 at 45°) while the deduction stays under two-tenths — a ramp is the one case where adding the arc matters and subtracting the corner almost does not. At 180° there is no deduction at all: the two tangents meet on the centreline, so there is no outside corner to deduct from; bend past 180° and it is two bends, not one bigger one. Swap the two at 90° and a #5 corner is wrong by 1.6 in, which is two and a half bar diameters on a tight stirrup.

Gain by bar size and angle — stirrup bend diameters

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Stirrup and tie bend diameters per ACI 318-19; gain is computed per angle from the arc and the tangents.

Gain by bar size and angle — standard hook bend diameters

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Standard hook bend diameters per ACI 318-19; gain is computed per angle from the arc and the tangents.

Read the matrix by row for a size, by column for an angle. Two cells are worth memorising because they carry most of the detail steel: the #5 stirrup corner at 90° is 3.04 in and the #8 stirrup hook at 135° is 8.25 in. The jump from #5 to #8 is not linear in the bar number — the bend diameter grows 85% (3.25 to 6.00 in) and the weight per foot grows 156% (1.043 to 2.670 lb/ft), so big stirrups are a budget line, not a rounding error.

Gains in inches, angle in radians × centreline radius. The 2.5 in minimum extension on a 180° standard hook is a floor, not geometry: on #3 (4db = 1.50 in) and #4 (4db = 2.00 in) the code tail is set by the floor, so the tail is longer than the bend geometry alone would suggest. Recompute, do not interpolate, if your drawing calls a different bend diameter.

The five-bend drawing is the whole bending chart in one picture. Every shop bend is some sequence of the same event — the centreline turns through an angle — so the only lookup a bender needs is which bend diameter (stirrup or standard) and what angle. The gain follows the angle; the deduction lags it until about 123°, then overtakes. What the chart cannot do is change the tail: the extension is a code minimum, not geometry, and it does not shrink when the bend gets shallower.

Why a bend changes the number

A straight bar has one length. Bend it and the bar still has that length — steel does not stretch along its centreline — but now there are three different numbers you could measure, and they are all different:

• Out-to-out legs. Measure each leg to the sharp outside corner, where the two legs would meet if the bend were a mitre, and add them. This sum is longer than the bar.
• Tangent-to-tangent runs. Measure each leg only to the point where the bend begins, and add them. This sum is shorter than the bar.
• The bar. The actual cut length, which follows the centreline through the arc.

The correction between the first number and the bar is the bend deduction — subtract it. The correction between the second number and the bar is the bend gain, also called the bend allowance — add it. Both come from the same piece of geometry, the arc around the bend pin.

The radius is set by the pin the bar is bent around, and the code fixes a minimum. ACI 318-19 requires a finished inside bend diameter of 6db for #3–#8, 8db for #9–#11 and 10db for #14 and #18 on standard hooks, and 4db for #3–#5 and 6db for #6–#8 on stirrups and ties. Bend a #5 bar on a 2 in pin instead of a 3.25 in pin and every gain on this page changes — the diameter is the input, the gain is the output. The size chart has the nominal diameters the db column is built from.

Step 1 — the hook extension

The extension is the straight tail past the end of the bend. It is a code requirement, not a geometric one: the tail is what lets the hook engage the concrete, and the code sets it as a multiple of the bar diameter. Three rules cover almost everything on a job:

• 90° standard hook (main bars): 12db. A #5 hook is 12 × 0.625 = 7.50 in.
• 180° standard hook: 4db, never less than 2.5 in. A #5 hook is max(2.5, 2.5) = 2.5 in; a #8 hook is 4 × 1.0 = 4.0 in.
• Stirrup, tie and hoop hooks (90° and 135°): 6db for #3–#5, never less than 3 in, and 12db for #6–#8. A #5 stirrup hook is 6 × 0.625 = 3.75 in; a #8 stirrup hook is 12 × 1.0 = 12.0 in.

Notice the jump between #5 and #6 in the stirrup row of the table above: the extension goes from 3.75 in to 9.00 in, not by a smooth multiple but because the rule itself changes from 6db to 12db. If you take one number away from this page, take that one — the stirrup extension rule is not a single multiplier.

Source: ACI 318-19 (standard hooks) and ACI 318-19 (stirrup, tie and hoop hooks); the dimensions match ANSI/CRSI IPG5.1-2026 and 7-3.

Step 2 — the bend gain (and the bend deduction)

The gain is the arc. It is the only part of the bar that a straight-line takeoff misses, and on a stirrup with four corners and two hooks it is added six times. Read the gain off the table, or compute it from the radius:

Now the deduction, which is what you use when the drawing is dimensioned out-to-out the way a CRSI bar list is. For a #5 bar at a 90° corner the deduction is 1.46 in per corner. A closed rectangular stirrup has four 90° corners, so its out-to-out perimeter overstates the bar by 4 × 1.46 = 5.83 in. The two corrections are not the same number and they do not cancel: 21.30 in of gain and 5.83 in of deduction describe the same stirrup from two different starting measurements.

Worked example — a #5 stirrup

A rectangular stirrup for a beam, 16 in × 24 in out-to-out, in #5 bar, with two 135° hooks. The bend diameter is the stirrup diameter, 3.25 in, so the centreline radius is (3.25 + 0.625) / 2 = 1.9375 in and every corner loses 2 × 1.9375 = 3.875 in of straight run.

