Two hundred dowels, all of them eleven inches short
The wall section shows a No. 5 dowel as an L. The vertical leg carries a dimension because somebody had to decide how far it projects for the wall above. The foot of the L carries no dimension at all — it carries the words std hk, and a bend symbol about four millimetres long on a plotted sheet. Whoever took the schedule off that section measured the leg, added the lap to the wall steel, and booked two hundred bars at the number their tape gave them.
The bars arrive cut and bent to the booked length. Every one of them is short by the hook, which for a No. 5 at ninety degrees is very close to eleven inches of steel: the arc the bar travels round the bend, plus a straight tail of twelve bar diameters beyond it. Two hundred of those is a hundred and eighty-two feet of bar, about a hundred and ninety pounds. As a material loss it is not worth an email. As a delivery it stops the pour, because there is no operation on a construction site that makes a piece of reinforcing bar longer.
That asymmetry is the whole subject. The hook is one of the smallest quantities on a reinforced concrete job and one of the most expensive to get wrong, and it goes wrong in a specific, repeatable way: the drawing shows the bar as a line, the line has a length, and the length is not the length of the bar. This page is about the arithmetic that closes that gap — what the code fixes, what it leaves to geometry, and how a schedule gets checked before it reaches the shear. Why a hook develops the bar at all, and what cover and confinement do to that, is the neighbouring article's job.
What the code fixes, and what it hands back to you
ACI 318 pins a standard hook down with two numbers and no more. The first is the minimum inside bend diameter, given in Table 25.3.1 as six bar diameters for No. 3 through No. 8 and eight bar diameters for No. 9 through No. 11 — a step that catches people out, because the jump from a No. 8 to a No. 9 is an eighth of an inch of bar and three inches of bend. The second is the straight tail beyond the bend: twelve bar diameters for a ninety degree hook, and the greater of four bar diameters and two and a half inches for a hundred and eighty. Larger bars step up again, which is why the calculator below stops at No. 11 rather than extrapolating.
Those two numbers describe the hook. They do not describe the piece of steel that makes it. The cut length is the developed length of the bar along its own centreline through the bend, plus the tail, and no code publishes it because it is geometry rather than policy — ACI 315, the guide to presenting reinforcing steel design details, sets the detailing convention and leaves the arithmetic where it belongs. In the United Kingdom, BS 8666 goes further and gives a total-length formula against each shape code so the schedule carries a cut length that already has the bend allowance in it, which is why a British schedule and an American one look so different for the same bar.
Two things get carried across from this table that should not be. Stirrup and tie hooks are a separate table in the same chapter of ACI 318, with their own bend diameters and their own extensions, and they are not the ones above; a schedule that gives every stirrup a twelve-diameter tail has bought steel nobody asked for and produced a tie that may not close in the member. And a seismic hook is a defined term in its own right, with a bend angle and an extension the code states explicitly, so a hoop in a special moment frame is not a tie with a note on it.
The development length is the other half of the answer and it uses none of the same reasoning. The hooked-bar development length is measured from the critical section to the far outside of the bend — not to where the bend starts, and not to the tip of the tail — and it is driven by concrete strength, steel grade, coating, confinement at the hook and how much side cover the tail has. Run both halves at once. The embedment tells you whether the detail fits in the member; the allowance tells you what to buy.
| Bar | Min inside bend diameter | Tail beyond the bend, 90 degrees | Bar a 90 degree hook consumes | Bar a 180 degree hook consumes |
|---|---|---|---|---|
| No. 3 | 2.25 in (6db) | 4.50 in | 6.56 in (17.50db) | 6.62 in |
| No. 4 | 3.00 in (6db) | 6.00 in | 8.75 in (17.50db) | 8.00 in |
| No. 5 | 3.75 in (6db) | 7.50 in | 10.94 in (17.50db) | 9.37 in |
| No. 6 | 4.50 in (6db) | 9.00 in | 13.12 in (17.50db) | 11.25 in |
| No. 7 | 5.25 in (6db) | 10.50 in | 15.31 in (17.50db) | 13.12 in |
| No. 8 | 6.00 in (6db) | 12.00 in | 17.50 in (17.50db) | 15.00 in |
| No. 9 | 9.02 in (8db) | 13.54 in | 21.51 in (19.07db) | 20.46 in |
| No. 10 | 10.16 in (8db) | 15.24 in | 24.22 in (19.07db) | 23.03 in |
| No. 11 | 11.28 in (8db) | 16.92 in | 26.89 in (19.07db) | 25.57 in |
The question the section drawing refuses to answer is how deep the hook has to reach and how much bar it costs to make, so put the bar size, the concrete and the confinement in and read both numbers together before the schedule is typed.
