Standard hook extensions and the bend gain for #3–#8 at 90°, 135° and 180° — and the cut length they add up to
← Back to the calculatorBending does not change the length of a bar, but it changes the number you compare it to. A bent bar is shorter than the sum of its out-to-out legs by the bend deduction, and longer than the sum of its tangent-to-tangent runs by the bend gain. This page gives both, per bar size, at all three hook angles.
Open the calculator for a whole slab, or read the two steps below for a single bent bar.
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 Table 8-1; 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).
| Bar size | db (in) | Bend Ø (in) | 90° ext | 90° gain | 135° ext | 135° gain | 180° ext | 180° gain |
|---|---|---|---|---|---|---|---|---|
| #3 | 0.375 | 2.00 | 3.00 | 1.87 | 3.00 | 2.80 | 2.50 | 3.73 |
| #4 | 0.500 | 2.50 | 3.00 | 2.36 | 3.00 | 3.53 | 2.50 | 4.71 |
| #5 | 0.625 | 3.25 | 3.75 | 3.04 | 3.75 | 4.57 | 2.50 | 6.09 |
| #6 | 0.750 | 4.50 | 9.00 | 4.12 | 9.00 | 6.19 | 3.00 | 8.25 |
| #7 | 0.875 | 5.25 | 10.50 | 4.81 | 10.50 | 7.22 | 3.50 | 9.62 |
| #8 | 1.000 | 6.00 | 12.00 | 5.50 | 12.00 | 8.25 | 4.00 | 11.00 |
Swipe the table sideways for more columns →
| Bar size | db (in) | Bend Ø (in) | 90° ext | 90° gain | 180° ext | 180° gain |
|---|---|---|---|---|---|---|
| #3 | 0.375 | 2.25 | 4.50 | 2.06 | 2.50 | 4.12 |
| #4 | 0.500 | 3.00 | 6.00 | 2.75 | 2.50 | 5.50 |
| #5 | 0.625 | 3.75 | 7.50 | 3.44 | 2.50 | 6.87 |
| #6 | 0.750 | 4.50 | 9.00 | 4.12 | 3.00 | 8.25 |
| #7 | 0.875 | 5.25 | 10.50 | 4.81 | 3.50 | 9.62 |
| #8 | 1.000 | 6.00 | 12.00 | 5.50 | 4.00 | 11.00 |
| #9 | 1.128 | 9.50 | 13.54 | 8.35 | 4.51 | 16.69 |
| #10 | 1.270 | 10.75 | 15.24 | 9.44 | 5.08 | 18.88 |
| #11 | 1.410 | 12.00 | 16.92 | 10.53 | 5.64 | 21.06 |
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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:
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.
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:
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.
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.
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.
| Piece of the bar | Length (in) | Share |
|---|---|---|
| Straight runs (centreline) | 62.00 | 68.3% |
| 4 corner bends, 90° (gain) | 12.17 | 13.4% |
| 2 hook bends, 135° (gain) | 9.13 | 10.1% |
| 2 hook tails, 6db (extension) | 7.50 | 8.3% |
| Cut length | 90.80 | 100% |
Swipe the table sideways for more columns →
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.
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.
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°.
ACI 318-19 Table 25.3.1 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. Table 25.3.2 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 Table 8-1 rounds these up to the finished bend diameters used in the tables above.
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.
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.
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.
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.