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Two checks worth doing on your own numbers. First, the hook tails and hook arcs are 16.6 in of the 90.8 in — 18% of the bar is in the two hooks, which is why a takeoff that counts the box and forgets the hooks runs short by nearly a fifth. Second, the naive out-to-out perimeter plus tails, 2 × (16 + 24) + 7.50 = 87.50 in, is 3.3 in short of the real cut, because it uses the outside dimensions and adds only the tails, not the arcs. On 40 of these stirrups that is 132 in, or 11 ft of bar, missing from the order.

Watch: the bending chart in 16 seconds

Common questions

How long is a rebar hook?

A standard 90° hook has a 12db extension and a standard 180° hook has a 4db extension, never less than 2.5 in. A stirrup, tie or hoop hook has a 6db extension for #3 to #5 (never less than 3 in) and 12db for #6 to #8, at both 90° and 135°. For a #5 bar the 90° standard hook extension is 7.5 in, the 180° standard hook is 2.5 in, and the stirrup 90° or 135° extension is 3.75 in.

What is bend gain in rebar?

Bend gain, also called the bend allowance, is the length of the bar centreline that the bend itself consumes: the arc. Bend gain = angle in radians × centreline radius, where centreline radius = (finished inside bend diameter + bar diameter) / 2. It is the length you add once per bend when your straight runs are measured to the tangent points. For a #5 bar in a stirrup (3.25 in bend diameter) the bend gain is 3.04 in at 90°, 4.57 in at 135° and 6.09 in at 180°.

What is the minimum bend diameter for rebar?

ACI 318-19 sets the minimum inside bend diameter for standard hooks at 6db for #3 to #8, 8db for #9 to #11 and 10db for #14 and #18. the ACI 318-19 table sets the minimum for bars used as stirrups, ties and hoops at 4db for #3 to #5 and 6db for #6 to #8. In inches: a #5 bar is 3.75 in as a standard hook and 2.50 in as a stirrup; a #8 bar is 6.00 in either way. ANSI/CRSI IPG5.1-2026 rounds these up to the finished bend diameters used in the tables above.

How do you calculate the cut length of a stirrup?

Take the out-to-out width and height, subtract one bar diameter for the centreline, then subtract twice the bend radius at each corner to get the straight runs. Add one bend gain per corner. Add one bend gain plus the extension for each hook. Worked on a #5 stirrup 16 in × 24 in out-to-out with two 135° hooks: straight runs 62.00 in, four 90° corner arcs 12.17 in, two 135° hook arcs 9.13 in, two hook extensions 7.50 in, total cut length 90.8 in or 7.57 ft.

Does bending make a rebar longer or shorter?

Bending does not change the length of the bar along its centreline. What changes is the number you compare it to. The sum of the two out-to-out legs is longer than the bar, because the arc cuts the corner; the difference is the bend deduction. The sum of the two tangent-to-tangent runs is shorter than the bar, because you still have to add the arc; that arc is the bend gain. A bent bar is always shorter than the sum of its out-to-out dimensions.

What is the difference between bend allowance and bend deduction?

Bend allowance, or bend gain, is the arc length of the bend, added once per bend when the straight runs are measured to the tangent points. Bend deduction is what you subtract once per bend when the legs are measured out-to-out to the sharp corner. For a #5 bar at a 90° corner the bend gain is 3.04 in and the bend deduction is 1.46 in. Use the one that matches how your drawing is dimensioned; mixing them double-counts the corner.

How much does a #5 stirrup weigh?

A #5 bar weighs 1.043 lb per foot. A 16 in × 24 in out-to-out #5 stirrup with two 135° hooks has a cut length of 90.8 in = 7.57 ft, so it weighs 7.89 lb. Rounding the cut length to a 7 ft 6¾ in shop mark gives 7.56 ft and 7.89 lb — the weight is small enough that rounding at the ¼ in mark does not move it. The weight page runs the same lb/ft multiplication for a single bar or a whole order.

What is the bend allowance for a 45° bend in rebar?

Same formula as every other angle — gain = radians(angle) × centreline radius. On the stirrup bend diameter a #5 bar has a centreline radius of 1.94 in, so a 45° bend adds 1.52 in of gain and deducts 0.34 in; on the standard hook diameter (3.75 in) the same 45° bend adds 1.72 in and deducts 0.35 in. The shallow angles are where the two numbers separate most: at 30° the gain is 5.3× the deduction, so a ramp needs its arc added back even though almost nothing comes off the corner. The bending chart above runs the same pair of formulas for seven angles and every bar size.

What is the bend deduction for a 135° hook?

On a #5 bar bent at the stirrup diameter (Ø 3.25 in) a 135° bend has a centreline radius of 1.94 in, so it adds 4.57 in of bend gain and deducts 6.30 in — the one angle on the chart where the corner takes back more than the arc gives, by 1.73 in. 135° is the angle of a standard seismic hook, so an out-to-out takeoff measured to the sharp corner must subtract the 6.30 in at every hook. Measured tangent-to-tangent the same hook adds 4.57 in and deducts nothing, so the two takeoffs land 1.73 in apart. The crossover is at about 123°: below it the gain leads, above it the deduction does. The hook tail is separate again — 6db = 3.75 in for a #5 stirrup hook — and is added whichever way the legs are measured. The bending chart gives the pair for every angle and bar size.

What this page does not do

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Published 10 October 2026 · Last reviewed 1 November 2026