The hooked bar, which sets both the development length and the bend geometry.
Whether the bar turns a quarter turn or doubles fully back on itself.
The specified compressive strength of the concrete the hook is embedded in.
The specified yield strength of the hooked bar.
Whether the bar carries an epoxy coating.
Whether ties or stirrups enclose the hook to the code's own requirement.
Whether the tail sits inside a confined core or in ordinary cover.
Enter 1.0 for normal-weight concrete and 0.75 for all-lightweight.
Hooked-bar development length ldh
14.8 in
ldh is measured from the critical section to the far outside of the bend, not to the start of the bend and not to the end of the tail. Detailing it to the wrong reference point is the commonest way a hook ends up short in the field.
- Minimum inside bend diameter
- 3.75 in
- Tail extension beyond the bend
- 7.5 in
- Bar consumed by the bend and tail
- 10.94 in
- Code floor for this bar
- 6 in
- Length the equation alone gives
- 14.77 in
- Concrete strength factor applied
- 0.87 x ldh
- Confinement and location factors combined
- 2 x ldh
They open the calculator with your figures already in it
Rebar Standard Hook Development and Cut-Length Calculator: 14.77 in — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Add the equipment this sizes
This result is a specification — 14.8 in — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
What this calculation does not cover
- Written for #11 bars and smaller; #14 and #18 hooks carry different factor conditions and are not offered.
- Tension hooks only. Hooks developed in compression are governed by separate provisions.
- The cut-length allowance is centreline geometry; a shop's own bend deduction table may differ slightly and should win.
- Confirm the equation form against the edition of ACI 318 your jurisdiction has adopted — earlier editions used a different expression.
This 90 degree hook develops 14.8 in (375 mm) measured to the outside of the bend, and takes 10.9 in (278 mm) of bar to make once the 3.8 in (95 mm) bend diameter and the tail are accounted for. Add that allowance to the straight legs when the cut list is written, or the fabricator's bar will be short by the bend.
A corner has two lengths and the drawing shows neither
Stand a hooked bar up and there are three lengths available to measure and only one of them is the bar. There is the sum of the two straight legs, which is what a tape on a plotted section gives you. There is the sum of the outside dimensions taken to the corner where the two outside faces would meet, which is what a bending schedule dimensions. And there is the developed length along the bar centreline, which is the piece of steel the shear cuts. All three are different, and the difference between the first and the third is what the last section was about.
The bar does not go to the corner. It cuts it, on a circular arc whose radius is measured to its own centreline: half the inside bend diameter plus half the bar diameter. That arc is shorter than the two setbacks it replaces, and the gap between them is the bend deduction. For any bend angle the relationship is fixed geometry, so it can be written once and applied to whatever bend diameter your code gives you rather than memorised per bar size.
For a right-angle bend the deduction lands at almost exactly two and a half bar diameters where the bend diameter is six db, and close to two point nine bar diameters where it is eight db. On a No. 8 that is two and a half inches taken off the sum of the outside dimensions; on a No. 11 it is four and an eighth. Neither is a rounding error on a bar that has to reach a critical section, and neither shows up if you take the outside dimensions off a schedule and add them.
So there are two failure directions and they pull opposite ways. Take off the drawn line and forget the hook, and the bar list is short by the whole allowance — the arc and the tail together — which is the failure this page opened on. Take off the outside dimensions from a bending schedule and add them without the deduction, and the bar list is long, which is cheaper but produces bars that will not sit in the forms because the leg overruns its cover. The only way through is to work in centreline length from the start and let the detailer, or the fabricator, convert to their own dimensioning convention.
- Take the straight legs off the section as the engineer dimensioned them, and note whether those dimensions are to the outside face of the bar, to its centreline, or to the concrete face they sit behind.
- Read the minimum inside bend diameter for that bar size from the governing code, not from the last job. It steps with bar size, and stirrups and ties read from a different table.
- Work the centreline bend radius as half the inside bend diameter plus half the bar diameter, then multiply by the bend angle in radians for the arc the bar actually travels.
- Add the code tail extension beyond the bend — twelve bar diameters for a standard ninety degree hook to ACI 318, and the greater of four bar diameters and two and a half inches for a hundred and eighty.
- If your legs were dimensioned to the outside corner rather than to the tangent point, subtract the setbacks the arc replaced before adding it back, or the corner gets counted twice.
- Round the finished cut length the way the fabricator schedules it, and put the rounded number on the schedule so the shop and the take-off agree on one figure rather than two that are nearly the same.
The hundred and eighty degree hook takes less steel, not more
Run the numbers across the bar range and something counter-intuitive falls out. A hundred and eighty degree hook doubles the bar fully back on itself and travels twice the arc of a right-angle hook, so it ought to be the greedier of the two. It is not. Its tail is four bar diameters against twelve, and that eight-diameter saving is larger than the extra half turn costs. For a No. 8 the ninety degree hook consumes seventeen and a half inches of bar and the hundred and eighty degree hook fifteen, a saving of two and a half inches on every bar. The only size where it reverses is a No. 3, where the two-and-a-half-inch minimum tail props the hundred and eighty degree hook back up, and even there the two are within about a sixteenth of an inch of each other.
None of which is a reason to change a detail. Both standard hooks develop the same embedment, so the choice between them is a fit decision made by whoever has to get the tail past the far face of the member, and the steel saving is the consequence rather than the argument. What it is good for is checking a schedule: if a substitution of hook type on a job showed the tonnage moving the other way, somebody has used the wrong tail extension for one of them, and that is worth finding before the bars are bent.
The other undrawn length: how many laps a wall generates
Hooks are the visible half of this problem. Laps are the larger half and they hide better, because a lap is not drawn at all on most sections — it is a note, a class letter, or a schedule line that says lap all bars, and the bar list has to derive how many of them a run of steel actually produces.
That derivation is a stock-length question before it is a structural one. Reinforcing bar is mill-supplied in standard lengths and a two-hundred-foot wall does not get built from two-hundred-foot bars, so the number of laps in a horizontal run is set by how many pieces the run breaks into, which is set by the stock length the fabricator buys and the length their truck and their shear can handle. Each break costs one lap length of steel that no drawing dimension contains. Get the count wrong by one break per course and the error compounds through every course in the wall.
Then stagger multiplies it. Splices are offset from course to course so the reduced section does not line up in a plane, and staggering means the pieces are no longer all the same length — a run that would have divided cleanly into four now divides into three and two part-lengths, and the drop from those part-lengths is real waste that has to be carried in the order. Detailers handle this as a matter of routine; estimators working off a plan and a bar spacing frequently do not, and the shortfall arrives looking exactly like the hook shortfall did.
Once you know how many breaks a run contains you need the length of each one, and it is not a single number for the job — it moves with bar size, concrete strength, coating and whether the bar sits in the top of the pour.
The bar's development length, computed before the top-bar and coating factors are applied.
The bar being spliced, which fixes the diameter used by the compression formula.
Which force the splice has to transfer at the section it sits in.
How much surplus area the section carries at the splice location.
What share of the bars at the section have their splice inside the same lap window.
Whether a deep lift of fresh concrete is placed beneath this bar.
Whether the bar is epoxy-coated, and if so how tightly it is covered and spaced.
The specified yield strength of the reinforcement.
The specified compressive strength of the concrete at the splice.
Required lap splice length
31.2 in
Class B applies, at 1.3 times the development length. Either the surplus steel is under two, or more than half the bars splice within one lap window — the breakdown shows which lever is available if a shorter lap is wanted.
- Splice class multiplier applied
- 1.3 x ld
- Combined top-bar and coating factor
- 1 ld
- Minimum offset between adjacent splices
- 31.2 in
- Development length used
- 24 in
- Bar diameter
- 0.63 in
- Tension lap for this bar
- 31.2 in
- Compression lap for this bar
- 18.75 in
They open the calculator with your figures already in it
Rebar Lap Splice Length Calculator (ACI 318): 31.2 in — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Add the equipment this sizes
This result is a specification — 31.2 in — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
What this calculation does not cover
- Mechanical and welded splices follow separate provisions and are not covered.
- Column compression laps enclosed by ties or spirals meeting the code's requirements may be reduced further; that reduction is not applied here.
- Bundled bars, and splices in tension tie members, carry additional requirements this page does not test.
- Bar spacing and cover at the splice must still satisfy the code independently of the length.
Class B applies. Getting to Class A needs BOTH a steel ratio of two or more and no more than half the bars spliced in one window — at present the ratio is 1.5 and 100% splice together. Offset neighbouring splices by at least 31.2 in (792 mm) and they fall outside one another's lap window, which is the geometry the percentage limit is written against.
Where the hook will not physically fit
A bend has an outside envelope, and it is bigger than people expect: the inside bend diameter plus two bar diameters. A No. 8 hook occupies eight inches across that envelope. A No. 11 occupies just over fourteen. Put that No. 11 in a twelve-inch wall and the hook does not fit at all — not marginally, not with reduced cover, not at all — and the detail has to change to a headed bar, a smaller bar at closer spacing, or a thicker wall.
The tail has its own fit problem and it is subtler, because the tail usually does fit and then lands somewhere useless. A beam bar hooked down into a column has to keep its tail inside the column core; a wall bar hooked into a footing has to keep its tail above the bottom mat and behind its own cover; a slab bar hooked at a discontinuous edge has to keep the tail out of the top surface. Draw the hook at scale in the section it actually lives in, with the ties and the perpendicular steel drawn too, before the schedule is issued. Congestion at a beam-column joint is discovered on paper for the price of an hour and on site for the price of a pour.
When it does not fit, the fix is an engineered one and there are several: a mechanical head qualified as an approved product, a mechanical splice or coupler, a change of bar size, or a revised member dimension. ACI 318 recognises mechanical splices in more than one class, with the more demanding class required where the splice sits in a region expected to yield, so a coupler is a specification decision rather than a hardware purchase. What is not on that list is opening the bend a little, shortening the tail, or turning the hook to face somewhere it has room. Those are the three field improvisations that turn a detailing problem into a structural one.
Field bending will not lengthen a bar
The temptation when short bars land is to fix them in the yard, and the material has opinions about that. ASTM A615 carbon-steel bar is specified for strength and bend, not for weldability or for repeated cold working; ASTM A706 low-alloy bar is the one written with controlled chemistry and better bend behaviour precisely because it is expected to be welded and bent. Which of them turned up is stamped on the bar. Rebending steel that has already been bent works it a second time in the same place, and the place is the one carrying the highest stress in the piece.
Heat is not a general permission either. Where the specification allows a bar to be bent hot it says so, with a temperature the crew has to control and a cooling regime, and epoxy-coated bar to ASTM A775 has a further problem: the coating cracks at the bend and the crack sits at the exact point moisture will collect. Field cutting is easier than field bending and still not free — a torch-cut end on a bar that was scheduled to a length is a change to a schedule the engineer approved. If bars are short, say so and get a coupler, a supplementary bar or a revised detail. A short bar made to fit is a short bar with a story attached.
From centreline lengths to something a truck can deliver
A bar list is only finished when it turns back into weight, because weight is what the fabricator prices, what the truck carries, what the crane lifts and what the deck has to hold while the bundle sits waiting to be tied. Standard bar sizes carry standard unit weights, so once the cut lengths are honest the conversion is mechanical — and once the cut lengths are honest is doing a great deal of work in that sentence, since it is the sum of every hook allowance, every lap and every stagger drop above it.
Bundle planning is where the hook allowance reappears in a form nobody expects. Bent bar does not stack like straight bar. A bundle of hooked dowels occupies far more volume than the same tonnage of stock length, needs more room on the deck or in the lay-down area, and cannot be banded as tightly. Order in tags that match the pour sequence, and get the tag numbers onto the schedule, or the crew spends the morning of the pour opening bundles to find out what is in them.
Compare the finished weight against a rough independent check before it goes out. Bar area divided by bar spacing, times the member area, times steel density gives a number good to a few per cent for a plain mat, and if the schedule comes out materially under it, the missing steel is almost always in the details the drawing did not dimension: hooks, laps and the stagger drop, in that order of likelihood.
Turn the finished cut lengths into the tonnage the order, the delivery ticket and the lift plan all have to agree on, and keep the hook and lap allowances inside that number rather than adding a percentage on afterwards.
The rebar bar size number, from the Rebar Calculator or your project plans.
The combined length of all rebar pieces in the project.
Total rebar weight
66.8 lb
- Total length
- 100 linear ft
They open the calculator with your figures already in it
Rebar Weight Calculator: 66.8 lb — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
What this calculation does not cover
- Only US customary bar sizes #3 through #6 are offered. There is nothing for #7 and larger — the sizes that show up in columns, beams and heavy footings — and no metric or Canadian designations (10M, 15M, 20M) or European mm bar. Picking the nearest available size instead will not give the right weight.
- The total length is taken exactly as you type it. Lap splices, hooks, bends, stirrups and ties, corner extras and cut-off waste all have to be inside that figure already, because nothing here derives them. The field also stops at about 16,400 ft (5,000 m) of bar, so a larger take-off has to be split and the parts added by hand.
- These are nominal per-foot weights for the bar size, not the weight your load will scale in at. Mill weight tolerance, deformation pattern, and epoxy or galvanized coating all shift the real figure, and a supplier invoices against their own weighed tonnage rather than a theoretical one.
- This is not a reinforcement design. It says nothing about which bar size, spacing, cover, grade or layout the job needs, and no result here indicates that the steel you have chosen is adequate. Bar size and placement come from the drawings or an engineer.
- Bars only. Tie wire, chairs, bolsters, spacers, dowels, mechanical couplers and welded wire mesh are all excluded, as is bundling and dunnage — so this is not a truck payload or a crane lift weight on its own.
Reading a bar bending schedule before it goes to the shop
A schedule is checkable in about twenty minutes and almost nobody checks it, because it arrives as a spreadsheet of mark numbers and looks like an administrative document. It is not. It is the last written statement of what the steel will be before it becomes steel, and every error in it becomes a physical object that has to be transported to site before anybody can see it.
Work through it against the sections rather than against the previous schedule, and read the totals last so the mark-by-mark check is not being anchored by a number you already believe.
- Confirm the dimensioning convention at the top of the sheet: whether lengths are to the outside of the bar or to its centreline, and whether the total length column already includes the bend allowances.
- Take a sample of marks that carry hooks and reconstruct the total length by hand from bend diameter, arc and tail. Three marks is enough to prove the convention; if all three agree, the sheet is internally consistent.
- Check the bend diameter against bar size for the step at No. 9, and check that stirrups and ties have been scheduled from the stirrup table rather than the longitudinal one.
- Check that every hooked mark can physically exist in its member: bend envelope against member thickness, and tail against the cover face it terminates behind.
- Count the laps in the longest continuous run and reconcile that count against the stock length the fabricator is buying, not the stock length you assume.
- Reconcile the schedule tonnage against an independent area-and-spacing estimate, and treat any shortfall as unfound hooks and laps until proven otherwise.
Before the schedule is issued
The checks that decide whether the steel arriving on the truck is the steel the drawing meant, taken in the order the arithmetic runs.
- Every hooked mark reconstructed from bend diameter, arc and tail — The drawn line is the straight leg only; the arc and the tail are additional steel no dimension on the section shows.
- Bend diameter read for the right bar size band — It steps at No. 9 under ACI 318, and stirrups and ties come from a separate table with different extensions.
- Dimensioning convention agreed with the detailer in writing — Outside dimensions need the bend deduction taken off; centreline lengths do not. Mixing the two loses about 2.5 bar diameters per corner.
- Bend envelope checked against member thickness — Inside bend diameter plus two bar diameters. A No. 11 hook needs over fourteen inches and will not go in a twelve-inch wall.
- Lap count derived from the fabricator's real stock length — Each break in a run costs a lap that no drawing dimensions, and stagger adds part-lengths that become drop.
- Schedule tonnage reconciled against an independent estimate — A shortfall against area times spacing is hooks and laps until something else explains it.
Opens the calculators above on one screen with the dimensions from this article already filled in. Quantities only — this site publishes no price list, because local prices vary too much to publish honestly.